QCD-inspired spectra from Blue's functions

NASA Astrophysics Data System (ADS)

Nowak, Maciej A.; Papp, Gábor; Zahed, Ismail

1996-02-01

We use the law of addition in random matrix theory to analyze the spectral distributions of a variety of chiral random matrix models as inspired from QCD whether through symmetries or models. In terms of the Blue's functions recently discussed by Zee, we show that most of the spectral distributions in the macroscopic limit and the quenched approximation, follow algebraically from the discontinuity of a pertinent solution to a cubic (Cardano) or a quartic (Ferrari) equation. We use the end-point equation of the energy spectra in chiral random matrix models to argue for novel phase structures, in which the Dirac density of states plays the role of an order parameter.

Linear-response time-dependent density-functional theory with pairing fields.

PubMed

Peng, Degao; van Aggelen, Helen; Yang, Yang; Yang, Weitao

2014-05-14

Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

The Feynman-Vernon Influence Functional Approach in QED

NASA Astrophysics Data System (ADS)

Biryukov, Alexander; Shleenkov, Mark

2016-10-01

In the path integral approach we describe evolution of interacting electromagnetic and fermionic fields by the use of density matrix formalism. The equation for density matrix and transitions probability for fermionic field is obtained as average of electromagnetic field influence functional. We obtain a formula for electromagnetic field influence functional calculating for its various initial and final state. We derive electromagnetic field influence functional when its initial and final states are vacuum. We present Lagrangian for relativistic fermionic field under influence of electromagnetic field vacuum.

Development of the Nuclear-Electronic Orbital Approach and Applications to Ionic Liquids and Tunneling Processes

DTIC Science & Technology

2010-02-24

electronic Schrodinger equation . In previous grant cycles, we implemented the NEO approach at the Hartree-Fock (NEO-HF),13 configuration interaction...electronic and nuclear molecular orbitals. The resulting electronic and nuclear Hartree-Fock-Roothaan equations are solved iteratively until self...directly into the standard Hartree- Fock-Roothaan equations , which are solved iteratively to self-consistency. The density matrix representation

Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations

NASA Astrophysics Data System (ADS)

Blanchet, Steve; Di Bari, Pasquale; Jones, David A.; Marzola, Luca

2013-01-01

Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N1-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.

Principles of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Landé, Alfred

2013-10-01

Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ρ (x) and σ (p); 11. Complementarity; 12. Mathematical relation between ρ (x) and σ (p) for free particles; 13. General relation between ρ (q) and σ (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ρ (t) and σ (є); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ρ and σ; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for Ψp (q) and Xq (p); 39. Differential equation for фβ (q); 40. The general probability amplitude Φβ' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schrödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.

Quantum Effects at a Proton Relaxation at Low Temperatures

NASA Astrophysics Data System (ADS)

Kalytka, V. A.; Korovkin, M. V.

2016-11-01

Quantum effects during migratory polarization in multi-well crystals (including multi-well silicates and crystalline hydrates) are investigated in a variable electric field at low temperatures by direct quantum-mechanical calculations. Based on analytical solution of the quantum Liouville kinetic equation in the linear approximation for the polarizing field, the non-stationary density matrix is calculated for an ensemble of non-interacting protons moving in the field of one-dimensional multi-well crystal potential relief of rectangular shape. An expression for the complex dielectric constant convenient for a comparison with experiment and calculation of relaxer parameters is derived using the nonequilibrium polarization density matrix. The density matrix apparatus can be used for analytical investigation of the quantum mechanism of spontaneous polarization of a ferroelectric material (KDP and DKDP).

Reexamination of relaxation of spins due to a magnetic field gradient: Identity of the Redfield and Torrey theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golub, R.; Rohm, Ryan M.; Swank, C. M.

2011-02-15

There is an extensive literature on magnetic-gradient-induced spin relaxation. Cates, Schaefer, and Happer, in a seminal publication, have solved the problem in the regime where diffusion theory (the Torrey equation) is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using the Redfield theory formulated in terms of the autocorrelation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion-theory Green's function. The results of both calculations were shown to agreemore » for a special case. In the present work, we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green's function for the diffusion equation, thus showing the identity of this approach with that of the Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus, the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.« less

A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-11-28

A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.

Combined natural gamma ray spectral/litho-density measurements applied to complex lithologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quirein, J.A.; Gardner, J.S.; Watson, J.T.

1982-09-01

Well log data has long been used to provide lithological descriptions of complex formations. Historically, most of the approaches used have been restrictive because they assumed fixed, known, and distinct lithologies for specified zones. The approach described in this paper attempts to alleviate this restriction by estimating the ''probability of a model'' for the models suggested as most likely by the reservoir geology. Lithological variables are simultaneously estimated from response equations for each model and combined in accordance with the probability of each respective model. The initial application of this approach has been the estimation of calcite, quartz, and dolomitemore » in the presence of clays, feldspars, anhydrite, or salt. Estimations were made by using natural gamma ray spectra, photoelectric effect, bulk density, and neutron porosity information. For each model, response equations and parameter selections are obtained from the thorium vs potassium crossplot and the apparent matrix density vs apparent volumetric photoelectric cross section crossplot. The thorium and potassium response equations are used to estimate the volumes of clay and feldspar. The apparent matrix density and volumetric cross section response equations can then be corrected for the presence of clay and feldspar. A test ensures that the clay correction lies within the limits for the assumed lithology model. Results are presented for varying lithologies. For one test well, 6,000 feet were processed in a single pass, without zoning and without adjusting more than one parameter pick. The program recognized sand, limestone, dolomite, clay, feldspar, anhydrite, and salt without analyst intervention.« less

Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations.

PubMed

Nick, H M; Paluszny, A; Blunt, M J; Matthai, S K

2011-11-01

A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density.

Comparison of the iterated equation of motion approach and the density matrix formalism for the quantum Rabi model

NASA Astrophysics Data System (ADS)

Kalthoff, Mona; Keim, Frederik; Krull, Holger; Uhrig, Götz S.

2017-05-01

The density matrix formalism and the equation of motion approach are two semi-analytical methods that can be used to compute the non-equilibrium dynamics of correlated systems. While for a bilinear Hamiltonian both formalisms yield the exact result, for any non-bilinear Hamiltonian a truncation is necessary. Due to the fact that the commonly used truncation schemes differ for these two methods, the accuracy of the obtained results depends significantly on the chosen approach. In this paper, both formalisms are applied to the quantum Rabi model. This allows us to compare the approximate results and the exact dynamics of the system and enables us to discuss the accuracy of the approximations as well as the advantages and the disadvantages of both methods. It is shown to which extent the results fulfill physical requirements for the observables and which properties of the methods lead to unphysical results.

GeV-scale hot sterile neutrino oscillations: a numerical solution

NASA Astrophysics Data System (ADS)

Ghiglieri, J.; Laine, M.

2018-02-01

The scenario of baryogenesis through GeV-scale sterile neutrino oscillations is governed by non-linear differential equations for the time evolution of a sterile neutrino density matrix and Standard Model lepton and baryon asymmetries. By employing up-to-date rate coefficients and a non-perturbatively estimated Chern-Simons diffusion rate, we present a numerical solution of this system, incorporating the full momentum and helicity dependences of the density matrix. The density matrix deviates significantly from kinetic equilibrium, with the IR modes equilibrating much faster than the UV modes. For equivalent input parameters, our final results differ moderately (˜50%) from recent benchmarks in the literature. The possibility of producing an observable baryon asymmetry is nevertheless confirmed. We illustrate the dependence of the baryon asymmetry on the sterile neutrino mass splitting and on the CP-violating phase measurable in active neutrino oscillation experiments.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2016-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2017-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer.

PubMed

Sharma, Sandeep; Yanai, Takeshi; Booth, George H; Umrigar, C J; Chan, Garnet Kin-Lic

2014-03-14

We combine explicit correlation via the canonical transcorrelation approach with the density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods to compute a near-exact beryllium dimer curve, without the use of composite methods. In particular, our direct density matrix renormalization group calculations produce a well-depth of D(e) = 931.2 cm(-1) which agrees very well with recent experimentally derived estimates D(e) = 929.7±2 cm(-1) [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)] and D(e) = 934.6 cm(-1) [K. Patkowski, V. Špirko, and K. Szalewicz, Science 326, 1382 (2009)], as well the best composite theoretical estimates, D(e) = 938±15 cm(-1) [K. Patkowski, R. Podeszwa, and K. Szalewicz, J. Phys. Chem. A 111, 12822 (2007)] and D(e) = 935.1±10 cm(-1) [J. Koput, Phys. Chem. Chem. Phys. 13, 20311 (2011)]. Our results suggest possible inaccuracies in the functional form of the potential used at shorter bond lengths to fit the experimental data [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)]. With the density matrix renormalization group we also compute near-exact vertical excitation energies at the equilibrium geometry. These provide non-trivial benchmarks for quantum chemical methods for excited states, and illustrate the surprisingly large error that remains for 1 ¹Σ(g)⁻ state with approximate multi-reference configuration interaction and equation-of-motion coupled cluster methods. Overall, we demonstrate that explicitly correlated density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods allow us to fully converge to the basis set and correlation limit of the non-relativistic Schrödinger equation in small molecules.

Alternative dimensional reduction via the density matrix

NASA Astrophysics Data System (ADS)

de Carvalho, C. A.; Cornwall, J. M.; da Silva, A. J.

2001-07-01

We give graphical rules, based on earlier work for the functional Schrödinger equation, for constructing the density matrix for scalar and gauge fields in equilibrium at finite temperature T. More useful is a dimensionally reduced effective action (DREA) constructed from the density matrix by further functional integration over the arguments of the density matrix coupled to a source. The DREA is an effective action in one less dimension which may be computed order by order in perturbation theory or by dressed-loop expansions; it encodes all thermal matrix elements. We term the DREA procedure alternative dimensional reduction, to distinguish it from the conventional dimensionally reduced field theory (DRFT) which applies at infinite T. The DREA is useful because it gives a dimensionally reduced theory usable at any T including infinity, where it yields the DRFT, and because it does not and cannot have certain spurious infinities which sometimes occur in the density matrix itself or the conventional DRFT; these come from ln T factors at infinite temperature. The DREA can be constructed to all orders (in principle) and the only regularizations needed are those which control the ultraviolet behavior of the zero-T theory. An example of spurious divergences in the DRFT occurs in d=2+1φ4 theory dimensionally reduced to d=2. We study this theory and show that the rules for the DREA replace these ``wrong'' divergences in physical parameters by calculable powers of ln T; we also compute the phase transition temperature of this φ4 theory in one-loop order. Our density-matrix construction is equivalent to a construction of the Landau-Ginzburg ``coarse-grained free energy'' from a microscopic Hamiltonian.

Excitation energies from range-separated time-dependent density and density matrix functional theory.

PubMed

Pernal, Katarzyna

2012-05-14

Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other excitations is in general much better than that offered by TD-DFT-LDA or TD-DMFT-BB approximations if the range-separation parameter is properly chosen. The latter remains an open problem.

Decoherence, discord, and the quantum master equation for cosmological perturbations

NASA Astrophysics Data System (ADS)

Hollowood, Timothy J.; McDonald, Jamie I.

2017-05-01

We examine environmental decoherence of cosmological perturbations in order to study the quantum-to-classical transition and the impact of noise on entanglement during inflation. Given an explicit interaction between the system and environment, we derive a quantum master equation for the reduced density matrix of perturbations, drawing parallels with quantum Brownian motion, where we see the emergence of fluctuation and dissipation terms. Although the master equation is not in Lindblad form, we see how typical solutions exhibit positivity on super-horizon scales, leading to a physically meaningful density matrix. This allows us to write down a Langevin equation with stochastic noise for the classical trajectories which emerge from the quantum system on super-horizon scales. In particular, we find that environmental decoherence increases in strength as modes exit the horizon, with the growth driven essentially by white noise coming from local contributions to environmental correlations. Finally, we use our master equation to quantify the strength of quantum correlations as captured by discord. We show that environmental interactions have a tendency to decrease the size of the discord and that these effects are determined by the relative strength of the expansion rate and interaction rate of the environment. We interpret this in terms of the competing effects of particle creation versus environmental fluctuations, which tend to increase and decrease the discord respectively.

Time dependent Schrödinger equation for black hole evaporation: No information loss

NASA Astrophysics Data System (ADS)

Corda, Christian

2015-02-01

In 1976 S. Hawking claimed that "Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state".1 In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking's claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect 't Hooft's assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.

Computing the Density Matrix in Electronic Structure Theory on Graphics Processing Units.

PubMed

Cawkwell, M J; Sanville, E J; Mniszewski, S M; Niklasson, Anders M N

2012-11-13

The self-consistent solution of a Schrödinger-like equation for the density matrix is a critical and computationally demanding step in quantum-based models of interatomic bonding. This step was tackled historically via the diagonalization of the Hamiltonian. We have investigated the performance and accuracy of the second-order spectral projection (SP2) algorithm for the computation of the density matrix via a recursive expansion of the Fermi operator in a series of generalized matrix-matrix multiplications. We demonstrate that owing to its simplicity, the SP2 algorithm [Niklasson, A. M. N. Phys. Rev. B2002, 66, 155115] is exceptionally well suited to implementation on graphics processing units (GPUs). The performance in double and single precision arithmetic of a hybrid GPU/central processing unit (CPU) and full GPU implementation of the SP2 algorithm exceed those of a CPU-only implementation of the SP2 algorithm and traditional matrix diagonalization when the dimensions of the matrices exceed about 2000 × 2000. Padding schemes for arrays allocated in the GPU memory that optimize the performance of the CUBLAS implementations of the level 3 BLAS DGEMM and SGEMM subroutines for generalized matrix-matrix multiplications are described in detail. The analysis of the relative performance of the hybrid CPU/GPU and full GPU implementations indicate that the transfer of arrays between the GPU and CPU constitutes only a small fraction of the total computation time. The errors measured in the self-consistent density matrices computed using the SP2 algorithm are generally smaller than those measured in matrices computed via diagonalization. Furthermore, the errors in the density matrices computed using the SP2 algorithm do not exhibit any dependence of system size, whereas the errors increase linearly with the number of orbitals when diagonalization is employed.

Hybrid reconstruction of quantum density matrix: when low-rank meets sparsity

NASA Astrophysics Data System (ADS)

Li, Kezhi; Zheng, Kai; Yang, Jingbei; Cong, Shuang; Liu, Xiaomei; Li, Zhaokai

2017-12-01

Both the mathematical theory and experiments have verified that the quantum state tomography based on compressive sensing is an efficient framework for the reconstruction of quantum density states. In recent physical experiments, we found that many unknown density matrices in which people are interested in are low-rank as well as sparse. Bearing this information in mind, in this paper we propose a reconstruction algorithm that combines the low-rank and the sparsity property of density matrices and further theoretically prove that the solution of the optimization function can be, and only be, the true density matrix satisfying the model with overwhelming probability, as long as a necessary number of measurements are allowed. The solver leverages the fixed-point equation technique in which a step-by-step strategy is developed by utilizing an extended soft threshold operator that copes with complex values. Numerical experiments of the density matrix estimation for real nuclear magnetic resonance devices reveal that the proposed method achieves a better accuracy compared to some existing methods. We believe that the proposed method could be leveraged as a generalized approach and widely implemented in the quantum state estimation.

Pseudomaster equation for the no-count process in a continuous photodetection

NASA Technical Reports Server (NTRS)

Lee, Ching-Tsung

1994-01-01

The detection of cavity radiation with the detector placed outside the cavity is studied. Each leaked photon has a certain probability of propagating away without being detected. It is viewed as a continuous quantum measurement in which the density matrix is continuously revised according to the readout of the detector. The concept of pseudomaster equation for the no-count process is introduced; its solution leads to the discovery of the superoperator for the same process. It has the potential to become the key equation for continuous measurement process.

Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurin, Péter; Varga, Szabolcs

2015-06-14

We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between σ and 3σ (σ is the side length of the square). The exact equation of state and the nearest neighbor distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers, and a solid-like structure where the fluidmore » layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e., no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore.« less

Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas.

PubMed

Malone, Fionn D; Blunt, N S; Brown, Ethan W; Lee, D K K; Spencer, J S; Foulkes, W M C; Shepherd, James J

2016-09-09

The density matrix quantum Monte Carlo (DMQMC) method is used to sample exact-on-average N-body density matrices for uniform electron gas systems of up to 10^{124} matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the k-space configuration path-integral formalism disagree by up to ∼10% at certain reduced temperatures T/T_{F}≤0.5 and densities r_{s}≤1. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that the DMQMC method can calculate free energies directly and present exact free energies for T/T_{F}≥1 and r_{s}≤2.

Efficient propagation-inside-layer expansion algorithm for solving the scattering from three-dimensional nested homogeneous dielectric bodies with arbitrary shape.

PubMed

Bellez, Sami; Bourlier, Christophe; Kubické, Gildas

2015-03-01

This paper deals with the evaluation of electromagnetic scattering from a three-dimensional structure consisting of two nested homogeneous dielectric bodies with arbitrary shape. The scattering problem is formulated in terms of a set of Poggio-Miller-Chang-Harrington-Wu integral equations that are afterwards converted into a system of linear equations (impedance matrix equation) by applying the Galerkin method of moments (MoM) with Rao-Wilton-Glisson basis functions. The MoM matrix equation is then solved by deploying the iterative propagation-inside-layer expansion (PILE) method in order to obtain the unknown surface current densities, which are thereafter used to handle the radar cross-section (RCS) patterns. Some numerical results for various structures including canonical geometries are presented and compared with those of the FEKO software in order to validate the PILE-based approach as well as to show its efficiency to analyze the full-polarized RCS patterns.

Density matrix embedding in an antisymmetrized geminal power bath

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsuchimochi, Takashi; Welborn, Matthew; Van Voorhis, Troy, E-mail: tvan@mit.edu

2015-07-14

Density matrix embedding theory (DMET) has emerged as a powerful tool for performing wave function-in-wave function embedding for strongly correlated systems. In traditional DMET, an accurate calculation is performed on a small impurity embedded in a mean field bath. Here, we extend the original DMET equations to account for correlation in the bath via an antisymmetrized geminal power (AGP) wave function. The resulting formalism has a number of advantages. First, it allows one to properly treat the weak correlation limit of independent pairs, which DMET is unable to do with a mean-field bath. Second, it associates a size extensive correlationmore » energy with a given density matrix (for the models tested), which AGP by itself is incapable of providing. Third, it provides a reasonable description of charge redistribution in strongly correlated but non-periodic systems. Thus, AGP-DMET appears to be a good starting point for describing electron correlation in molecules, which are aperiodic and possess both strong and weak electron correlation.« less

Radiative Transfer Theory Verified by Controlled Laboratory Experiments

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Goldstein, Dennis H.; Chowdhary, Jacek; Lompado, Arthur

2013-01-01

We report the results of high-accuracy controlled laboratory measurements of the Stokes reflection matrix for suspensions of submicrometer-sized latex particles in water and compare them with the results of a numerically exact computer solution of the vector radiative transfer equation (VRTE). The quantitative performance of the VRTE is monitored by increasing the volume packing density of the latex particles from 2 to 10. Our results indicate that the VRTE can be applied safely to random particulate media with packing densities up to 2. VRTE results for packing densities of the order of 5 should be taken with caution, whereas the polarized bidirectional reflectivity of suspensions with larger packing densities cannot be accurately predicted. We demonstrate that a simple modification of the phase matrix entering the VRTE based on the so-called static structure factor can be a promising remedy that deserves further examination.

A new approach for the calculation of response spectral density of a linear stationary random multidegree of freedom system

NASA Astrophysics Data System (ADS)

Sharan, A. M.; Sankar, S.; Sankar, T. S.

1982-08-01

A new approach for the calculation of response spectral density for a linear stationary random multidegree of freedom system is presented. The method is based on modifying the stochastic dynamic equations of the system by using a set of auxiliary variables. The response spectral density matrix obtained by using this new approach contains the spectral densities and the cross-spectral densities of the system generalized displacements and velocities. The new method requires significantly less computation time as compared to the conventional method for calculating response spectral densities. Two numerical examples are presented to compare quantitatively the computation time.

Interaction between a circular inclusion and an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.; Ratwani, M.

1975-01-01

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Electron momentum densities in disordered muffin-tin alloys

NASA Astrophysics Data System (ADS)

Bansil, A.; Rao, R. S.; Mijnarends, P. E.; Schwartz, L.

1981-04-01

The application of average t-matrix (ATA) and coherent potential (CPA) approximations to the calculation of average electron momentum density ρ(p-->) in random muffin-tin alloys AxB1-x is considered. The necessary equations for the general matrix elements of the operators describing scattering by the CPA atom and also by an A or B atom embedded in the effective medium are derived. Various versions of the ATA for ρ(p-->) are discussed. Several ρ(p-->) curves calculated on the basis of the CPA and ATA in CuxNi1-x are presented. These results are used to delineate the effects on ρ(p-->) of self-consistency in the treatment of disorder.

Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Zhu, Ying; Herbert, John M.

2018-01-01

The "real time" formulation of time-dependent density functional theory (TDDFT) involves integration of the time-dependent Kohn-Sham (TDKS) equation in order to describe the time evolution of the electron density following a perturbation. This approach, which is complementary to the more traditional linear-response formulation of TDDFT, is more efficient for computation of broad-band spectra (including core-excited states) and for systems where the density of states is large. Integration of the TDKS equation is complicated by the time-dependent nature of the effective Hamiltonian, and we introduce several predictor/corrector algorithms to propagate the density matrix, one of which can be viewed as a self-consistent extension of the widely used modified-midpoint algorithm. The predictor/corrector algorithms facilitate larger time steps and are shown to be more efficient despite requiring more than one Fock build per time step, and furthermore can be used to detect a divergent simulation on-the-fly, which can then be halted or else the time step modified.

Aspects géométriques et intégrables des modèles de matrices aléatoires

NASA Astrophysics Data System (ADS)

Marchal, Olivier

2010-12-01

This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of integrable systems. The variety of these applications shows why matrix models are important from a mathematical point of view. First, the thesis will focus on the study of the merging of two intervals of the eigenvalues density near a singular point. Specifically, we will show why this special limit gives universal equations from the Painlevé II hierarchy of integrable systems theory. Then, following the approach of (bi) orthogonal polynomials introduced by Mehta to compute partition functions, we will find Riemann-Hilbert and isomonodromic problems connected to matrix models, making the link with the theory of Jimbo, Miwa and Ueno. In particular, we will describe how the hermitian two-matrix models provide a degenerate case of Jimbo-Miwa-Ueno's theory that we will generalize in this context. Furthermore, the loop equations method, with its central notions of spectral curve and topological expansion, will lead to the symplectic invariants of algebraic geometry recently proposed by Eynard and Orantin. This last point will be generalized to the case of non-hermitian matrix models (arbitrary beta) paving the way to "quantum algebraic geometry" and to the generalization of symplectic invariants to "quantum curves". Finally, this set up will be applied to combinatorics in the context of topological string theory, with the explicit computation of an hermitian random matrix model enumerating the Gromov-Witten invariants of a toric Calabi-Yau threefold.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

PubMed

Chen, Xin; Wu, Yinghua; Batista, Victor S

2005-02-08

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

Watching excitons move: the time-dependent transition density matrix

NASA Astrophysics Data System (ADS)

Ullrich, Carsten

2012-02-01

Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

Evolution equation of population genetics: Relation to the density-matrix theory of quasiparticles with general dispersion laws

NASA Astrophysics Data System (ADS)

Bezák, V.

2003-02-01

The Waxman-Peck theory of population genetics is discussed in regard of soil bacteria. Each bacterium is understood as a carrier of a phenotypic parameter p. The central objective is the calculation of the probability density with respect to p, Φ(p,t;p0), of the carriers living at time t>0, provided that initially at t0=0, all bacteria carried the phenotypic parameter p0=0. The theory involves two small parameters: the mutation probability μ and a parameter γ involved in a function w(p) defining the fitness of the bacteria to survive the generation time τ and give birth to an offspring. The mutation from a state p to a state q is defined by a Gaussian with a dispersion σ2m. The author focuses our attention on a function φ(p,t) which determines uniquely the function Φ(p,t;p0) and satisfies a linear equation (Waxman’s equation). The Green function of this equation is mathematically identical with the one-particle Bloch density matrix, where μ characterizes the order of magnitude of the potential energy. (In the x representation, the potential energy is proportional to the inverted Gaussian with the dispersion σ2m). The author solves Waxman’s equation in the standard style of a perturbation theory and discusses how the solution depends on the choice of the fitness function w(p). In a sense, the function c(p)=1-w(p)/w(0) is analogous to the dispersion function E(p) of fictitious quasiparticles. In contrast to Waxman’s approximation, where c(p) was taken as a quadratic function, c(p)≈γp2, the author exemplifies the problem with another function, c(p)=γ[1-exp(-ap2)], where γ is small but a may be large. The author shows that the use of this function in the theory of the population genetics is the same as the use of a nonparabolic dispersion law E=E(p) in the density-matrix theory. With a general function c(p), the distribution function Φ(p,t;0) is composed of a δ-function component, N(t)δ(p), and a blurred component. When discussing the limiting transition for t→∞, the author shows that his function c(p) implies that N(t)→N(∞)≠0 in contrast with the asymptotics N(t)→0 resulting from the use of Waxman’s function c(p)˜p2.

Study of laser cooling in deep optical lattice: two-level quantum model

NASA Astrophysics Data System (ADS)

Prudnikov, O. N.; Il'enkov, R. Ya.; Taichenachev, A. V.; Yudin, V. I.; Rasel, E. M.

2018-01-01

We study a possibility of laser cooling of 24Mg atoms in deep optical lattice formed by intense off-resonant laser field in a presence of cooling field resonant to narrow (3s3s) 1 S 0 → (3s3p)3 P 1 (λ = 457 nm) optical transition. For description of laser cooling with taking into account quantum recoil effects we consider two quantum models. The first one is based on direct numerical solution of quantum kinetic equation for atom density matrix and the second one is simplified model based on decomposition of atom density matrix over vibration states in the lattice wells. We search cooling field intensity and detuning for minimum cooling energy and fast laser cooling.

Gravitational collapse and Hawking-like radiation of a shell in AdS spacetime

NASA Astrophysics Data System (ADS)

Saini, Anshul; Stojkovic, Dejan

2018-01-01

In this paper, we study the collapse of a massive shell in 2 +1 and 3 +1 dimensional gravity with anti-de Sitter asymptotics. Using the Gauss-Codazzi method, we derive gravitational equations of motion of the shell. We then use the functional Schrödinger formalism to calculate the spectrum of particles produced during the collapse. At the late time, radiation agrees very well with the standard Hawking results. In 3 +1 dimensions, we reproduce the Hawking-Page transition. We then construct the density matrix of this collapsing system and analyze the information content in the emitted radiation. We find that the off-diagonal elements of the density matrix are very important in preserving the unitarity of the system.

Time dependent Schrödinger equation for black hole evaporation: No information loss

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corda, Christian, E-mail: cordac.galilei@gmail.com

2015-02-15

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state”. This was the starting point of the popular “black hole (BH) information paradox”. In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model,more » a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking’s claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect ’t Hooft’s assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.« less

The rate constant of a quantum-diffusion-controlled bimolecular reaction

NASA Astrophysics Data System (ADS)

Bondarev, B. V.

1986-04-01

A quantum-mechanical equation is derived in the tight-bond approximation which describes the motion and chemical interaction of a pair of species A and B when their displacement in the matrix is caused by tunnelling. Within the framework of the discrete model of random walks, definitions are given of the probability and rate constant of a reaction A + B → P (products) proceeding in a condensed medium. A method is suggested for calculating the rate constant of a quantum-diffusion-controlled bimolecular reaction. By this method, an expression is obtained for the rate constant in the stationary spherically symmetrical case. An equation for the density matrix is also proposed which describes the motion and chemical interaction of a pair of species when the quantum and classical diffusion are competitive.

Quasiclassical description of a superconductor with a spin density wave

NASA Astrophysics Data System (ADS)

Moor, A.; Volkov, A. F.; Efetov, K. B.

2011-04-01

We derive equations for the quasiclassical Green’s functions ǧ within a simple model of a two-band superconductor with a spin density wave (SDW). The elements of the matrix ǧ are the retarded, advanced, and Keldysh functions, each of which is an 8×8 matrix in the Gor’kov-Nambu, the spin, and the band space. In equilibrium, these equations are a generalization of the Eilenberger equation. On the basis of the derived equations, we analyze the Knight shift, the proximity, and the dc Josephson effects in the superconductors under consideration. The Knight shift is shown to depend on the orientation of the external magnetic field with respect to the direction of the vector of the magnetization of the SDW. The proximity effect is analyzed for an interface between a superconductor with the SDW and a normal metal. The function describing both superconducting and magnetic correlations is shown to penetrate the normal metal or a metal with the SDW due to the proximity effect. The dc Josephson current in an SSDW/N/SSDW junction is also calculated as a function of the phase difference φ. It is shown that in our model, the Josephson current does not depend on the mutual orientation of the magnetic moments in the superconductors SSDW and is proportional to sinφ. The dissipationless spin current jsp depends on the angle α between the magnetization vectors in the same way (jsp~sinα) and is not zero above the superconducting transition temperature.

Kinetic experiments for evaluating the Nernst-Monod model for anode-respiring bacteria (ARB) in a biofilm anode.

PubMed

Torres, César I; Marcus, Andrew Kato; Parameswaran, Prathap; Rittmann, Bruce E

2008-09-01

Anode-respiring bacteria (ARB) are able to transfer electrons from reduced substrates to a solid electrode. Previously, we developed a biofilm model based on the Nernst-Monod equation to describe the anode potential losses of ARB that transfer electrons through a solid conductive matrix. In this work, we develop an experimental setup to demonstrate how well the Nernst-Monod equation is able to represent anode potential losses in an ARB biofilm. We performed low-scan cyclic voltammetry (LSCV) throughout the growth phase of an ARB biofilm on a graphite electrode growing on acetate in continuous mode. The (j)V response of 9 LSCVs corresponded well to the Nernst-Monod equation, and the half-saturation potential (E(KA)) was -0.425 +/- 0.002 V vs Ag/AgCl at 30 degrees C (-0.155 +/- 0.002 V vs SHE). Anode-potential losses from the potential of acetate reached approximately 0.225 V at current density saturation, and this loss was determined by our microbial community's E(KA) value. The LSCVs at high current densities showed no significant deviation from the Nernst-Monod ideal shape, indicating that the conductivity of the biofilm matrix (kappa(bio)) was high enough (> or = 0.5 mS/cm) that potential loss did not affect the performance of the biofilm anode. Our results confirm the applicability of the Nernst-Monod equation for a conductive biofilm anode and give insights of the processes that dominate anode potential losses in microbial fuel cells.

A cross-diffusion system derived from a Fokker-Planck equation with partial averaging

NASA Astrophysics Data System (ADS)

Jüngel, Ansgar; Zamponi, Nicola

2017-02-01

A cross-diffusion system for two components with a Laplacian structure is analyzed on the multi-dimensional torus. This system, which was recently suggested by P.-L. Lions, is formally derived from a Fokker-Planck equation for the probability density associated with a multi-dimensional Itō process, assuming that the diffusion coefficients depend on partial averages of the probability density with exponential weights. A main feature is that the diffusion matrix of the limiting cross-diffusion system is generally neither symmetric nor positive definite, but its structure allows for the use of entropy methods. The global-in-time existence of positive weak solutions is proved and, under a simplifying assumption, the large-time asymptotics is investigated.

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Veneva, Milena; Ayriyan, Alexander

2018-04-01

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed - diagonal dominantization and symbolic algorithms.

An efficient method for quantum transport simulations in the time domain

NASA Astrophysics Data System (ADS)

Wang, Y.; Yam, C.-Y.; Frauenheim, Th.; Chen, G. H.; Niehaus, T. A.

2011-11-01

An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. The density matrix of the device region is propagated according to the Liouville-von Neumann equation. The semi-infinite leads give rise to dissipative terms in the equation of motion which are calculated from first principles in the wide band limit. In contrast to earlier ab initio implementations of this formalism, the Hamiltonian is here approximated in the spirit of the density functional based tight-binding (DFTB) method. Results are presented for two prototypical molecular devices and compared to full TDDFT calculations. The temporal profile of the current traces is qualitatively well captured by the DFTB scheme. Steady state currents show considerable variations, both in comparison of approximate and full TDDFT, but also among TDDFT calculations with different basis sets.

Continuum Level Density of a Coupled-Channel System in the Complex Scaling Method

NASA Astrophysics Data System (ADS)

Suzuki, R.; Kruppa, A. T.; Giraud, B. G.; Katō, K.

2008-06-01

We study the continuum level density (CLD) in the formalism of the complex scaling method (CSM) for coupled-channel systems. We apply the formalism to the ^{4}He = [^{3}H + p] + [^3{He} + n] coupled-channel cluster model where there are resonances at low energy. Numerical calculations of the CLD in the CSM with a finite number of L^{2} basis functions are consistent with the exact result calculated from the S-matrix by solving coupled-channel equations. We also study channel densities. In this framework, the extended completeness relation (ECR) plays an important role.

Interacting hadron resonance gas model in the K -matrix formalism

NASA Astrophysics Data System (ADS)

Dash, Ashutosh; Samanta, Subhasis; Mohanty, Bedangadas

2018-05-01

An extension of hadron resonance gas (HRG) model is constructed to include interactions using relativistic virial expansion of partition function. The noninteracting part of the expansion contains all the stable baryons and mesons and the interacting part contains all the higher mass resonances which decay into two stable hadrons. The virial coefficients are related to the phase shifts which are calculated using K -matrix formalism in the present work. We have calculated various thermodynamics quantities like pressure, energy density, and entropy density of the system. A comparison of thermodynamic quantities with noninteracting HRG model, calculated using the same number of hadrons, shows that the results of the above formalism are larger. A good agreement between equation of state calculated in K -matrix formalism and lattice QCD simulations is observed. Specifically, the lattice QCD calculated interaction measure is well described in our formalism. We have also calculated second-order fluctuations and correlations of conserved charges in K -matrix formalism. We observe a good agreement of second-order fluctuations and baryon-strangeness correlation with lattice data below the crossover temperature.

Nonlinear programming models to optimize uneven-aged loblolly pine management

Treesearch

Benedict J. Schulte; Joseph. Buongiorno; Kenneth Skog

1999-01-01

Nonlinear programming models of uneven-aged loblolly pine (Pinus taeda L.) management were developed to identify sustainable management regimes which optimize: 1) soil expectation value (SEV), 2) tree diversity, or 3) annual sawtimber yields. The models use the equations of SouthPro, a site- and density-dependent, multi-species matrix growth and yield model that...

A frequency domain global parameter estimation method for multiple reference frequency response measurements

NASA Astrophysics Data System (ADS)

Shih, C. Y.; Tsuei, Y. G.; Allemang, R. J.; Brown, D. L.

1988-10-01

A method of using the matrix Auto-Regressive Moving Average (ARMA) model in the Laplace domain for multiple-reference global parameter identification is presented. This method is particularly applicable to the area of modal analysis where high modal density exists. The method is also applicable when multiple reference frequency response functions are used to characterise linear systems. In order to facilitate the mathematical solution, the Forsythe orthogonal polynomial is used to reduce the ill-conditioning of the formulated equations and to decouple the normal matrix into two reduced matrix blocks. A Complex Mode Indicator Function (CMIF) is introduced, which can be used to determine the proper order of the rational polynomials.

Elementary solutions of coupled model equations in the kinetic theory of gases

NASA Technical Reports Server (NTRS)

Kriese, J. T.; Siewert, C. E.; Chang, T. S.

1974-01-01

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

Numerical simulations of electromagnetic scattering by Solar system objects

NASA Astrophysics Data System (ADS)

Dlugach, Janna M.

2016-11-01

Having been profoundly stimulated by the seminal work of Viktor V. Sobolev, I have been involved in multi-decadal research in the fields of radiative transfer, electromagnetic scattering by morphologically complex particles and particulate media, and planetary remote sensing. Much of this research has been done in close collaboration with other "descendants" of Academician Sobolev. This tutorial paper gives a representative overview of the results of extensive numerical simulations (in the vast majority carried out in collaboration with Michael Mishchenko) used to analyze remote-sensing observations of Solar system objects and based on highly accurate methods of the radiative transfer theory and direct computer solvers of the Maxwell equations. Using the atmosphere of Jupiter as a proving ground and performing T-matrix and radiative-transfer calculations helps demonstrate the strong effect of aerosol-particle shapes on the accuracy of remote-sensing retrievals. I then discuss the application of the T-matrix method, a numerically exact solution of the vector radiative transfer equation, and the theory of coherent backscattering to an analysis of polarimetric radar observations of Saturn's rings. Numerical modeling performed by using the superposition T-matrix method in application to cometary dust in the form of aggregates serves to reproduce the results of polarimetric observations of the distant comet C/2010 S1. On the basis of direct computer solutions of the Maxwell equations, it is demonstrated that all backscattering effects predicted by the low-density theories of radiative transfer and coherent backscattering can also be identified for media with volume packing densities typically encountered in natural and artificial environments. This result implies that spectacular opposition effects observed for some high-albedo atmoshereless Solar system bodies can be attributed to coherent backscattering of sunlight by regolith layers composed of microscopic particles.

Solvable Hydrodynamics of Quantum Integrable Systems

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2017-12-01

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.

Solution of weakly compressible isothermal flow in landfill gas collection networks

NASA Astrophysics Data System (ADS)

Nec, Y.; Huculak, G.

2017-12-01

Pipe networks collecting gas in sanitary landfills operate under the regime of a weakly compressible isothermal flow of ideal gas. The effect of compressibility has been traditionally neglected in this application in favour of simplicity, thereby creating a conceptual incongruity between the flow equations and thermodynamic equation of state. Here the flow is solved by generalisation of the classic Darcy-Weisbach equation for an incompressible steady flow in a pipe to an ordinary differential equation, permitting continuous variation of density, viscosity and related fluid parameters, as well as head loss or gain due to gravity, in isothermal flow. The differential equation is solved analytically in the case of ideal gas for a single edge in the network. Thereafter the solution is used in an algorithm developed to construct the flow equations automatically for a network characterised by an incidence matrix, and determine pressure distribution, flow rates and all associated parameters therein.

Numerical simulation of freshwater/seawater interaction in a dual-permeability karst system with conduits: the development of discrete-continuum VDFST-CFP model

NASA Astrophysics Data System (ADS)

Xu, Zexuan; Hu, Bill

2016-04-01

Dual-permeability karst aquifers of porous media and conduit networks with significant different hydrological characteristics are widely distributed in the world. Discrete-continuum numerical models, such as MODFLOW-CFP and CFPv2, have been verified as appropriate approaches to simulate groundwater flow and solute transport in numerical modeling of karst hydrogeology. On the other hand, seawater intrusion associated with fresh groundwater resources contamination has been observed and investigated in numbers of coastal aquifers, especially under conditions of sea level rise. Density-dependent numerical models including SEAWAT are able to quantitatively evaluate the seawater/freshwater interaction processes. A numerical model of variable-density flow and solute transport - conduit flow process (VDFST-CFP) is developed to provide a better description of seawater intrusion and submarine groundwater discharge in a coastal karst aquifer with conduits. The coupling discrete-continuum VDFST-CFP model applies Darcy-Weisbach equation to simulate non-laminar groundwater flow in the conduit system in which is conceptualized and discretized as pipes, while Darcy equation is still used in continuum porous media. Density-dependent groundwater flow and solute transport equations with appropriate density terms in both conduit and porous media systems are derived and numerically solved using standard finite difference method with an implicit iteration procedure. Synthetic horizontal and vertical benchmarks are created to validate the newly developed VDFST-CFP model by comparing with other numerical models such as variable density SEAWAT, couplings of constant density groundwater flow and solute transport MODFLOW/MT3DMS and discrete-continuum CFPv2/UMT3D models. VDFST-CFP model improves the simulation of density dependent seawater/freshwater mixing processes and exchanges between conduit and matrix. Continuum numerical models greatly overestimated the flow rate under turbulent flow condition but discrete-continuum models provide more accurate results. Parameters sensitivities analysis indicates that conduit diameter and friction factor, matrix hydraulic conductivity and porosity are important parameters that significantly affect variable-density flow and solute transport simulation. The pros and cons of model assumptions, conceptual simplifications and numerical techniques in VDFST-CFP are discussed. In general, the development of VDFST-CFP model is an innovation in numerical modeling methodology and could be applied to quantitatively evaluate the seawater/freshwater interaction in coastal karst aquifers. Keywords: Discrete-continuum numerical model; Variable density flow and transport; Coastal karst aquifer; Non-laminar flow

The Liouville equation for flavour evolution of neutrinos and neutrino wave packets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, Rasmus Sloth Lundkvist; Smirnov, Alexei Yu., E-mail: rasmus@mpi-hd.mpg.de, E-mail: smirnov@mpi-hd.mpg.de

We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over amore » trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.« less

Compliance matrices for cracked bodies

NASA Technical Reports Server (NTRS)

Ballarini, R.

1986-01-01

An algorithm is developed to construct the compliance matrix for a cracked solid in the integral-equation formulation of two-dimensional linear-elastic fracture mechanics. The integral equation is reduced to a system of algebraic equations for unknown values of the dislocation-density function at discrete points on the interval from -1 to 1, using the numerical procedure described by Gerasoulis (1982). Sample numerical results are presented, and it is suggested that the algorithm is especially useful in cases where iterative solutions are required; e.g., models of fiber-reinforced concrete, rocks, or ceramics where microcracking, fiber bridging, and other nonlinear effects are treated as nonlinear springs along the crack surfaces (Ballarini et al., 1984).

Optoelectronics of inverted type-I CdS/CdSe core/crown quantum ring

NASA Astrophysics Data System (ADS)

Bose, Sumanta; Fan, Weijun; Zhang, Dao Hua

2017-10-01

Inverted type-I heterostructure core/crown quantum rings (QRs) are quantum-efficient luminophores, whose spectral characteristics are highly tunable. Here, we study the optoelectronic properties of type-I core/crown CdS/CdSe QRs in the zincblende phase—over contrasting lateral size and crown width. For this, we inspect their strain profiles, transition energies, transition matrix elements, spatial charge densities, electronic bandstructures, band-mixing probabilities, optical gain spectra, maximum optical gains, and differential optical gains. Our framework uses an effective-mass envelope function theory based on the 8-band k ṡ p method employing the valence force field model for calculating the atomic strain distributions. The gain calculations are based on the density-matrix equation and take into consideration the excitonic effects with intraband scattering. Variations in the QR lateral size and relative widths of core and crown (ergo the composition) affect their energy levels, band-mixing probabilities, optical transition matrix elements, emission wavelengths/intensities, etc. The optical gain of QRs is also strongly dimension and composition dependent with further dependency on the injection carrier density causing the band-filling effect. They also affect the maximum and differential gain at varying dimensions and compositions.

On regularizing the MCTDH equations of motion

NASA Astrophysics Data System (ADS)

Meyer, Hans-Dieter; Wang, Haobin

2018-03-01

The Multiconfiguration Time-Dependent Hartree (MCTDH) approach leads to equations of motion (EOM) which become singular when there are unoccupied so-called single-particle functions (SPFs). Starting from a Hartree product, all SPFs, except the first one, are unoccupied initially. To solve the MCTDH-EOMs numerically, one therefore has to remove the singularity by a regularization procedure. Usually the inverse of a density matrix is regularized. Here we argue and show that regularizing the coefficient tensor, which in turn regularizes the density matrix as well, leads to an improved performance of the EOMs. The initially unoccupied SPFs are rotated faster into their "correct direction" in Hilbert space and the final results are less sensitive to the choice of the value of the regularization parameter. For a particular example (a spin-boson system studied with a transformed Hamiltonian), we could even show that only with the new regularization scheme could one obtain correct results. Finally, in Appendix A, a new integration scheme for the MCTDH-EOMs developed by Lubich and co-workers is discussed. It is argued that this scheme does not solve the problem of the unoccupied natural orbitals because this scheme ignores the latter and does not propagate them at all.

Effects of the U boson on the inner edge of neutron star crusts

NASA Astrophysics Data System (ADS)

Zheng, Hao; Chen, Lie-Wen

2012-02-01

We explore effects of the light vector U boson, which is weakly coupled to nucleons, on the transition density ρt and pressure Pt at the inner edge separating the liquid core from the solid crust of neutron stars. Three methods, i.e., the thermodynamical approach, the curvature matrix approach, and the Vlasov equation approach, are used to determine the transition density ρt with the Skyrme effective nucleon-nucleon interactions. We find that the ρt and Pt depend on not only the ratio of coupling strength to mass squared of the U boson g2/μ2 but also its mass μ due to the finite-range interaction from the U-boson exchange. In particular, our results indicate that the ρt and Pt are sensitive to both g2/μ2 and μ if the U-boson mass μ is larger than about 2 MeV. Furthermore, we show that both g2/μ2 and μ can have significant influence on the mass-radius relation and the crustal fraction of total moment of inertia of neutron stars. In addition, we study the exchange term contribution of the U boson based on the density matrix expansion method, and demonstrate that the exchange term effects on the nuclear matter equation of state as well as the ρt and Pt are generally negligible.

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

DOE PAGES

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory; ...

2015-02-25

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Thermal constitutive matrix applied to asynchronous electrical machine using the cell method

NASA Astrophysics Data System (ADS)

Domínguez, Pablo Ignacio González; Monzón-Verona, José Miguel; Rodríguez, Leopoldo Simón; Sánchez, Adrián de Pablo

2018-03-01

This work demonstrates the equivalence of two constitutive equations. One is used in Fourier's law of the heat conduction equation, the other in electric conduction equation; both are based on the numerical Cell Method, using the Finite Formulation (FF-CM). A 3-D pure heat conduction model is proposed. The temperatures are in steady state and there are no internal heat sources. The obtained results are compared with an equivalent model developed using the Finite Elements Method (FEM). The particular case of 2-D was also studied. The errors produced are not significant at less than 0.2%. The number of nodes is the number of the unknowns and equations to resolve. There is no significant gain in precision with increasing density of the mesh.

Crystallization of dense neutron matter

NASA Technical Reports Server (NTRS)

Canuto, V.; Chitre, S. M.

1974-01-01

The equation of state for cold neutron matter at high density is studied in the t-matrix formulation, and it is shown that energetically it is convenient to have neutrons in a crystalline configuration rather than in a liquid state for values of the density exceeding 1600 Tg/cu cm. The study of the mechanical properties indicates that the system is stable against shearing stresses. A solid core in the deep interior of heavy neutron stars appears to offer the most plausible explanation of speed-ups observed in the Vela pulsar.

Nonlinear properties of gated graphene in a strong electromagnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avetisyan, A. A., E-mail: artakav@ysu.am; Djotyan, A. P., E-mail: adjotyan@ysu.am; Moulopoulos, K., E-mail: cos@ucy.ac.cy

We develop a microscopic theory of a strong electromagnetic field interaction with gated bilayer graphene. Quantum kinetic equations for density matrix are obtained using a tight binding approach within second quantized Hamiltonian in an intense laser field. We show that adiabatically changing the gate potentials with time may produce (at resonant photon energy) a full inversion of the electron population with high density between valence and conduction bands. In the linear regime, excitonic absorption of an electromagnetic radiation in a graphene monolayer with opened energy gap is also studied.

Mean, covariance, and effective dimension of stochastic distributed delay dynamics

NASA Astrophysics Data System (ADS)

René, Alexandre; Longtin, André

2017-11-01

Dynamical models are often required to incorporate both delays and noise. However, the inherently infinite-dimensional nature of delay equations makes formal solutions to stochastic delay differential equations (SDDEs) challenging. Here, we present an approach, similar in spirit to the analysis of functional differential equations, but based on finite-dimensional matrix operators. This results in a method for obtaining both transient and stationary solutions that is directly amenable to computation, and applicable to first order differential systems with either discrete or distributed delays. With fewer assumptions on the system's parameters than other current solution methods and no need to be near a bifurcation, we decompose the solution to a linear SDDE with arbitrary distributed delays into natural modes, in effect the eigenfunctions of the differential operator, and show that relatively few modes can suffice to approximate the probability density of solutions. Thus, we are led to conclude that noise makes these SDDEs effectively low dimensional, which opens the possibility of practical definitions of probability densities over their solution space.

A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets.

PubMed

Chen, Jiao; Weihs, Daphne; Vermolen, Fred J

2018-04-01

Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler-Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of T-lymphocytes through changing direction of their migration.

BRST technique for the cosmological density matrix

NASA Astrophysics Data System (ADS)

Barvinsky, A. O.

2013-10-01

The microcanonical density matrix in closed cosmology has a natural definition as a projector on the space of solutions of Wheeler-DeWitt equations, which is motivated by the absence of global non-vanishing charges and energy in spatially closed gravitational systems. Using the BRST/BFV formalism in relativistic phase space of gauge and ghost variables we derive the path integral representation for this projector and the relevant statistical sum. This derivation circumvents the difficulties associated with the open algebra of noncommutative quantum Dirac constraints and the construction/regularization of the physical inner product in the subspace of BRS singlets. This inner product is achieved via the Batalin-Marnelius gauge fixing in the space of BRS-invariant states, which in its turn is shown to be a result of truncation of the BRST/BFV formalism to the "matter" sector of relativistic phase space.

Intersubband Transitions in InAs/AlSb Quantum Wells

NASA Technical Reports Server (NTRS)

Li, J.; Koloklov, K.; Ning, C. Z.; Larraber, D. C.; Khodaparast, G. A.; Kono, J.; Ueda, K.; Nakajima, Y.; Sasa, S.; Inoue, M.

2003-01-01

We have studied intersubband transitions in InAs/AlSb quantum wells experimentally and theoretically. Experimentally, we performed polarization-resolved infrared absorption spectroscopy to measure intersubband absorption peak frequencies and linewidths as functions of temperature (from 4 K to room temperature) and quantum well width (from a few nm to 10 nm). To understand experimental results, we performed a self-consistent 8-band k-p band-structure calculation including spatial charge separation. Based on the calculated band structure, we developed a set of density matrix equations to compute TE and TM optical transitions self-consistently, including both interband and intersubband channels. This density matrix formalism is also ideal for the inclusion of various many-body effects, which are known to be important for intersubband transitions. Detailed comparison between experimental data and theoretical simulations is presented.

Quasi-particle energy spectra in local reduced density matrix functional theory.

PubMed

Lathiotakis, Nektarios N; Helbig, Nicole; Rubio, Angel; Gidopoulos, Nikitas I

2014-10-28

Recently, we introduced [N. N. Lathiotakis, N. Helbig, A. Rubio, and N. I. Gidopoulos, Phys. Rev. A 90, 032511 (2014)] local reduced density matrix functional theory (local RDMFT), a theoretical scheme capable of incorporating static correlation effects in Kohn-Sham equations. Here, we apply local RDMFT to molecular systems of relatively large size, as a demonstration of its computational efficiency and its accuracy in predicting single-electron properties from the eigenvalue spectrum of the single-particle Hamiltonian with a local effective potential. We present encouraging results on the photoelectron spectrum of molecular systems and the relative stability of C20 isotopes. In addition, we propose a modelling of the fractional occupancies as functions of the orbital energies that further improves the efficiency of the method useful in applications to large systems and solids.

The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Hajarian, Masoud

2012-08-01

A matrix P is called a symmetric orthogonal if P = P T = P -1. A matrix X is said to be a generalised bisymmetric with respect to P if X = X T = PXP. It is obvious that any symmetric matrix is also a generalised bisymmetric matrix with respect to I (identity matrix). By extending the idea of the Jacobi and the Gauss-Seidel iterations, this article proposes two new iterative methods, respectively, for computing the generalised bisymmetric (containing symmetric solution as a special case) and skew-symmetric solutions of the generalised Sylvester matrix equation ? (including Sylvester and Lyapunov matrix equations as special cases) which is encountered in many systems and control applications. When the generalised Sylvester matrix equation has a unique generalised bisymmetric (skew-symmetric) solution, the first (second) iterative method converges to the generalised bisymmetric (skew-symmetric) solution of this matrix equation for any initial generalised bisymmetric (skew-symmetric) matrix. Finally, some numerical results are given to illustrate the effect of the theoretical results.

An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations

NASA Astrophysics Data System (ADS)

Daud, Wan Suhana Wan; Ahmad, Nazihah; Malkawi, Ghassan

2017-11-01

Sylvester matrix equations played a prominent role in various areas including control theory. Considering to any un-certainty problems that can be occurred at any time, the Sylvester matrix equation has to be adapted to the fuzzy environment. Therefore, in this study, an algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equation is constructed. The construction of the algorithm is based on the max-min arithmetic multiplication operation. Besides that, an associated arbitrary matrix equation is modified in obtaining the final solution. Finally, some numerical examples are presented to illustrate the proposed algorithm.

The Dielectric Permittivity of Crystals in the Reduced Hartree-Fock Approximation

NASA Astrophysics Data System (ADS)

Cancès, Éric; Lewin, Mathieu

2010-07-01

In a recent article (Cancès et al. in Commun Math Phys 281:129-177, 2008), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree-Fock model, the ground state electronic density matrix is decomposed as {γ = γ^0_per + Q_{ν,\\varepsilon_F}}, where {γ^0_per} is the ground state density matrix of the host crystal and {Q_{ν,\\varepsilon_F}} the modification of the electronic density matrix generated by a modification ν of the nuclear charge of the host crystal, the Fermi level ɛ F being kept fixed. The purpose of the present article is twofold. First, we study in more detail the mathematical properties of the density matrix {Q_{ν,\\varepsilon_F}} (which is known to be a self-adjoint Hilbert-Schmidt operator on {L^2(mathbb{R}^3)}). We show in particular that if {int_{mathbb{R}^3} ν neq 0, Q_{ν,\\varepsilon_F}} is not trace-class. Moreover, the associated density of charge is not in {L^1(mathbb{R}^3)} if the crystal exhibits anisotropic dielectric properties. These results are obtained by analyzing, for a small defect ν, the linear and nonlinear terms of the resolvent expansion of {Q_{ν,\\varepsilon_F}}. Second, we show that, after an appropriate rescaling, the potential generated by the microscopic total charge (nuclear plus electronic contributions) of the crystal in the presence of the defect converges to a homogenized electrostatic potential solution to a Poisson equation involving the macroscopic dielectric permittivity of the crystal. This provides an alternative (and rigorous) derivation of the Adler-Wiser formula.

Growth model for uneven-aged loblolly pine stands : simulations and management implications

Treesearch

C.-R. Lin; J. Buongiorno; Jeffrey P. Prestemon; K. E. Skog

1998-01-01

A density-dependent matrix growth model of uneven-aged loblolly pine stands was developed with data from 991 permanent plots in the southern United States. The model predicts the number of pine, soft hardwood, and hard hardwood trees in 13 diameter classes, based on equations for ingrowth, upgrowth, and mortality. Projections of 6 to 10 years agreed with the growth...

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Equilibrium problems for Raney densities

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Liu, Dang-Zheng; Zinn-Justin, Paul

2015-07-01

The Raney numbers are a class of combinatorial numbers generalising the Fuss-Catalan numbers. They are indexed by a pair of positive real numbers (p, r) with p > 1 and 0 < r ⩽ p, and form the moments of a probability density function. For certain (p, r) the latter has the interpretation as the density of squared singular values for certain random matrix ensembles, and in this context equilibrium problems characterising the Raney densities for (p, r) = (θ + 1, 1) and (θ/2 + 1, 1/2) have recently been proposed. Using two different techniques—one based on the Wiener-Hopf method for the solution of integral equations and the other on an analysis of the algebraic equation satisfied by the Green's function—we establish the validity of the equilibrium problems for general θ > 0 and similarly use both methods to identify the equilibrium problem for (p, r) = (θ/q + 1, 1/q), θ > 0 and q \\in Z+ . The Wiener-Hopf method is used to extend the latter to parameters (p, r) = (θ/q + 1, m + 1/q) for m a non-negative integer, and also to identify the equilibrium problem for a family of densities with moments given by certain binomial coefficients.

Gauge invariance of phenomenological models of the interaction of quantum dissipative systems with electromagnetic fields

NASA Astrophysics Data System (ADS)

Tokman, M. D.

2009-05-01

We discuss specific features of the electrodynamic characteristics of quantum systems within the framework of models that include a phenomenological description of the relaxation processes. As is shown by W. E. Lamb, Jr., R. R. Schlicher, and M. O. Scully [Phys. Rev. A 36, 2763 (1987)], the use of phenomenological relaxation operators, which adequately describe the attenuation of eigenvibrations of a quantum system, may lead to incorrect solutions in the presence of external electromagnetic fields determined by the vector potential for different resonance processes. This incorrectness can be eliminated by giving a gauge-invariant form to the relaxation operator. Lamb, Jr., proposed the corresponding gauge-invariant modification for the Weisskopf-Wigner relaxation operator, which is introduced directly into the Schrödinger equation within the framework of the two-level approximation. In the present paper, this problem is studied for the von Neumann equation supplemented by a relaxation operator. First, we show that the solution of the equation for the density matrix with the relaxation operator correctly obtained “from the first principles” has properties that ensure gauge invariance for the observables. Second, we propose a common recipe for transformation of the phenomenological relaxation operator into the correct (gauge-invariant) form in the density-matrix equations for a multilevel system. Also, we discuss the methods of elimination of other inaccuracies (not related to the gauge-invariance problem) which arise if the electrodynamic response of a dissipative quantum system is calculated within the framework of simplified relaxation models (first of all, the model corresponding to constant relaxation rates of coherences in quantum transitions). Examples illustrating the correctness of the results obtained within the framework of the proposed methods in contrast to inaccuracy of the results of the standard calculation techniques are given.

Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

Multireference configuration interaction theory using cumulant reconstruction with internal contraction of density matrix renormalization group wave function.

PubMed

Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi

2013-07-28

We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE Office of Scientific and Technical Information (OSTI.GOV)

None, None

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE PAGES

None, None

2016-11-21

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Density matrix modeling of quantum cascade lasers without an artificially localized basis: A generalized scattering approach

NASA Astrophysics Data System (ADS)

Pan, Andrew; Burnett, Benjamin A.; Chui, Chi On; Williams, Benjamin S.

2017-08-01

We derive a density matrix (DM) theory for quantum cascade lasers (QCLs) that describes the influence of scattering on coherences through a generalized scattering superoperator. The theory enables quantitative modeling of QCLs, including localization and tunneling effects, using the well-defined energy eigenstates rather than the ad hoc localized basis states required by most previous DM models. Our microscopic approach to scattering also eliminates the need for phenomenological transition or dephasing rates. We discuss the physical interpretation and numerical implementation of the theory, presenting sets of both energy-resolved and thermally averaged equations, which can be used for detailed or compact device modeling. We illustrate the theory's applications by simulating a high performance resonant-phonon terahertz (THz) QCL design, which cannot be easily or accurately modeled using conventional DM methods. We show that the theory's inclusion of coherences is crucial for describing localization and tunneling effects consistent with experiment.

Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach

NASA Astrophysics Data System (ADS)

Borrelli, Raffaele; Gelin, Maxim F.

2016-12-01

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.

Reduced-Density-Matrix Description of Decoherence and Relaxation Processes for Electron-Spin Systems

NASA Astrophysics Data System (ADS)

Jacobs, Verne

2017-04-01

Electron-spin systems are investigated using a reduced-density-matrix description. Applications of interest include trapped atomic systems in optical lattices, semiconductor quantum dots, and vacancy defect centers in solids. Complimentary time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are self-consistently developed. The general non-perturbative and non-Markovian formulations provide a fundamental framework for systematic evaluations of corrections to the standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations. Particular attention is given to decoherence and relaxation processes, as well as spectral-line broadening phenomena, that are induced by interactions with photons, phonons, nuclear spins, and external electric and magnetic fields. These processes are treated either as coherent interactions or as environmental interactions. The environmental interactions are incorporated by means of the general expressions derived for the time-domain and frequency-domain Liouville-space self-energy operators, for which the tetradic-matrix elements are explicitly evaluated in the diagonal-resolvent, lowest-order, and Markov (short-memory time) approximations. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

NASA Astrophysics Data System (ADS)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

A general parallel sparse-blocked matrix multiply for linear scaling SCF theory

NASA Astrophysics Data System (ADS)

Challacombe, Matt

2000-06-01

A general approach to the parallel sparse-blocked matrix-matrix multiply is developed in the context of linear scaling self-consistent-field (SCF) theory. The data-parallel message passing method uses non-blocking communication to overlap computation and communication. The space filling curve heuristic is used to achieve data locality for sparse matrix elements that decay with “separation”. Load balance is achieved by solving the bin packing problem for blocks with variable size.With this new method as the kernel, parallel performance of the simplified density matrix minimization (SDMM) for solution of the SCF equations is investigated for RHF/6-31G ∗∗ water clusters and RHF/3-21G estane globules. Sustained rates above 5.7 GFLOPS for the SDMM have been achieved for (H 2 O) 200 with 95 Origin 2000 processors. Scalability is found to be limited by load imbalance, which increases with decreasing granularity, due primarily to the inhomogeneous distribution of variable block sizes.

Lindblad and Bloch equations for conversion of a neutron into an antineutron

NASA Astrophysics Data System (ADS)

Kerbikov, B. O.

2018-07-01

We propose a new approach based on the Lindblad and Bloch equations for the density matrix to the problem of a neutron into an antineutron conversion. We consider three strategies to search for conversion: experiments with trapped neutrons, oscillations in nuclei, and quasi-free propagation. We draw a distinction between n n bar oscillations in which the probability that a neutron transforms into an antineutron depends on time according to the sine-square law and the non-oscillatory overdamped n n bar conversion. We show that in all three cases decoherence due to the interaction with the environment leads to non-oscillatory evolution.

Development of a size reduction equation for woody biomass: The influence of branch wood properties on Rittinger's constant

DOE PAGES

Naimi, Ladan J.; Sokhansanj, Shahabaddine; Bi, Xiaotao; ...

2015-11-25

Size reduction is an essential but energy-intensive process for preparing biomass for conversion processes. Three well-known scaling equations (Bond, Kick, and Rittinger) are used to estimate energy input for grinding minerals and food particles. Previous studies have shown that the Rittinger equation has the best fit to predict energy input for grinding cellulosic biomass. In the Rittinger equation, Rittinger's constant (k R) is independent of the size of ground particles, yet we noted large variations in k R among similar particle size ranges. In this research, the dependence of k R on the physical structure and chemical composition of amore » number of woody materials was explored. Branches from two softwood species (Douglas fir and pine) and two hardwood species (aspen and poplar) were ground in a laboratory knife mill. The recorded data included power input, mass flow rate, and particle size before and after grinding. Nine material properties were determined: particle density, solid density (pycnometer and x-ray diffraction methods), microfibril angle, fiber coarseness, fiber length, and composition (lignin and cellulose glucan contents). The correlation matrix among the nine properties revealed high degrees of interdependence between properties. The k R value had the largest positive correlation (+0.60) with particle porosity across the species tested. As a result, particle density was strongly correlated with lignin content (0.85), microfibril angle (0.71), fiber length (0.87), and fiber coarseness (0.78). An empirical model relating k R to particle density was developed.« less

Development of a size reduction equation for woody biomass: The influence of branch wood properties on Rittinger's constant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naimi, Ladan J.; Sokhansanj, Shahabaddine; Bi, Xiaotao

Size reduction is an essential but energy-intensive process for preparing biomass for conversion processes. Three well-known scaling equations (Bond, Kick, and Rittinger) are used to estimate energy input for grinding minerals and food particles. Previous studies have shown that the Rittinger equation has the best fit to predict energy input for grinding cellulosic biomass. In the Rittinger equation, Rittinger's constant (k R) is independent of the size of ground particles, yet we noted large variations in k R among similar particle size ranges. In this research, the dependence of k R on the physical structure and chemical composition of amore » number of woody materials was explored. Branches from two softwood species (Douglas fir and pine) and two hardwood species (aspen and poplar) were ground in a laboratory knife mill. The recorded data included power input, mass flow rate, and particle size before and after grinding. Nine material properties were determined: particle density, solid density (pycnometer and x-ray diffraction methods), microfibril angle, fiber coarseness, fiber length, and composition (lignin and cellulose glucan contents). The correlation matrix among the nine properties revealed high degrees of interdependence between properties. The k R value had the largest positive correlation (+0.60) with particle porosity across the species tested. As a result, particle density was strongly correlated with lignin content (0.85), microfibril angle (0.71), fiber length (0.87), and fiber coarseness (0.78). An empirical model relating k R to particle density was developed.« less

Fragmentation and matrix contrast favor understory plants through negative cascading effects on a strong competitor palm.

PubMed

Hernández-Ruedas, Manuel A; Arroyo-Rodríguez, Víctor; Morante-Filho, José Carlos; Meave, Jorge A; Martínez-Ramos, Miguel

2018-05-04

Understanding the patterns and processes driving biodiversity maintenance in fragmented tropical forests is urgently needed for conservation planning, especially in species-rich forest reserves. Of particular concern are the effects that habitat modifications at the landscape scale may have on forest regeneration and ecosystem functioning: a topic that has received limited attention. Here, we assessed the effects of landscape structure (i.e., forest cover, open area matrices, forest fragmentation, and mean inter-patch isolation distance) on understory plant assemblages in the Los Tuxtlas Biosphere Reserve, Mexico. Previous studies suggest that the demographic burst of the strong competitor palm Astrocaryum mexicanum in the core area of this reserve limits plant recruitment and imperils biodiversity conservation within this protected area. Yet, the local and landscape predictors of this palm, and its impact on tree recruitment at a regional scale are unknown. Thus, we used structural equation modeling to assess the direct and cascading effects of landscape structure on stem and species density in the understory of 20 forest sites distributed across this biodiversity hotspot. Indirect paths included the effect of landscape structure on tree basal area (a proxy of local disturbance), and the effects of these variables on A. mexicanum. Density of A. mexicanum mainly increased with decreasing both fragmentation and open areas in the matrix (matrix contrast, hereafter), and such an increase in palm density negatively affected stem and species density in the understory. The negative direct effect of matrix contrast on stem density was overridden by the indirect positive effects (i.e., through negative cascading effects on A. mexicanum), resulting in a weak effect of matrix contrast on stem density. These findings suggest that dispersal limitation and negative edge effects in more fragmented landscapes dominated by open areas prevent the proliferation of this palm species, enhancing the diversity and abundance of understory trees. This "positive" news adds to an increasing line of evidence suggesting that fragmentation may have some positive effects on biodiversity, in this case by preventing the proliferation of species that can jeopardize biodiversity conservation within tropical reserves. © 2018 by the Ecological Society of America.

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

PubMed Central

Putz, Mihai V.

2009-01-01

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. PMID:20087467

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

PubMed

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.

Quantum-mechanical transport equation for atomic systems.

NASA Technical Reports Server (NTRS)

Berman, P. R.

1972-01-01

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Collective modes of a two-dimensional Fermi gas at finite temperature

NASA Astrophysics Data System (ADS)

Mulkerin, Brendan C.; Liu, Xia-Ji; Hu, Hui

2018-05-01

We examine the breathing mode of a strongly interacting two-dimensional Fermi gas and the role of temperature on the anomalous breaking of scale invariance. By calculating the equation of state with different many-body T -matrix theories and the virial expansion, we obtain a hydrodynamic equation of the harmonically trapped Fermi gas (with trapping frequency ω0) through the local density approximation. By solving the hydrodynamic equations, we determine the breathing mode frequencies as a function of interaction strength and temperature. We find that the breathing mode anomaly depends sensitively on both interaction strength and temperature. In particular, in the strongly interacting regime, we predict a significant downshift of the breathing mode frequency, below the scale invariant value of 2 ω0 , for temperatures of the order of the Fermi temperature.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Algebraic reconstruction for 3D magnetic resonance-electrical impedance tomography (MREIT) using one component of magnetic flux density.

PubMed

Ider, Y Ziya; Onart, Serkan

2004-02-01

Magnetic resonance-electrical impedance tomography (MREIT) algorithms fall into two categories: those utilizing internal current density and those utilizing only one component of measured magnetic flux density. The latter group of algorithms have the advantage that the object does not have to be rotated in the magnetic resonance imaging (MRI) system. A new algorithm which uses only one component of measured magnetic flux density is developed. In this method, the imaging problem is formulated as the solution of a non-linear matrix equation which is solved iteratively to reconstruct resistivity. Numerical simulations are performed to test the algorithm both for noise-free and noisy cases. The uniqueness of the solution is monitored by looking at the singular value behavior of the matrix and it is shown that at least two current injection profiles are necessary. The method is also modified to handle region-of-interest reconstructions. In particular it is shown that, if the image of a certain xy-slice is sought for, then it suffices to measure the z-component of magnetic flux density up to a distance above and below that slice. The method is robust and has good convergence behavior for the simulation phantoms used.

The open quantum Brownian motions

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2014-09-01

Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H_z : orbital (walker) Hilbert space, {C}^{{Z}} in the discrete, L^2({R}) in the continuum H_c : internal spin (or gyroscope) Hilbert space H_sys=H_z\\otimesH_c : system Hilbert space H_p : probe (or quantum coin) Hilbert space, H_p={C}^2 \\rho^tot_t : density matrix for the total system (walker + internal spin + quantum coins) \\bar \\rho_t : reduced density matrix on H_sys : \\bar\\rho_t=\\int dxdy\\, \\bar\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | \\hat \\rho_t : system density matrix in a quantum trajectory: \\hat\\rho_t=\\int dxdy\\, \\hat\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | . If diagonal and localized in position: \\hat \\rho_t=\\rho_t\\otimes| X_t \\rangle _z\\langle X_t | ρt: internal density matrix in a simple quantum trajectory Xt: walker position in a simple quantum trajectory Bt: normalized Brownian motion ξt, \\xi_t^\\dagger : quantum noises

A finite element code for modelling tracer transport in a non-isothermal two-phase flow system for CO2 geological storage characterization

NASA Astrophysics Data System (ADS)

Tong, F.; Niemi, A. P.; Yang, Z.; Fagerlund, F.; Licha, T.; Sauter, M.

2011-12-01

This paper presents a new finite element method (FEM) code for modeling tracer transport in a non-isothermal two-phase flow system. The main intended application is simulation of the movement of so-called novel tracers for the purpose of characterization of geologically stored CO2 and its phase partitioning and migration in deep saline formations. The governing equations are based on the conservation of mass and energy. Among the phenomena accounted for are liquid-phase flow, gas flow, heat transport and the movement of the novel tracers. The movement of tracers includes diffusion and the advection associated with the gas and liquid flow. The temperature, gas pressure, suction, concentration of tracer in liquid phase and concentration of tracer in gas phase are chosen as the five primary variables. Parameters such as the density, viscosity, thermal expansion coefficient are expressed in terms of the primary variables. The governing equations are discretized in space using the Galerkin finite element formulation, and are discretized in time by one-dimensional finite difference scheme. This leads to an ill-conditioned FEM equation that has many small entries along the diagonal of the non-symmetric coefficient matrix. In order to deal with the problem of non-symmetric ill-conditioned matrix equation, special techniques are introduced . Firstly, only nonzero elements of the matrix need to be stored. Secondly, it is avoided to directly solve the whole large matrix. Thirdly, a strategy has been used to keep the diversity of solution methods in the calculation process. Additionally, an efficient adaptive mesh technique is included in the code in order to track the wetting front. The code has been validated against several classical analytical solutions, and will be applied for simulating the CO2 injection experiment to be carried out at the Heletz site, Israel, as part of the EU FP7 project MUSTANG.

Thermal and active fluctuations of a compressible bilayer vesicle

NASA Astrophysics Data System (ADS)

Sachin Krishnan, T. V.; Yasuda, Kento; Okamoto, Ryuichi; Komura, Shigeyuki

2018-05-01

We discuss thermal and active fluctuations of a compressible bilayer vesicle by using the results of hydrodynamic theory for vesicles. Coupled Langevin equations for the membrane deformation and the density fields are employed to calculate the power spectral density matrix of membrane fluctuations. Thermal contribution is obtained by means of the fluctuation dissipation theorem, whereas active contribution is calculated from exponentially decaying time correlation functions of active random forces. We obtain the total power spectral density as a sum of thermal and active contributions. An apparent response function is further calculated in order to compare with the recent microrheology experiment on red blood cells. An enhanced response is predicted in the low-frequency regime for non-thermal active fluctuations.

Stability and Physical Accuracy Analysis of the Numerical Solutions to Wigner-Poisson Modeling of Resonant Tunneling Diodes

DTIC Science & Technology

2013-03-22

discrete Wigner function is periodic in momentum space. The periodicity follows from the Fourier transform of the density matrix. The inverse...resonant-tunneling diode . The Green function method has been one of alternatives. Another alternative was to utilize the Wigner function . The Wigner ... function approach to the simulation of a resonant-tunneling diode offers many advantages. In the limit of the classical physics the Wigner equation

Accelerating molecular property calculations with nonorthonormal Krylov space methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Furche, Filipp; Krull, Brandon T.; Nguyen, Brian D.

Here, we formulate Krylov space methods for large eigenvalue problems and linear equation systems that take advantage of decreasing residual norms to reduce the cost of matrix-vector multiplication. The residuals are used as subspace basis without prior orthonormalization, which leads to generalized eigenvalue problems or linear equation systems on the Krylov space. These nonorthonormal Krylov space (nKs) algorithms are favorable for large matrices with irregular sparsity patterns whose elements are computed on the fly, because fewer operations are necessary as the residual norm decreases as compared to the conventional method, while errors in the desired eigenpairs and solution vectors remainmore » small. We consider real symmetric and symplectic eigenvalue problems as well as linear equation systems and Sylvester equations as they appear in configuration interaction and response theory. The nKs method can be implemented in existing electronic structure codes with minor modifications and yields speed-ups of 1.2-1.8 in typical time-dependent Hartree-Fock and density functional applications without accuracy loss. The algorithm can compute entire linear subspaces simultaneously which benefits electronic spectra and force constant calculations requiring many eigenpairs or solution vectors. The nKs approach is related to difference density methods in electronic ground state calculations, and particularly efficient for integral direct computations of exchange-type contractions. By combination with resolution-of-the-identity methods for Coulomb contractions, three- to fivefold speed-ups of hybrid time-dependent density functional excited state and response calculations are achieved.« less

Accelerating molecular property calculations with nonorthonormal Krylov space methods

DOE PAGES

Furche, Filipp; Krull, Brandon T.; Nguyen, Brian D.; ...

2016-05-03

Here, we formulate Krylov space methods for large eigenvalue problems and linear equation systems that take advantage of decreasing residual norms to reduce the cost of matrix-vector multiplication. The residuals are used as subspace basis without prior orthonormalization, which leads to generalized eigenvalue problems or linear equation systems on the Krylov space. These nonorthonormal Krylov space (nKs) algorithms are favorable for large matrices with irregular sparsity patterns whose elements are computed on the fly, because fewer operations are necessary as the residual norm decreases as compared to the conventional method, while errors in the desired eigenpairs and solution vectors remainmore » small. We consider real symmetric and symplectic eigenvalue problems as well as linear equation systems and Sylvester equations as they appear in configuration interaction and response theory. The nKs method can be implemented in existing electronic structure codes with minor modifications and yields speed-ups of 1.2-1.8 in typical time-dependent Hartree-Fock and density functional applications without accuracy loss. The algorithm can compute entire linear subspaces simultaneously which benefits electronic spectra and force constant calculations requiring many eigenpairs or solution vectors. The nKs approach is related to difference density methods in electronic ground state calculations, and particularly efficient for integral direct computations of exchange-type contractions. By combination with resolution-of-the-identity methods for Coulomb contractions, three- to fivefold speed-ups of hybrid time-dependent density functional excited state and response calculations are achieved.« less

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

DOE PAGES

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris; ...

2018-04-23

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Molecular dynamics modeling of helium bubbles in austenitic steels

NASA Astrophysics Data System (ADS)

Jelea, A.

2018-06-01

The austenitic steel devices from pressurized water reactors are continuously subjected to neutron irradiation that produces crystalline point defects and helium atoms in the steel matrix. These species evolve into large defects such as dislocation loops and helium filled bubbles. This paper analyzes, through molecular dynamics simulations with recently developed interatomic potentials, the impact of the helium/steel interface on the helium behavior in nanosize bubbles trapped in an austenitic steel matrix. It is shown that the repulsive helium-steel interactions induce higher pressures in the bubble compared to bulk helium at the same temperature and average density. A new equation of state for helium is proposed in order to take into account these interface effects.

Solution of matrix equations using sparse techniques

NASA Technical Reports Server (NTRS)

Baddourah, Majdi

1994-01-01

The solution of large systems of matrix equations is key to the solution of a large number of scientific and engineering problems. This talk describes the sparse matrix solver developed at Langley which can routinely solve in excess of 263,000 equations in 40 seconds on one Cray C-90 processor. It appears that for large scale structural analysis applications, sparse matrix methods have a significant performance advantage over other methods.

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

NASA Astrophysics Data System (ADS)

Badia, Santiago; Martín, Alberto F.; Planas, Ramon

2014-10-01

The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.

Universal shocks in the Wishart random-matrix ensemble.

PubMed

Blaizot, Jean-Paul; Nowak, Maciej A; Warchoł, Piotr

2013-05-01

We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of N, the size of the matrix. In the large N limit, this equation generalizes the simple inviscid Burgers equation that has been obtained earlier for Hermitian or unitary matrices. The solution, through the method of characteristics, presents singularities that we relate to the precursors of shock formation in the Burgers equation. The finite N effects appear as a viscosity term in the Burgers equation. Using a scaling analysis of the complete equation for the characteristic polynomial, in the vicinity of the shocks, we recover in a simple way the universal Bessel oscillations (so-called hard-edge singularities) familiar in random-matrix theory.

Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2012-09-01

It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are "locked" inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.

Instability of the cored barotropic disc: the linear eigenvalue formulation

NASA Astrophysics Data System (ADS)

Polyachenko, E. V.

2018-05-01

Gaseous rotating razor-thin discs are a testing ground for theories of spiral structure that try to explain appearance and diversity of disc galaxy patterns. These patterns are believed to arise spontaneously under the action of gravitational instability, but calculations of its characteristics in the gas are mostly obscured. The paper suggests a new method for finding the spiral patterns based on an expansion of small amplitude perturbations over Lagrange polynomials in small radial elements. The final matrix equation is extracted from the original hydrodynamical equations without the use of an approximate theory and has a form of the linear algebraic eigenvalue problem. The method is applied to a galactic model with the cored exponential density profile.

NMR lineshape equations for hindered methyl group: a comparison of the semi-classical and quantum mechanical models

NASA Astrophysics Data System (ADS)

Bernatowicz, P.; Szymański, S.

2003-09-01

The semiclassical and quantum mechanical NMR lineshape equations for a hindered methyl group are compared. In both the approaches, the stochastic dynamics can be interpreted in terms of a progressive symmetrization of the spin density matrix. However, the respective ways of achieving the same limiting symmetry can be remarkably different. From numerical lineshape simulations it is inferred that in the regime of intermediate exchange, where the conventional theory predicts occurrence of a single Lorentzian, the actual spectrum can have nontrivial features. This observation may open new perspectives in the search for nonclassical effects in the stochastic behavior of methyl groups in liquid-phase NMR.

Real-time optical laboratory solution of parabolic differential equations

NASA Technical Reports Server (NTRS)

Casasent, David; Jackson, James

1988-01-01

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Linear absorptive dielectrics

NASA Astrophysics Data System (ADS)

Tip, A.

1998-06-01

Starting from Maxwell's equations for a linear, nonconducting, absorptive, and dispersive medium, characterized by the constitutive equations D(x,t)=ɛ1(x)E(x,t)+∫t-∞dsχ(x,t-s)E(x,s) and H(x,t)=B(x,t), a unitary time evolution and canonical formalism is obtained. Given the complex, coordinate, and frequency-dependent, electric permeability ɛ(x,ω), no further assumptions are made. The procedure leads to a proper definition of band gaps in the periodic case and a new continuity equation for energy flow. An S-matrix formalism for scattering from lossy objects is presented in full detail. A quantized version of the formalism is derived and applied to the generation of Čerenkov and transition radiation as well as atomic decay. The last case suggests a useful generalization of the density of states to the absorptive situation.

Time-delayed behaviors of transient four-wave mixing signal intensity in inverted semiconductor with carrier-injection pumping

NASA Astrophysics Data System (ADS)

Hu, Zhenhua; Gao, Shen; Xiang, Bowen

2016-01-01

An analytical expression of transient four-wave mixing (TFWM) in inverted semiconductor with carrier-injection pumping was derived from both the density matrix equation and the complex stochastic stationary statistical method of incoherent light. Numerical analysis showed that the TFWM decayed decay is towards the limit of extreme homogeneous and inhomogeneous broadenings in atoms and the decaying time is inversely proportional to half the power of the net carrier densities for a low carrier-density injection and other high carrier-density injection, while it obeys an usual exponential decay with other decaying time that is inversely proportional to half the power of the net carrier density or it obeys an unusual exponential decay with the decaying time that is inversely proportional to a third power of the net carrier density for a moderate carrier-density injection. The results can be applied to studying ultrafast carrier dephasing in the inverted semiconductors such as semiconductor laser amplifier and semiconductor optical amplifier.

Decoherence in quantum lossy systems: superoperator and matrix techniques

NASA Astrophysics Data System (ADS)

Yazdanpanah, Navid; Tavassoly, Mohammad Kazem; Moya-Cessa, Hector Manuel

2017-06-01

Due to the unavoidably dissipative interaction between quantum systems with their environments, the decoherence flows inevitably into the systems. Therefore, to achieve a better understanding on how decoherence affects on the damped systems, a fundamental investigation of master equation seems to be required. In this regard, finding out the missed information which has been lost due to irreversibly of the dissipative systems, is also of practical importance in quantum information science. Motivating by these facts, in this work we want to use superoperator and matrix techniques, by which we are able to illustrate two methods to obtain the explicit form of density operators corresponding to damped systems at arbitrary temperature T ≥ 0. To establish the potential abilities of the suggested methods, we apply them to deduce the density operator of some practical well-known quantum systems. Using the superoperator techniques, at first we obtain the density operator of a damped system which includes a qubit interacting with a single-mode quantized field within an optical cavity. As the second system, we study the decoherence of a quantized field within an optical damped cavity. We also use our proposed matrix method to study the decoherence of a system which includes two qubits in the interaction with each other via dipole-dipole interaction and at the same time with a quantized field in a lossy cavity. The influences of dissipation on the decoherence of dynamical properties of these systems are also numerically investigated. At last, the advantages of the proposed superoperator techniques in comparison with matrix method are explained.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blanchet, Steve; Bari, Pasquale Di; Jones, David A.

Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate thatmore » is halved compared to that one acting on the total asymmetry. In the N{sub 1}-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.« less

The supersymmetric method in random matrix theory and applications to QCD

NASA Astrophysics Data System (ADS)

Verbaarschot, Jacobus

2004-12-01

The supersymmetric method is a powerful method for the nonperturbative evaluation of quenched averages in disordered systems. Among others, this method has been applied to the statistical theory of S-matrix fluctuations, the theory of universal conductance fluctuations and the microscopic spectral density of the QCD Dirac operator. We start this series of lectures with a general review of Random Matrix Theory and the statistical theory of spectra. An elementary introduction of the supersymmetric method in Random Matrix Theory is given in the second and third lecture. We will show that a Random Matrix Theory can be rewritten as an integral over a supermanifold. This integral will be worked out in detail for the Gaussian Unitary Ensemble that describes level correlations in systems with broken time-reversal invariance. We especially emphasize the role of symmetries. As a second example of the application of the supersymmetric method we discuss the calculation of the microscopic spectral density of the QCD Dirac operator. This is the eigenvalue density near zero on the scale of the average level spacing which is known to be given by chiral Random Matrix Theory. Also in this case we use symmetry considerations to rewrite the generating function for the resolvent as an integral over a supermanifold. The main topic of the second last lecture is the recent developments on the relation between the supersymmetric partition function and integrable hierarchies (in our case the Toda lattice hierarchy). We will show that this relation is an efficient way to calculate superintegrals. Several examples that were given in previous lectures will be worked out by means of this new method. Finally, we will discuss the quenched QCD Dirac spectrum at nonzero chemical potential. Because of the nonhermiticity of the Dirac operator the usual supersymmetric method has not been successful in this case. However, we will show that the supersymmetric partition function can be evaluated by means of the replica limit of the Toda lattice equation.

Ultrafast energy transfer with competing channels: Non-equilibrium Förster and Modified Redfield theories

NASA Astrophysics Data System (ADS)

Seibt, Joachim; Mančal, Tomáš

2017-05-01

We derive equations of motion for the reduced density matrix of a molecular system which undergoes energy transfer dynamics competing with fast internal conversion channels. Environmental degrees of freedom of such a system have no time to relax to quasi-equilibrium in the electronic excited state of the donor molecule, and thus the conditions of validity of Förster and Modified Redfield theories in their standard formulations do not apply. We derive non-equilibrium versions of the two well-known rate theories and apply them to the case of carotenoid-chlorophyll energy transfer. Although our reduced density matrix approach does not account for the formation of vibronic excitons, it still confirms the important role of the donor ground-state vibrational states in establishing the resonance energy transfer conditions. We show that it is essential to work with a theory valid in a strong system-bath interaction regime to obtain correct dependence of the rates on donor-acceptor energy gap.

A unique set of micromechanics equations for high temperature metal matrix composites

NASA Technical Reports Server (NTRS)

Hopkins, D. A.; Chamis, C. C.

1985-01-01

A unique set of micromechanic equations is presented for high temperature metal matrix composites. The set includes expressions to predict mechanical properties, thermal properties and constituent microstresses for the unidirectional fiber reinforced ply. The equations are derived based on a mechanics of materials formulation assuming a square array unit cell model of a single fiber, surrounding matrix and an interphase to account for the chemical reaction which commonly occurs between fiber and matrix. A three-dimensional finite element analysis was used to perform a preliminary validation of the equations. Excellent agreement between properties predicted using the micromechanics equations and properties simulated by the finite element analyses are demonstrated. Implementation of the micromechanics equations as part of an integrated computational capability for nonlinear structural analysis of high temperature multilayered fiber composites is illustrated.

Projected quasiparticle theory for molecular electronic structure

NASA Astrophysics Data System (ADS)

Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Samanta, Kousik; Ellis, Jason K.

2011-09-01

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.

Effects of the oceans on polar motion: Extended investigations

NASA Technical Reports Server (NTRS)

Dickman, Steven R.

1986-01-01

A method was found for expressing the tide current velocities in terms of the tide height (with all variables expanded in spherical harmonics). All time equations were then combined into a single, nondifferential matrix equation involving only the unknown tide height. The pole tide was constrained so that no tidewater flows across continental boundaries. The constraint was derived for the case of turbulent oceans; with the tide velocities expressed in terms of the tide height. The two matrix equations were combined. Simple matrix inversion then yielded the constrained solution. Programs to construct and invert the matrix equations were written. Preliminary results were obtained and are discussed.

Energy Finite Element Analysis for Computing the High Frequency Vibration of the Aluminum Testbed Cylinder and Correlating the Results to Test Data

NASA Technical Reports Server (NTRS)

Vlahopoulos, Nickolas

2005-01-01

The Energy Finite Element Analysis (EFEA) is a finite element based computational method for high frequency vibration and acoustic analysis. The EFEA solves with finite elements governing differential equations for energy variables. These equations are developed from wave equations. Recently, an EFEA method for computing high frequency vibration of structures either in vacuum or in contact with a dense fluid has been presented. The presence of fluid loading has been considered through added mass and radiation damping. The EFEA developments were validated by comparing EFEA results to solutions obtained by very dense conventional finite element models and solutions from classical techniques such as statistical energy analysis (SEA) and the modal decomposition method for bodies of revolution. EFEA results have also been compared favorably with test data for the vibration and the radiated noise generated by a large scale submersible vehicle. The primary variable in EFEA is defined as the time averaged over a period and space averaged over a wavelength energy density. A joint matrix computed from the power transmission coefficients is utilized for coupling the energy density variables across any discontinuities, such as change of plate thickness, plate/stiffener junctions etc. When considering the high frequency vibration of a periodically stiffened plate or cylinder, the flexural wavelength is smaller than the interval length between two periodic stiffeners, therefore the stiffener stiffness can not be smeared by computing an equivalent rigidity for the plate or cylinder. The periodic stiffeners must be regarded as coupling components between periodic units. In this paper, Periodic Structure (PS) theory is utilized for computing the coupling joint matrix and for accounting for the periodicity characteristics.

Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach

NASA Astrophysics Data System (ADS)

Fugger, Delia M.; Dorda, Antonius; Schwarz, Frauke; von Delft, Jan; Arrigoni, Enrico

2018-01-01

We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage ϕ and a magnetic field B. We investigate the interplay between the shift ({ω }B) of the Kondo peak in the spin-resolved density of states (DOS) and the one ({φ }B) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of B down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as {φ }B only for | g| {μ }BB\\gg {k}B{T}K. Our auxiliary master equation approach yields highly accurate nonequilibrium results for the DOS and for the conductance all the way from within the Kondo up to the charge fluctuation regime, showing excellent agreement with a recently introduced scheme based on a combination of numerical renormalization group with time-dependent density matrix renormalization group.

Strong diffusion formulation of Markov chain ensembles and its optimal weaker reductions

NASA Astrophysics Data System (ADS)

Güler, Marifi

2017-10-01

Two self-contained diffusion formulations, in the form of coupled stochastic differential equations, are developed for the temporal evolution of state densities over an ensemble of Markov chains evolving independently under a common transition rate matrix. Our first formulation derives from Kurtz's strong approximation theorem of density-dependent Markov jump processes [Stoch. Process. Their Appl. 6, 223 (1978), 10.1016/0304-4149(78)90020-0] and, therefore, strongly converges with an error bound of the order of lnN /N for ensemble size N . The second formulation eliminates some fluctuation variables, and correspondingly some noise terms, within the governing equations of the strong formulation, with the objective of achieving a simpler analytic formulation and a faster computation algorithm when the transition rates are constant or slowly varying. There, the reduction of the structural complexity is optimal in the sense that the elimination of any given set of variables takes place with the lowest attainable increase in the error bound. The resultant formulations are supported by numerical simulations.

Quantum trajectories for time-dependent adiabatic master equations

NASA Astrophysics Data System (ADS)

Yip, Ka Wa; Albash, Tameem; Lidar, Daniel A.

2018-02-01

We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension N instead of a complex density matrix of dimension N2, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor N advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor N2 is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for 8-qubit quantum annealing examples. We also apply the quantum trajectories method to a 16-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.

The Existence of the Solution to One Kind of Algebraic Riccati Equation

NASA Astrophysics Data System (ADS)

Liu, Jianming

2018-03-01

The matrix equation ATX + XA + XRX + Q = O is called algebraic Riccati equation, which is very important in the fields of automatic control and other engineering applications. Many researchers have studied the solutions to various algebraic Riccati equations and most of them mainly applied the matrix methods, while few used the functional analysis theories. This paper mainly studies the existence of the solution to the following kind of algebraic Riccati equation from the functional view point: ATX + XA + XRX ‑λX + Q = O Here, X, A, R, Q ∈ n×n , Q is a symmetric matrix, and R is a positive or negative semi-definite matrix, λ is arbitrary constants. This paper uses functional approach such as fixed point theorem and contraction mapping thinking so as to provide two sufficient conditions for the solvability about this kind of Riccati equation and to arrive at some relevant conclusions.

Multipolar Ewald methods, 1: theory, accuracy, and performance.

PubMed

Giese, Timothy J; Panteva, Maria T; Chen, Haoyuan; York, Darrin M

2015-02-10

The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.

Analysis of band structure, transmission properties, and dispersion behavior of THz wave in one-dimensional parabolic plasma photonic crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Askari, Nasim; Eslami, Esmaeil, E-mail: eeslami@iust.ac.ir; Mirzaie, Reza

2015-11-15

The photonic band gap of obliquely incident terahertz electromagnetic waves in a one-dimensional plasma photonic crystal is studied. The periodic structure consists of lossless dielectric and inhomogeneous plasma with a parabolic density profile. The dispersion relation and the THz wave transmittance are analyzed based on the electromagnetic equations and transfer matrix method. The dependence of effective plasma frequency and photonic band gap characteristics on dielectric and plasma thickness, plasma density, and incident angle are discussed in detail. A theoretical calculation for effective plasma frequency is presented and compared with numerical results. Results of these two methods are in good agreement.

Ultrafast Saturation of Electronic-Resonance-Enhanced Coherent Anti-Stokes Raman Scattering and Comparison for Pulse Durations in the Nanosecond to Femtosecond Regime

DTIC Science & Technology

2016-02-05

electronic-resonance-enhanced CARS (ERE- CARS ) configuration is calculated. We demonstrate that while underdamping condition is a suffi- cient condition for...saturation of ERE- CARS with the long-pulse excitations, a transient-gain must be achieved to saturate ERE- CARS signal for ultrafast probe regime. We...ultrafast ERE- CARS . From a simplified analytical solution and a detailed numerical calculation based on density-matrix equations, the saturation threshold

Complex absorbing potential based Lorentzian fitting scheme and time dependent quantum transport.

PubMed

Xie, Hang; Kwok, Yanho; Jiang, Feng; Zheng, Xiao; Chen, GuanHua

2014-10-28

Based on the complex absorbing potential (CAP) method, a Lorentzian expansion scheme is developed to express the self-energy. The CAP-based Lorentzian expansion of self-energy is employed to solve efficiently the Liouville-von Neumann equation of one-electron density matrix. The resulting method is applicable for both tight-binding and first-principles models and is used to simulate the transient currents through graphene nanoribbons and a benzene molecule sandwiched between two carbon-atom chains.

Universality of quantum information in chaotic CFTs

NASA Astrophysics Data System (ADS)

Lashkari, Nima; Dymarsky, Anatoly; Liu, Hong

2018-03-01

We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.

The Physics of Polarization

NASA Astrophysics Data System (ADS)

Landi Degl'Innocenti, Egidio

2015-10-01

The introductory lecture that has been delivered at this Symposium is a condensed version of an extended course held by the author at the XII Canary Island Winter School from November 13 to November 21, 2000. The full series of lectures can be found in Landi Degl'Innocenti (2002). The original reference is organized in 20 Sections that are here itemized: 1. Introduction, 2. Description of polarized radiation, 3. Polarization and optical devices: Jones calculus and Muller matrices, 4. The Fresnel equations, 5. Dichroism and anomalous dispersion, 6. Polarization in everyday life, 7. Polarization due to radiating charges, 8. The linear antenna, 9. Thomson scattering, 10. Rayleigh scattering, 11. A digression on Mie scattering, 12. Bremsstrahlung radiation, 13. Cyclotron radiation, 14. Synchrotron radiation, 15. Polarization in spectral lines, 16. Density matrix and atomic polarization, 17. Radiative transfer and statistical equilibrium equations, 18. The amplification condition in polarized radiative transfer, and 19. Coupling radiative transfer and statistical equilibrium equations.

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

NASA Technical Reports Server (NTRS)

Burnett, K.; Cooper, J.

1980-01-01

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Entanglement classification in the noninteracting Fermi gas

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Eghbalifam, F.; Nami, S.; Yahyavi, M.

In this paper, entanglement classification shared among the spins of localized fermions in the noninteracting Fermi gas is studied. It is proven that the Fermi gas density matrix is block diagonal on the basis of the projection operators to the irreducible representations of symmetric group Sn. Every block of density matrix is in the form of the direct product of a matrix and identity matrix. Then it is useful to study entanglement in every block of density matrix separately. The basis of corresponding Hilbert space are identified from the Schur-Weyl duality theorem. Also, it can be shown that the symmetric part of the density matrix is fully separable. Then it has been shown that the entanglement measure which is introduced in Eltschka et al. [New J. Phys. 10, 043104 (2008)] and Guhne et al. [New J. Phys. 7, 229 (2005)], is zero for the even n qubit Fermi gas density matrix. Then by focusing on three spin reduced density matrix, the entanglement classes have been investigated. In three qubit states there is an entanglement measure which is called 3-tangle. It can be shown that 3-tangle is zero for three qubit density matrix, but the density matrix is not biseparable for all possible values of its parameters and its eigenvectors are in the form of W-states. Then an entanglement witness for detecting non-separable state and an entanglement witness for detecting nonbiseparable states, have been introduced for three qubit density matrix by using convex optimization problem. Finally, the four spin reduced density matrix has been investigated by restricting the density matrix to the irreducible representations of Sn. The restricted density matrix to the subspaces of the irreducible representations: Ssym, S3,1 and S2,2 are denoted by ρsym, ρ3,1 and ρ2,2, respectively. It has been shown that some highly entangled classes (by using the results of Miyake [Phys. Rev. A 67, 012108 (2003)] for entanglement classification) do not exist in the blocks of density matrix ρ3,1 and ρ2,2, so these classes do not exist in the total Fermi gas density matrix.

Corrigendum: New Form of Kane's Equations of Motion for Constrained Systems

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Bajodah, Abdulrahman H.; Hodges, Dewey H.; Chen, Ye-Hwa

2007-01-01

A correction to the previously published article "New Form of Kane's Equations of Motion for Constrained Systems" is presented. Misuse of the transformation matrix between time rates of change of the generalized coordinates and generalized speeds (sometimes called motion variables) resulted in a false conclusion concerning the symmetry of the generalized inertia matrix. The generalized inertia matrix (sometimes referred to as the mass matrix) is in fact symmetric and usually positive definite when one forms nonminimal Kane's equations for holonomic or simple nonholonomic systems, systems subject to nonlinear nonholonomic constraints, and holonomic or simple nonholonomic systems subject to impulsive constraints according to Refs. 1, 2, and 3, respectively. The mass matrix is of course symmetric when one forms minimal equations for holonomic or simple nonholonomic systems using Kane s method as set forth in Ref. 4.

Computationally efficient modeling and simulation of large scale systems

NASA Technical Reports Server (NTRS)

Jain, Jitesh (Inventor); Cauley, Stephen F. (Inventor); Li, Hong (Inventor); Koh, Cheng-Kok (Inventor); Balakrishnan, Venkataramanan (Inventor)

2010-01-01

A method of simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof. A matrix X and a matrix Y containing different combinations of passive circuit element values for the interconnect structure are obtained where the element values for each matrix include inductance L and inverse capacitance P. An adjacency matrix A associated with the interconnect structure is obtained. Numerical integration is used to solve first and second equations, each including as a factor the product of the inverse matrix X.sup.1 and at least one other matrix, with first equation including X.sup.1Y, X.sup.1A, and X.sup.1P, and the second equation including X.sup.1A and X.sup.1P.

A matrix equation solution by an optimization technique

NASA Technical Reports Server (NTRS)

Johnson, M. J.; Mittra, R.

1972-01-01

The computer solution of matrix equations is often difficult to accomplish due to an ill-conditioned matrix or high noise levels. Two methods of solution are compared for matrices of various degrees of ill-conditioning and for various noise levels in the right hand side vector. One method employs the usual Gaussian elimination. The other solves the equation by an optimization technique and employs a function minimization subroutine.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sechin, Ivan, E-mail: shnbuz@gmail.com, E-mail: zotov@mi.ras.ru; ITEP, B. Cheremushkinskaya Str. 25, Moscow 117218; Zotov, Andrei, E-mail: shnbuz@gmail.com, E-mail: zotov@mi.ras.ru

In this paper we propose versions of the associative Yang-Baxter equation and higher order R-matrix identities which can be applied to quantum dynamical R-matrices. As is known quantum non-dynamical R-matrices of Baxter-Belavin type satisfy this equation. Together with unitarity condition and skew-symmetry it provides the quantum Yang-Baxter equation and a set of identities useful for different applications in integrable systems. The dynamical R-matrices satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation between the dynamical and non-dynamical cases is described by the IRF (interaction-round-a-face)-Vertex transformation. An alternative approach to quantum (semi-)dynamical R-matrices and related quantum algebras was suggested by Arutyunov, Chekhov,more » and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The purpose of this paper is twofold. First, we prove that the ACF elliptic R-matrix satisfies the associative Yang-Baxter equation with shifted spectral parameters. Second, we directly prove a simple relation of the IRF-Vertex type between the Baxter-Belavin and the ACF elliptic R-matrices predicted previously by Avan and Rollet. It provides the higher order R-matrix identities and an explanation of the obtained equations through those for non-dynamical R-matrices. As a by-product we also get an interpretation of the intertwining transformation as matrix extension of scalar theta function likewise R-matrix is interpreted as matrix extension of the Kronecker function. Relations to the Gervais-Neveu-Felder equation and identities for the Felder’s elliptic R-matrix are also discussed.« less

Quantum Stochastic Trajectories: The Fokker-Planck-Bohm Equation Driven by the Reduced Density Matrix.

PubMed

Avanzini, Francesco; Moro, Giorgio J

2018-03-15

The quantum molecular trajectory is the deterministic trajectory, arising from the Bohm theory, that describes the instantaneous positions of the nuclei of molecules by assuring the agreement with the predictions of quantum mechanics. Therefore, it provides the suitable framework for representing the geometry and the motions of molecules without neglecting their quantum nature. However, the quantum molecular trajectory is extremely demanding from the computational point of view, and this strongly limits its applications. To overcome such a drawback, we derive a stochastic representation of the quantum molecular trajectory, through projection operator techniques, for the degrees of freedom of an open quantum system. The resulting Fokker-Planck operator is parametrically dependent upon the reduced density matrix of the open system. Because of the pilot role played by the reduced density matrix, this stochastic approach is able to represent accurately the main features of the open system motions both at equilibrium and out of equilibrium with the environment. To verify this procedure, the predictions of the stochastic and deterministic representation are compared for a model system of six interacting harmonic oscillators, where one oscillator is taken as the open quantum system of interest. The undeniable advantage of the stochastic approach is that of providing a simplified and self-contained representation of the dynamics of the open system coordinates. Furthermore, it can be employed to study the out of equilibrium dynamics and the relaxation of quantum molecular motions during photoinduced processes, like photoinduced conformational changes and proton transfers.

Quantum spectral curve for ( q, t)-matrix model

NASA Astrophysics Data System (ADS)

Zenkevich, Yegor

2018-02-01

We derive quantum spectral curve equation for ( q, t)-matrix model, which turns out to be a certain difference equation. We show that in Nekrasov-Shatashvili limit this equation reproduces the Baxter TQ equation for the quantum XXZ spin chain. This chain is spectral dual to the Seiberg-Witten integrable system associated with the AGT dual gauge theory.

Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

High Strain Rate Deformation Modeling of a Polymer Matrix Composite. Part 1; Matrix Constitutive Equations

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Stouffer, Donald C.

1998-01-01

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.

Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

NASA Astrophysics Data System (ADS)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

Effects of autoionising states on the single and double ionisation yields of neon with soft X-ray fields. JMO Series: Attosecond and Strong Field Science

NASA Astrophysics Data System (ADS)

Middleton, D. P. W.; Nikolopoulos, L. A. A.

2012-11-01

In this work, single and double ionisation yields of neon under extreme ultraviolet free-electron laser (FEL) radiation tuned in the vicinity of the autoionising states (AIS) of Ne+ were studied. Density matrix equations were developed and were used to calculate the dependence of the branching ratios of singly and doubly ionised neon on the field intensity and its duration. In addition, in response to a recent experiment [M. Martins et al., Phys. Rev. A 2011, 80, 023411], a quantitative analysis was undertaken in order to reproduce the magnitude of the branching ratios by varying the FEL photon frequency in the range 41.0-42.0 eV in accordance with the experimental report. While the reported variations of the species' branching ratios as a function of the FEL field's photon energy were found, their magnitude and shape differ. In general, the branching ratios are found to be heavily dependent on the given combination of the peak intensity and the pulse duration. Furthermore, the FEL's stochastic fluctuation has been modelled by solving the average density matrix equations and it was found that stochastic effects should also affect branching ratios, mainly due to the increase in the effective bandwidth of the pulse in comparison with the AIS's decay ionisation width. Our calculations suggest that field fluctuations generally diminish the resonance features of the branching ratios.

Reduced order feedback control equations for linear time and frequency domain analysis

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1981-01-01

An algorithm was developed which can be used to obtain the equations. In a more general context, the algorithm computes a real nonsingular similarity transformation matrix which reduces a real nonsymmetric matrix to block diagonal form, each block of which is a real quasi upper triangular matrix. The algorithm works with both defective and derogatory matrices and when and if it fails, the resultant output can be used as a guide for the reformulation of the mathematical equations that lead up to the ill conditioned matrix which could not be block diagonalized.

A new lumped-parameter approach to simulating flow processes in unsaturated dual-porosity media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zimmerman, R.W.; Hadgu, T.; Bodvarsson, G.S.

We have developed a new lumped-parameter dual-porosity approach to simulating unsaturated flow processes in fractured rocks. Fluid flow between the fracture network and the matrix blocks is described by a nonlinear equation that relates the imbibition rate to the local difference in liquid-phase pressure between the fractures and the matrix blocks. This equation is a generalization of the Warren-Root equation, but unlike the Warren-Root equation, is accurate in both the early and late time regimes. The fracture/matrix interflow equation has been incorporated into a computational module, compatible with the TOUGH simulator, to serve as a source/sink term for fracture elements.more » The new approach achieves accuracy comparable to simulations in which the matrix blocks are discretized, but typically requires an order of magnitude less computational time.« less

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

Numerical solutions for Helmholtz equations using Bernoulli polynomials

NASA Astrophysics Data System (ADS)

Bicer, Kubra Erdem; Yalcinbas, Salih

2017-07-01

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

Symmetry properties of the electron density and following from it limits on the KS-DFT applications

NASA Astrophysics Data System (ADS)

Kaplan, Ilya G.

2018-03-01

At present, the Density Functional Theory (DFT) approach elaborated by Kohn with co-authors more than 50 years ago became the most widely used method for study molecules and solids. Using modern computation facilities, it can be applied to systems with million atoms. In the atmosphere of such great popularity, it is particularly important to know the limits of the applicability of DFT methods. In this report, I will discuss two cases when the conventional DFT approaches, using only electron density ρ and its gradients, cannot be applied (I will not consider the Ψ-versions of DFT). The first case is quite evident. In the degenerated states, the electron density may not be defined, since electronic and nuclear motions cannot be separated, the vibronic interaction mixed them. The second case is related to the spin of the state. As it was rigorously proved by group theoretical methods at the theorem level, the electron density does not depend on the total spin S of the arbitrary N-electron state. It means that the Kohn-Sham equations have the same form for states with different S. The critical survey of elaborated DFT procedures, taking into account spin, shows that they modified only exchange functionals, the correlation functionals do not correspond to the spin of the state. The point is that the conception of spin cannot be defined in the framework of the electron density formalism, which corresponds to the one-particle reduced density matrix. This is the main reason of the problems arising in the study by DFT of magnetic properties of the transition metals. The possible way of resolving these problems can be found in the two-particle reduced density matrix formulation of DFT.

Application of symbolic/numeric matrix solution techniques to the NASTRAN program

NASA Technical Reports Server (NTRS)

Buturla, E. M.; Burroughs, S. H.

1977-01-01

The matrix solving algorithm of any finite element algorithm is extremely important since solution of the matrix equations requires a large amount of elapse time due to null calculations and excessive input/output operations. An alternate method of solving the matrix equations is presented. A symbolic processing step followed by numeric solution yields the solution very rapidly and is especially useful for nonlinear problems.

Dynamics and thermodynamics of linear quantum open systems.

PubMed

Martinez, Esteban A; Paz, Juan Pablo

2013-03-29

We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.

Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr

General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele,more » Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.« less

Ultrastable light sources in the crossover from superradiance to lasing

NASA Astrophysics Data System (ADS)

Xu, Minghui; Tieri, David; Holland, Murray

2013-05-01

We theoretically investigate the crossover from steady-state superradiance to optical lasing. An exact solution of the quantum master equation is difficult to obtain due to the exponential scaling of the Hilbert space dimension with system size. However, since Lindblad operators in the master equation are invariant under SU(4) transformations, we are able to reduce the exponential scaling of the problem to cubic by expanding the density matrix in terms of an SU(4) basis. In this way, we obtain exact quantum solutions of the superradiance-laser crossover. We use this theory to investigate the potential for ultrastable lasers in the millihertz linewidth regime, and find the behavior of important observables, such as intensity, linewidth, spin-correlation, and entanglement. This work was supported by the DARPA QUASAR program and NSF.

Three Interpretations of the Matrix Equation Ax = b

ERIC Educational Resources Information Center

Larson, Christine; Zandieh, Michelle

2013-01-01

Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Markley, F. Landis

1990-01-01

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

Baritzhack, Itzhack Y.; Markley, F. Landis

1988-01-01

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Dark channels in resonant tunneling transport through artificial atoms.

PubMed

Vaz, Eduardo; Kyriakidis, Jordan

2008-07-14

We investigate sequential tunneling through a multilevel quantum dot confining multiple electrons in the regime where several channels are available for transport within the bias window. By analyzing solutions to the master equations of the reduced density matrix, we give general conditions on when the presence of a second transport channel in the bias window quenches transport through the quantum dot. These conditions are in terms of distinct tunneling anisotropies which may aid in explaining the occurrence of negative differential conductance in quantum dots in the nonlinear regime.

Some conservative estimates in quantum cryptography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Molotkov, S. N.

2006-08-15

Relationship is established between the security of the BB84 quantum key distribution protocol and the forward and converse coding theorems for quantum communication channels. The upper bound Q{sub c} {approx} 11% on the bit error rate compatible with secure key distribution is determined by solving the transcendental equation H(Q{sub c})=C-bar({rho})/2, where {rho} is the density matrix of the input ensemble, C-bar({rho}) is the classical capacity of a noiseless quantum channel, and H(Q) is the capacity of a classical binary symmetric channel with error rate Q.

Algebraic methods for the solution of some linear matrix equations

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

Release from or through a wax matrix system. I. Basic release properties of the wax matrix system.

PubMed

Yonezawa, Y; Ishida, S; Sunada, H

2001-11-01

Release properties from a wax matrix tablet was examined. To obtain basic release properties, the wax matrix tablet was prepared from a physical mixture of drug and wax powder (hydrogenated caster oil) at a fixed mixing ratio. Properties of release from the single flat-faced surface or curved side surface of the wax matrix tablet were examined. The applicability of the square-root time law and of Higuchi equations was confirmed. The release rate constant obtained as g/min(1/2) changed with the release direction. However, the release rate constant obtained as g/cm2 x min(1/2) was almost the same. Hence it was suggested that the release property was almost the same and the wax matrix structure was uniform independent of release surface or direction at a fixed mixing ratio. However, these equations could not explain the entire release process. The applicability of a semilogarithmic equation was not as good compared with the square-root time law or Higuchi equation. However, it was revealed that the semilogarithmic equation was available to simulate the entire release process, even though the fit was somewhat poor. Hence it was suggested that the semilogarithmic equation was sufficient to describe the release process. The release rate constant was varied with release direction. However, these release rate constants were expressed by a function of the effective surface area and initial amount, independent of the release direction.

Modeling techniques for quantum cascade lasers

NASA Astrophysics Data System (ADS)

Jirauschek, Christian; Kubis, Tillmann

2014-03-01

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

Modeling techniques for quantum cascade lasers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jirauschek, Christian; Kubis, Tillmann

2014-03-15

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation ofmore » quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.« less

Dynamics of open quantum systems by interpolation of von Neumann and classical master equations, and its application to quantum annealing

NASA Astrophysics Data System (ADS)

Kadowaki, Tadashi

2018-02-01

We propose a method to interpolate dynamics of von Neumann and classical master equations with an arbitrary mixing parameter to investigate the thermal effects in quantum dynamics. The two dynamics are mixed by intervening to continuously modify their solutions, thus coupling them indirectly instead of directly introducing a coupling term. This maintains the quantum system in a pure state even after the introduction of thermal effects and obtains not only a density matrix but also a state vector representation. Further, we demonstrate that the dynamics of a two-level system can be rewritten as a set of standard differential equations, resulting in quantum dynamics that includes thermal relaxation. These equations are equivalent to the optical Bloch equations at the weak coupling and asymptotic limits, implying that the dynamics cause thermal effects naturally. Numerical simulations of ferromagnetic and frustrated systems support this idea. Finally, we use this method to study thermal effects in quantum annealing, revealing nontrivial performance improvements for a spin glass model over a certain range of annealing time. This result may enable us to optimize the annealing time of real annealing machines.

Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thingna, Juzar; Wang, Jian-Sheng; Haenggi, Peter

A novel scheme for the steady state solution of the standard Redfield quantum master equation is developed which yields agreement with the exact result for the corresponding reduced density matrix up to second order in the system-bath coupling strength. We achieve this objective by use of an analytic continuation of the off-diagonal matrix elements of the Redfield solution towards its diagonal limit. Notably, our scheme does not require the provision of yet higher order relaxation tensors. Testing this modified method for a heat bath consisting of a collection of harmonic oscillators we assess that the system relaxes towards its correctmore » coupling-dependent, generalized quantum Gibbs state in second order. We numerically compare our formulation for a damped quantum harmonic system with the nonequilibrium Green's function formalism: we find good agreement at low temperatures for coupling strengths that are even larger than expected from the very regime of validity of the second-order Redfield quantum master equation. Yet another advantage of our method is that it markedly reduces the numerical complexity of the problem; thus, allowing to study efficiently large-sized system Hilbert spaces.« less

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

NASA Technical Reports Server (NTRS)

Barth, T. J.; Steger, J. L.

1985-01-01

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

Response of a Rotating Propeller to Aerodynamic Excitation

NASA Technical Reports Server (NTRS)

Arnoldi, Walter E.

1949-01-01

The flexural vibration of a rotating propeller blade with clamped shank is analyzed with the object of presenting, in matrix form, equations for the elastic bending moments in forced vibration resulting from aerodynamic forces applied at a fixed multiple of rotational speed. Matrix equations are also derived which define the critical speeds end mode shapes for any excitation order and the relation between critical speed and blade angle. Reference is given to standard works on the numerical solution of matrix equations of the forms derived. The use of a segmented blade as an approximation to a continuous blade provides a simple means for obtaining the matrix solution from the integral equation of equilibrium, so that, in the numerical application of the method presented, the several matrix arrays of the basic physical characteristics of the propeller blade are of simple form, end their simplicity is preserved until, with the solution in sight, numerical manipulations well-known in matrix algebra yield the desired critical speeds and mode shapes frame which the vibration at any operating condition may be synthesized. A close correspondence between the familiar Stodola method and the matrix method is pointed out, indicating that any features of novelty are characteristic not of the analytical procedure but only of the abbreviation, condensation, and efficient organization of the numerical procedure made possible by the use of classical matrix theory.

A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Danabasoglu, G.; Biringen, S.

1989-01-01

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Werry, Jason L.; Gould, Mark D.; Isaac, Phillip S.

The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations which include the contravariant tensor representations and an additional class of essentially typical representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.

Isotropic matrix elements of the collision integral for the Boltzmann equation

NASA Astrophysics Data System (ADS)

Ender, I. A.; Bakaleinikov, L. A.; Flegontova, E. Yu.; Gerasimenko, A. B.

2017-09-01

We have proposed an algorithm for constructing matrix elements of the collision integral for the nonlinear Boltzmann equation isotropic in velocities. These matrix elements have been used to start the recurrent procedure for calculating matrix elements of the velocity-nonisotropic collision integral described in our previous publication. In addition, isotropic matrix elements are of independent interest for calculating isotropic relaxation in a number of physical kinetics problems. It has been shown that the coefficients of expansion of isotropic matrix elements in Ω integrals are connected by the recurrent relations that make it possible to construct the procedure of their sequential determination.

A computer program to generate equations of motion matrices, L217 (EOM). Volume 1: Engineering and usage

NASA Technical Reports Server (NTRS)

Kroll, R. I.; Clemmons, R. E.

1979-01-01

The equations of motion program L217 formulates the matrix coefficients for a set of second order linear differential equations that describe the motion of an airplane relative to its level equilibrium flight condition. Aerodynamic data from FLEXSTAB or Doublet Lattice (L216) programs can be used to derive the equations for quasi-steady or full unsteady aerodynamics. The data manipulation and the matrix coefficient formulation are described.

Estimated Satellite Cluster Elements in Near Circular Orbit

DTIC Science & Technology

1988-12-01

cluster is investigated. TheAon-board estimator is the U-D covariance factor’xzatiion’filter with dynamics based on the Clohessy - Wiltshire equations...Appropriate values for the velocity vector vi can be found irom the Clohessy - Wiltshire equations [9] (these equations will be explained in detail in the...explained in this text is the f matrix. The state transition matrix was developed from the Clohessy - Wiltshire equations of motion [9:page 3] as i - 2qý

Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bozkaya, Uğur, E-mail: ugur.bozkaya@hacettepe.edu.tr; Department of Chemistry, Atatürk University, Erzurum 25240; Sherrill, C. David

2016-05-07

An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the “gradient terms”: computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbitalmore » (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C{sub 10}H{sub 22}), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.« less

An information theory model for dissipation in open quantum systems

NASA Astrophysics Data System (ADS)

Rogers, David M.

2017-08-01

This work presents a general model for open quantum systems using an information game along the lines of Jaynes’ original work. It is shown how an energy based reweighting of propagators provides a novel moment generating function at each time point in the process. Derivatives of the generating function give moments of the time derivatives of observables. Aside from the mathematically helpful properties, the ansatz reproduces key physics of stochastic quantum processes. At high temperature, the average density matrix follows the Caldeira-Leggett equation. Its associated Langevin equation clearly demonstrates the emergence of dissipation and decoherence time scales, as well as an additional diffusion due to quantum confinement. A consistent interpretation of these results is that decoherence and wavefunction collapse during measurement are directly related to the degree of environmental noise, and thus occur because of subjective uncertainty of an observer.

Basic mechanisms in the laser control of non-Markovian dynamics

NASA Astrophysics Data System (ADS)

Puthumpally-Joseph, R.; Mangaud, E.; Chevet, V.; Desouter-Lecomte, M.; Sugny, D.; Atabek, O.

2018-03-01

Referring to a Fano-type model qualitative analogy we develop a comprehensive basic mechanism for the laser control of the non-Markovian bath response and fully implement it in a realistic control scheme, in strongly coupled open quantum systems. Converged hierarchical equations of motion are worked out to numerically solve the master equation of a spin-boson Hamiltonian to reach the reduced electronic density matrix of a heterojunction in the presence of strong terahertz laser pulses. Robust and efficient control is achieved increasing by a factor of 2 the non-Markovianity measured by the time evolution of the volume of accessible states. The consequences of such fields on the central system populations and coherence are examined, putting the emphasis on the relation between the increase of non-Markovianity and the slowing down of decoherence processes.

An efficient formulation and implementation of the analytic energy gradient method to the single and double excitation coupled-cluster wave function - Application to Cl2O2

NASA Technical Reports Server (NTRS)

Rendell, Alistair P.; Lee, Timothy J.

1991-01-01

The analytic energy gradient for the single and double excitation coupled-cluster (CCSD) wave function has been reformulated and implemented in a new set of programs. The reformulated set of gradient equations have a smaller computational cost than any previously published. The iterative solution of the linear equations and the construction of the effective density matrices are fully vectorized, being based on matrix multiplications. The new method has been used to investigate the Cl2O2 molecule, which has recently been postulated as an important intermediate in the destruction of ozone in the stratosphere. In addition to reporting computational timings, the CCSD equilibrium geometries, harmonic vibrational frequencies, infrared intensities, and relative energetics of three isomers of Cl2O2 are presented.

A new lumped-parameter model for flow in unsaturated dual-porosity media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zimmerman, Robert W.; Hadgu, Teklu; Bodvarsson, Gudmundur S.

A new lumped-parameter approach to simulating unsaturated flow processes in dual-porosity media such as fractured rocks or aggregated soils is presented. Fluid flow between the fracture network and the matrix blocks is described by a non-linear equation that relates the imbibition rate to the local difference in liquid-phase pressure between the fractures and the matrix blocks. Unlike a Warren-Root-type equation, this equation is accurate in both the early and late time regimes. The fracture/matrix interflow equation has been incorporated into an existing unsaturated flow simulator, to serve as a source/sink term for fracture gridblocks. Flow processes are then simulated usingmore » only fracture gridblocks in the computational grid. This new lumped-parameter approach has been tested on two problems involving transient flow in fractured/porous media, and compared with simulations performed using explicit discretization of the matrix blocks. The new procedure seems to accurately simulate flow processes in unsaturated fractured rocks, and typically requires an order of magnitude less computational time than do simulations using fully-discretized matrix blocks. [References: 37]« less

MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion

NASA Astrophysics Data System (ADS)

Zhang, Yunong; Chen, Ke; Ma, Weimu; Li, Xiao-Dong

This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.

Superfluidity, Bose-Einstein condensation, and structure in one-dimensional Luttinger liquids

NASA Astrophysics Data System (ADS)

Vranješ Markić, L.; Vrcan, H.; Zuhrianda, Z.; Glyde, H. R.

2018-01-01

We report diffusion Monte Carlo (DMC) and path integral Monte Carlo (PIMC) calculations of the properties of a one-dimensional (1D) Bose quantum fluid. The equation of state, the superfluid fraction ρS/ρ0 , the one-body density matrix n (x ) , the pair distribution function g (x ) , and the static structure factor S (q ) are evaluated. The aim is to test Luttinger liquid (LL) predictions for 1D fluids over a wide range of fluid density and LL parameter K . The 1D Bose fluid examined is a single chain of 4He atoms confined to a line in the center of a narrow nanopore. The atoms cannot exchange positions in the nanopore, the criterion for 1D. The fluid density is varied from the spinodal density where the 1D liquid is unstable to droplet formation to the density of bulk liquid 4He. In this range, K varies from K >2 at low density, where a robust superfluid is predicted, to K <0.5 , where fragile 1D superflow and solidlike peaks in S (q ) are predicted. For uniform pore walls, the ρS/ρ0 scales as predicted by LL theory. The n (x ) and g (x ) show long range oscillations and decay with x as predicted by LL theory. The amplitude of the oscillations is large at high density (small K ) and small at low density (large K ). The K values obtained from different properties agree well verifying the internal structure of LL theory. In the presence of disorder, the ρS/ρ0 does not scale as predicted by LL theory. A single vJ parameter in the LL theory that recovers LL scaling was not found. The one body density matrix (OBDM) in disorder is well predicted by LL theory. The "dynamical" superfluid fraction, ρSD/ρ0 , is determined. The physics of the deviation from LL theory in disorder and the "dynamical" ρSD/ρ0 are discussed.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Cluster-enriched Yang-Baxter equation from SUSY gauge theories

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-04-01

We propose a new generalization of the Yang-Baxter equation, where the R-matrix depends on cluster y-variables in addition to the spectral parameters. We point out that we can construct solutions to this new equation from the recently found correspondence between Yang-Baxter equations and supersymmetric gauge theories. The S^2 partition function of a certain 2d N=(2,2) quiver gauge theory gives an R-matrix, whereas its FI parameters can be identified with the cluster y-variables.

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1977-01-01

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

Direct Solve of Electrically Large Integral Equations for Problem Sizes to 1M Unknowns

NASA Technical Reports Server (NTRS)

Shaeffer, John

2008-01-01

Matrix methods for solving integral equations via direct solve LU factorization are presently limited to weeks to months of very expensive supercomputer time for problems sizes of several hundred thousand unknowns. This report presents matrix LU factor solutions for electromagnetic scattering problems for problem sizes to one million unknowns with thousands of right hand sides that run in mere days on PC level hardware. This EM solution is accomplished by utilizing the numerical low rank nature of spatially blocked unknowns using the Adaptive Cross Approximation for compressing the rank deficient blocks of the system Z matrix, the L and U factors, the right hand side forcing function and the final current solution. This compressed matrix solution is applied to a frequency domain EM solution of Maxwell's equations using standard Method of Moments approach. Compressed matrix storage and operations count leads to orders of magnitude reduction in memory and run time.

Theory of biaxial graded-index optical fiber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Kawalko, Stephen F.

1990-01-01

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kaon-nucleus scattering

NASA Technical Reports Server (NTRS)

Hong, Byungsik; Maung, Khin Maung; Wilson, John W.; Buck, Warren W.

1989-01-01

The derivations of the Lippmann-Schwinger equation and Watson multiple scattering are given. A simple optical potential is found to be the first term of that series. The number density distribution models of the nucleus, harmonic well, and Woods-Saxon are used without t-matrix taken from the scattering experiments. The parameterized two-body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to the imaginary part of the forward elastic scattering amplitude, are presented. The eikonal approximation was chosen as our solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.

Three-Flavoured Non-Resonant Leptogenesis at Intermediate Scales

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moffat, K.; Pascoli, S.; Petcov, S. T.

Leptogenesis can successfully explain the matter-antimatter asymmetry via out-of-equilibrium decays of heavy Majorana neutrinos in the early Universe. In this article we focus on non-resonant thermal leptogenesis and we study the possibility of lowering its scale through flavour effects in an exhaustive exploration of the model parameter space. We numerically solve the density matrix equations for one and two decaying heavy Majorana neutrinos and present the level of fine-tuning of the light neutrino masses within these scenarios. We demonstrate that the scale of thermal leptogenesis may be as low as $10^6$ GeV.

Enhanced Kerr nonlinearity in a quantized four-level graphene nanostructure

NASA Astrophysics Data System (ADS)

Ghahraman, Solookinejad; M, Panahi; E, Ahmadi; Seyyed, Hossein Asadpour

2016-07-01

In this paper, a new model is proposed for manipulating the Kerr nonlinearity of right-hand circular probe light in a monolayer of graphene nanostructure. By using the density matrix equations and quantum optical approach, the third-order susceptibility of probe light is explored numerically. It is realized that the enhanced Kerr nonlinearity with zero linear absorption can be provided by selecting the appropriate quantities of controllable parameters, such as Rabi frequency and elliptical parameter of elliptical polarized coupling field. Our results may be useful applications in future all-optical system devices in nanostructures.

Delay differential equations via the matrix Lambert W function and bifurcation analysis: application to machine tool chatter.

PubMed

Yi, Sun; Nelson, Patrick W; Ulsoy, A Galip

2007-04-01

In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert W function approach to solve systems of DDEs. The essential advantages of the matrix Lambert W approach are not only the similarity to the concept of the state transition matrix in lin ear ordinary differential equations, enabling its use for general classes of linear delay differential equations, but also the observation that we need only the principal branch among an infinite number of roots to determine the stability of a system of DDEs. The bifurcation method combined with Sturm sequences provides an algorithm for determining the stability of DDEs without restrictive geometric analysis. With this approach, one can obtain the critical values of delay, which determine the stability of a system and hence the preferred operating spindle speed without chatter. We apply both the matrix Lambert W function and the bifurcation analysis approach to the problem of chatter stability in turning, and compare the results obtained to existing methods. The two new approaches show excellent accuracy and certain other advantages, when compared to traditional graphical, computational and approximate methods.

N-representability-driven reconstruction of the two-electron reduced-density matrix for a real-time time-dependent electronic structure method

NASA Astrophysics Data System (ADS)

Jeffcoat, David B.; DePrince, A. Eugene

2014-12-01

Propagating the equations of motion (EOM) for the one-electron reduced-density matrix (1-RDM) requires knowledge of the corresponding two-electron RDM (2-RDM). We show that the indeterminacy of this expression can be removed through a constrained optimization that resembles the variational optimization of the ground-state 2-RDM subject to a set of known N-representability conditions. Electronic excitation energies can then be obtained by propagating the EOM for the 1-RDM and following the dipole moment after the system interacts with an oscillating external electric field. For simple systems with well-separated excited states whose symmetry differs from that of the ground state, excitation energies obtained from this method are comparable to those obtained from full configuration interaction computations. Although the optimized 2-RDM satisfies necessary N-representability conditions, the procedure cannot guarantee a unique mapping from the 1-RDM to the 2-RDM. This deficiency is evident in the mean-field-quality description of transitions to states of the same symmetry as the ground state, as well as in the inability of the method to describe Rabi oscillations.

Density matrix renormalization group simulations of SU(N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

NASA Astrophysics Data System (ADS)

Nataf, Pierre; Mila, Frédéric

2018-04-01

We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.

A propagator matrix method for the Rayleigh-Taylor instability of multiple layers: a case study on crustal delamination in the early Earth

NASA Astrophysics Data System (ADS)

Mondal, Puskar; Korenaga, Jun

2018-03-01

The dispersion relation of the Rayleigh-Taylor instability, a gravitational instability associated with unstable density stratification, is of profound importance in various geophysical contexts. When more than two layers are involved, a semi-analytical technique based on the biharmonic formulation of Stokes flow has been extensively used to obtain such dispersion relation. However, this technique may become cumbersome when applied to lithospheric dynamics, where a number of layers are necessary to represent the continuous variation of viscosity over many orders of magnitude. Here, we present an alternative and more efficient method based on the propagator matrix formulation of Stokes flow. With this approach, the original instability problem is reduced to a compact eigenvalue equation whose size is solely determined by the number of primary density contrasts. We apply this new technique to the stability of the early crust, and combined with the Monte Carlo sensitivity analysis, we derive an empirical formula to compute the growth rate of the Rayleigh-Taylor instability for this particular geophysical setting. Our analysis indicates that the likelihood of crustal delamination hinges critically on the effective viscosity of eclogite.

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure.

PubMed

Muhlestein, Michael B; Haberman, Michael R

2016-08-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure

PubMed Central

Haberman, Michael R.

2016-01-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed. PMID:27616932

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure

NASA Astrophysics Data System (ADS)

Muhlestein, Michael B.; Haberman, Michael R.

2016-08-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

Using Redundancy To Reduce Errors in Magnetometer Readings

NASA Technical Reports Server (NTRS)

Kulikov, Igor; Zak, Michail

2004-01-01

A method of reducing errors in noisy magnetic-field measurements involves exploitation of redundancy in the readings of multiple magnetometers in a cluster. By "redundancy"is meant that the readings are not entirely independent of each other because the relationships among the magnetic-field components that one seeks to measure are governed by the fundamental laws of electromagnetism as expressed by Maxwell's equations. Assuming that the magnetometers are located outside a magnetic material, that the magnetic field is steady or quasi-steady, and that there are no electric currents flowing in or near the magnetometers, the applicable Maxwell 's equations are delta x B = 0 and delta(raised dot) B = 0, where B is the magnetic-flux-density vector. By suitable algebraic manipulation, these equations can be shown to impose three independent constraints on the values of the components of B at the various magnetometer positions. In general, the problem of reducing the errors in noisy measurements is one of finding a set of corrected values that minimize an error function. In the present method, the error function is formulated as (1) the sum of squares of the differences between the corrected and noisy measurement values plus (2) a sum of three terms, each comprising the product of a Lagrange multiplier and one of the three constraints. The partial derivatives of the error function with respect to the corrected magnetic-field component values and the Lagrange multipliers are set equal to zero, leading to a set of equations that can be put into matrix.vector form. The matrix can be inverted to solve for a vector that comprises the corrected magnetic-field component values and the Lagrange multipliers.

Quantum transport under ac drive from the leads: A Redfield quantum master equation approach

NASA Astrophysics Data System (ADS)

Purkayastha, Archak; Dubi, Yonatan

2017-08-01

Evaluating the time-dependent dynamics of driven open quantum systems is relevant for a theoretical description of many systems, including molecular junctions, quantum dots, cavity-QED experiments, cold atoms experiments, and more. Here, we formulate a rigorous microscopic theory of an out-of-equilibrium open quantum system of noninteracting particles on a lattice weakly coupled bilinearly to multiple baths and driven by periodically varying thermodynamic parameters like temperature and chemical potential of the bath. The particles can be either bosonic or fermionic and the lattice can be of any dimension and geometry. Based on the Redfield quantum master equation under Born-Markov approximation, we derive a linear differential equation for an equal time two point correlation matrix, sometimes also called a single-particle density matrix, from which various physical observables, for example, current, can be calculated. Various interesting physical effects, such as resonance, can be directly read off from the equations. Thus, our theory is quite general and gives quite transparent and easy-to-calculate results. We validate our theory by comparing with exact numerical simulations. We apply our method to a generic open quantum system, namely, a double quantum dot coupled to leads with modulating chemical potentials. The two most important experimentally relevant insights from this are as follows: (i) Time-dependent measurements of current for symmetric oscillating voltages (with zero instantaneous voltage bias) can point to the degree of asymmetry in the system-bath coupling and (ii) under certain conditions time-dependent currents can exceed time-averaged currents by several orders of magnitude, and can therefore be detected even when the average current is below the measurement threshold.

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

NASA Astrophysics Data System (ADS)

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 the unknown HK functional, associated with the theorem of Hohenberg and Kohn. The latter is provided by the calculation of helium correlation energy, where we test approximating the second-order density function by the leading term of its McLaurin's series expansion.

Anisotropic Damage Mechanics Modeling in Metal Matrix Composites

DTIC Science & Technology

1993-05-15

conducted on a titanium aluminide SiC-reinforced metal matrix composite. Center-cracked plates with laminate layups of (0/90) and (±45). were tested... interfacial damage mechanisms as debonding or delamination. Equations (2.14) and (2.15) represent the damage transformation equations for the stress... titanium aluminide SiC 46 continuous reinforced metal matrix composite. As a means of enforcing quality assurance, all manufacturing and cutting of the

Recurrent procedure for constructing nonisotropic matrix elements of the collision integral of the nonlinear Boltzmann equation

NASA Astrophysics Data System (ADS)

Ender, I. A.; Bakaleinikov, L. A.; Flegontova, E. Yu.; Gerasimenko, A. B.

2017-08-01

We have proposed an algorithm for the sequential construction of nonisotropic matrix elements of the collision integral, which are required to solve the nonlinear Boltzmann equation using the moments method. The starting elements of the matrix are isotropic and assumed to be known. The algorithm can be used for an arbitrary law of interactions for any ratio of the masses of colliding particles.

GPU acceleration of the Locally Selfconsistent Multiple Scattering code for first principles calculation of the ground state and statistical physics of materials

NASA Astrophysics Data System (ADS)

Eisenbach, Markus; Larkin, Jeff; Lutjens, Justin; Rennich, Steven; Rogers, James H.

2017-02-01

The Locally Self-consistent Multiple Scattering (LSMS) code solves the first principles Density Functional theory Kohn-Sham equation for a wide range of materials with a special focus on metals, alloys and metallic nano-structures. It has traditionally exhibited near perfect scalability on massively parallel high performance computer architectures. We present our efforts to exploit GPUs to accelerate the LSMS code to enable first principles calculations of O(100,000) atoms and statistical physics sampling of finite temperature properties. We reimplement the scattering matrix calculation for GPUs with a block matrix inversion algorithm that only uses accelerator memory. Using the Cray XK7 system Titan at the Oak Ridge Leadership Computing Facility we achieve a sustained performance of 14.5PFlop/s and a speedup of 8.6 compared to the CPU only code.

GPU acceleration of the Locally Selfconsistent Multiple Scattering code for first principles calculation of the ground state and statistical physics of materials

DOE PAGES

Eisenbach, Markus; Larkin, Jeff; Lutjens, Justin; ...

2016-07-12

The Locally Self-consistent Multiple Scattering (LSMS) code solves the first principles Density Functional theory Kohn–Sham equation for a wide range of materials with a special focus on metals, alloys and metallic nano-structures. It has traditionally exhibited near perfect scalability on massively parallel high performance computer architectures. In this paper, we present our efforts to exploit GPUs to accelerate the LSMS code to enable first principles calculations of O(100,000) atoms and statistical physics sampling of finite temperature properties. We reimplement the scattering matrix calculation for GPUs with a block matrix inversion algorithm that only uses accelerator memory. Finally, using the Craymore » XK7 system Titan at the Oak Ridge Leadership Computing Facility we achieve a sustained performance of 14.5PFlop/s and a speedup of 8.6 compared to the CPU only code.« less

Numerical solution of quadratic matrix equations for free vibration analysis of structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

Matrix approaches to assess terrestrial nitrogen scheme in CLM4.5

NASA Astrophysics Data System (ADS)

Du, Z.

2017-12-01

Terrestrial carbon (C) and nitrogen (N) cycles have been commonly represented by a series of balance equations to track their influxes into and effluxes out of individual pools in earth system models (ESMs). This representation matches our understanding of C and N cycle processes well but makes it difficult to track model behaviors. To overcome these challenges, we developed a matrix approach, which reorganizes the series of terrestrial C and N balance equations in the CLM4.5 into two matrix equations based on original representation of C and N cycle processes and mechanisms. The matrix approach would consequently help improve the comparability of models and data, evaluate impacts of additional model components, facilitate benchmark analyses, model intercomparisons, and data-model fusion, and improve model predictive power.

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

Research on the application of a decoupling algorithm for structure analysis

NASA Technical Reports Server (NTRS)

Denman, E. D.

1980-01-01

The mathematical theory for decoupling mth-order matrix differential equations is presented. It is shown that the decoupling precedure can be developed from the algebraic theory of matrix polynomials. The role of eigenprojectors and latent projectors in the decoupling process is discussed and the mathematical relationships between eigenvalues, eigenvectors, latent roots, and latent vectors are developed. It is shown that the eigenvectors of the companion form of a matrix contains the latent vectors as a subset. The spectral decomposition of a matrix and the application to differential equations is given.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishimoto, Yoshio, E-mail: nishimoto.yoshio@fukui.kyoto-u.ac.jp

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 themore » 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.« less

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

PubMed

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.

Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chung, Moses; Qin, Hong; Davidson, Ronald C.

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. Here in this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. Themore » new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. Finally, the corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed design and analysis of high-intensity beam manipulations, for which previous theoretical models are not easily applicable.« less

Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

DOE PAGES

Chung, Moses; Qin, Hong; Davidson, Ronald C.; ...

2016-11-23

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. Here in this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. Themore » new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. Finally, the corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed design and analysis of high-intensity beam manipulations, for which previous theoretical models are not easily applicable.« less

Resonance line polarization and the Hanle effect in optically thick media. I - Formulation for the two-level atom

NASA Astrophysics Data System (ADS)

Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S.

1990-08-01

A general formalism is presented to describe resonance line polarization for a two-level atom in an optically thick, three-dimensional medium embedded in an arbitrary varying magnetic field and irradiated by an arbitrary radiation field. The magnetic field is supposed sufficiently small to induce a Zeeman splitting much smaller than the typical line width. By neglecting atomic polarization in the lower level and stimulated emission, an integral equation is derived for the multipole moments of the density matrix of the upper level. This equation shows how the multipole moments at any assigned point of the medium are coupled to the multipole moments relative at a different point as a consequence of the propagation of polarized radiation between the two points. The equation also accounts for the effect of the magnetic field, described by a kernel locally connecting multipole moments of the same rank, and for the role of inelastic and elastic (or depolarizing) collisions. After having given its formal derivation for the general case, the integral equation is particularized to the one-dimensional and two-dimensional cases. For the one-dimensional case of a plane parallel atmosphere, neglecting both the magnetic field and depolarizing collisions, the equation here derived reduces to a previous one given by Rees (1978).

Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Alexander, Steven; Coldwell, R. L.

2015-03-01

The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

PubMed

Murase, Kenya

2016-01-01

In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

Non-Markovianity in the optimal control of an open quantum system described by hierarchical equations of motion

NASA Astrophysics Data System (ADS)

Mangaud, E.; Puthumpally-Joseph, R.; Sugny, D.; Meier, C.; Atabek, O.; Desouter-Lecomte, M.

2018-04-01

Optimal control theory is implemented with fully converged hierarchical equations of motion (HEOM) describing the time evolution of an open system density matrix strongly coupled to the bath in a spin-boson model. The populations of the two-level sub-system are taken as control objectives; namely, their revivals or exchange when switching off the field. We, in parallel, analyze how the optimal electric field consequently modifies the information back flow from the environment through different non-Markovian witnesses. Although the control field has a dipole interaction with the central sub-system only, its indirect influence on the bath collective mode dynamics is probed through HEOM auxiliary matrices, revealing a strong correlation between control and dissipation during a non-Markovian process. A heterojunction is taken as an illustrative example for modeling in a realistic way the two-level sub-system parameters and its spectral density function leading to a non-perturbative strong coupling regime with the bath. Although, due to strong system-bath couplings, control performances remain rather modest, the most important result is a noticeable increase of the non-Markovian bath response induced by the optimally driven processes.

Nonequilibrium BN-ZnO: Optical properties and excitonic effects from first principles

NASA Astrophysics Data System (ADS)

Zhang, Xiao; Schleife, André

2018-03-01

The nonequilibrium boron nitride (BN) phase of zinc oxide (ZnO) has been reported for thin films and nanostructures, however, its properties are not well understood due to a persistent controversy that prevents reconciling experimental and first-principles results for its atomic coordinates. We use first-principles theoretical spectroscopy to accurately compute electronic and optical properties, including single-quasiparticle and excitonic effects: Band structures and densities of states are computed using density functional theory, hybrid functionals, and the G W approximation. Accurate optical absorption spectra and exciton binding energies are computed by solving the Bethe-Salpeter equation for the optical polarization function. Using this data we show that the band-gap difference between BN-ZnO and wurtzite (WZ) ZnO agrees very well with experiment when the theoretical lattice geometry is used, but significantly disagrees for the experimental atomic coordinates. We also show that the optical anisotropy of BN-ZnO differs significantly from that of WZ-ZnO, allowing us to optically distinguish both polymorphs. By using the transfer-matrix method to solve Maxwell's equations for thin films composed of both polymorphs, we illustrate that this opens up a promising route for tuning optical properties.

Hyperbolicity of the Nonlinear Models of Maxwell's Equations

NASA Astrophysics Data System (ADS)

Serre, Denis

. We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.

A Comparative Study of Collagen Matrix Density Effect on Endothelial Sprout Formation Using Experimental and Computational Approaches.

PubMed

Shamloo, Amir; Mohammadaliha, Negar; Heilshorn, Sarah C; Bauer, Amy L

2016-04-01

A thorough understanding of determining factors in angiogenesis is a necessary step to control the development of new blood vessels. Extracellular matrix density is known to have a significant influence on cellular behaviors and consequently can regulate vessel formation. The utilization of experimental platforms in combination with numerical models can be a powerful method to explore the mechanisms of new capillary sprout formation. In this study, using an integrative method, the interplay between the matrix density and angiogenesis was investigated. Owing the fact that the extracellular matrix density is a global parameter that can affect other parameters such as pore size, stiffness, cell-matrix adhesion and cross-linking, deeper understanding of the most important biomechanical or biochemical properties of the ECM causing changes in sprout morphogenesis is crucial. Here, we implemented both computational and experimental methods to analyze the mechanisms responsible for the influence of ECM density on the sprout formation that is difficult to be investigated comprehensively using each of these single methods. For this purpose, we first utilized an innovative approach to quantify the correspondence of the simulated collagen fibril density to the collagen density in the experimental part. Comparing the results of the experimental study and computational model led to some considerable achievements. First, we verified the results of the computational model using the experimental results. Then, we reported parameters such as the ratio of proliferating cells to migrating cells that was difficult to obtain from experimental study. Finally, this integrative system led to gain an understanding of the possible mechanisms responsible for the effect of ECM density on angiogenesis. The results showed that stable and long sprouts were observed at an intermediate collagen matrix density of 1.2 and 1.9 mg/ml due to a balance between the number of migrating and proliferating cells. As a result of weaker connections between the cells and matrix, a lower collagen matrix density (0.7 mg/ml) led to unstable and broken sprouts. However, higher matrix density (2.7 mg/ml) suppressed sprout formation due to the high level of matrix entanglement, which inhibited cell migration. This study also showed that extracellular matrix density can influence sprout branching. Our experimental results support this finding.

The Replicator Equation on Graphs

PubMed Central

Ohtsuki, Hisashi; Nowak, Martin A.

2008-01-01

We study evolutionary games on graphs. Each player is represented by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payoff from interaction with all their immediate neighbors. We consider three different update rules, called ‘birth-death’, ‘death-birth’ and ‘imitation’. A fourth update rule, ‘pairwise comparison’, is shown to be equivalent to birth-death updating in our model. We use pair-approximation to describe the evolutionary game dynamics on regular graphs of degree k. In the limit of weak selection, we can derive a differential equation which describes how the average frequency of each strategy on the graph changes over time. Remarkably, this equation is a replicator equation with a transformed payoff matrix. Therefore, moving a game from a well-mixed population (the complete graph) onto a regular graph simply results in a transformation of the payoff matrix. The new payoff matrix is the sum of the original payoff matrix plus another matrix, which describes the local competition of strategies. We discuss the application of our theory to four particular examples, the Prisoner’s Dilemma, the Snow-Drift game, a coordination game and the Rock-Scissors-Paper game. PMID:16860343

The spectral applications of Beer-Lambert law for some biological and dosimetric materials

NASA Astrophysics Data System (ADS)

Içelli, Orhan; Yalçin, Zeynel; Karakaya, Vatan; Ilgaz, Işıl P.

2014-08-01

The aim of this study is to conduct quantitative and qualitative analysis of biological and dosimetric materials which contain organic and inorganic materials and to make the determination by using the spectral theorem Beer-Lambert law. Beer-Lambert law is a system of linear equations for the spectral theory. It is possible to solve linear equations with a non-zero coefficient matrix determinant forming linear equations. Characteristic matrix of the linear equation with zero determinant is called point spectrum at the spectral theory.

Generalized Courant-Snyder Theory and Kapchinskij-Vladimirskij Distribution For High-intensity Beams In A Coupled Transverse Focusing Lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong QIn, Ronald Davidson

2011-07-18

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in a uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are non-commutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant.more » This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation, and reduces beam pulsation.« less

Generalized Courant-Snyder theory and Kapchinskij-Vladimirskij distribution for high-intensity beams in a coupled transverse focusing lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qin Hong; Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026; Davidson, Ronald C.

2011-05-15

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in an uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are noncommutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant.more » This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation and reduces beam pulsation.« less

Multilayer-MCTDH approach to the energy transfer dynamics in the LH2 antenna complex

NASA Astrophysics Data System (ADS)

Shibl, Mohamed F.; Schulze, Jan; Al-Marri, Mohammed J.; Kühn, Oliver

2017-09-01

The multilayer multiconfiguration time-dependent Hartree method is used to study the coupled exciton-vibrational dynamics in a high-dimensional nonameric model of the LH2 antenna complex of purple bacteria. The exciton-vibrational coupling is parametrized within the Huang-Rhys model according to phonon and intramolecular vibrational modes derived from an experimental bacteriochlorophyll spectral density. In contrast to reduced density matrix approaches, the Schrödinger equation is solved explicitly, giving access to the full wave function. This facilitates an unbiased analysis in terms of the coupled dynamics of excitonic and vibrational degrees of freedom. For the present system, we identify spectator modes for the B800 to B800 transfer and we find a non-additive effect of phonon and intramolecular vibrational modes on the B800 to B850 exciton transfer.

Turbidimetric method for the determination of particle sizes in polypropylene/clay-composites during extrusion.

PubMed

Becker, Wolfgang; Guschin, Viktor; Mikonsaari, Irma; Teipel, Ulrich; Kölle, Sabine; Weiss, Patrick

2017-01-01

Nanocomposites with polypropylene as matrix material and nanoclay as filler were produced in a double twin screw extruder. The extrusion was monitored with a spectrometer in the visible and near-infrared spectral region with a diode array spectrometer. Two probes were installed at the end at the extruder die and the transmission spectra were measured during the extrusion. After measuring the transmission spectra and converting into turbidity units, the particle distribution density was calculated via numerical linear equation system. The distribution density function shows either a bimodal or mono modal shape in dependence of the processing parameters like screw speed, dosage, and concentration of the nanoclays. The method was verified with SEM measurements which yield comparable results. The method is suitable for industrial in-line processing monitoring of particle radii and dispersion process, respectively.

Lax representations for matrix short pulse equations

NASA Astrophysics Data System (ADS)

Popowicz, Z.

2017-10-01

The Lax representation for different matrix generalizations of Short Pulse Equations (SPEs) is considered. The four-dimensional Lax representations of four-component Matsuno, Feng, and Dimakis-Müller-Hoissen-Matsuno equations are obtained. The four-component Feng system is defined by generalization of the two-dimensional Lax representation to the four-component case. This system reduces to the original Feng equation, to the two-component Matsuno equation, or to the Yao-Zang equation. The three-component version of the Feng equation is presented. The four-component version of the Matsuno equation with its Lax representation is given. This equation reduces the new two-component Feng system. The two-component Dimakis-Müller-Hoissen-Matsuno equations are generalized to the four-parameter family of the four-component SPE. The bi-Hamiltonian structure of this generalization, for special values of parameters, is defined. This four-component SPE in special cases reduces to the new two-component SPE.

Neutrino quantum kinetic equations: The collision term

DOE PAGES

Blaschke, Daniel N.; Cirigliano, Vincenzo

2016-08-01

We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes ofmore » the two helicity states. As a result, the isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.« less

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

The pointwise estimates of diffusion wave of the compressible micropolar fluids

NASA Astrophysics Data System (ADS)

Wu, Zhigang; Wang, Weike

2018-09-01

The pointwise estimates for the compressible micropolar fluids in dimension three are given, which exhibit generalized Huygens' principle for the fluid density and fluid momentum as the compressible Navier-Stokes equation, while the micro-rational momentum behaves like the fluid momentum of the Euler equation with damping. To circumvent the complexity from 7 × 7 Green's matrix, we use the decomposition of fluid part and electromagnetic part for the momentums to study three smaller Green's matrices. The following from this decomposition is that we have to deal with the new problem that the nonlinear terms contain nonlocal operators. We solve it by using the natural match of these new Green's functions and the nonlinear terms. Moreover, to derive the different pointwise estimates for different unknown variables such that the estimate of each unknown variable is in agreement with its Green's function, we develop some new estimates on the nonlinear interplay between different waves.

Matrix approach to land carbon cycle modeling: A case study with the Community Land Model.

PubMed

Huang, Yuanyuan; Lu, Xingjie; Shi, Zheng; Lawrence, David; Koven, Charles D; Xia, Jianyang; Du, Zhenggang; Kluzek, Erik; Luo, Yiqi

2018-03-01

The terrestrial carbon (C) cycle has been commonly represented by a series of C balance equations to track C influxes into and effluxes out of individual pools in earth system models (ESMs). This representation matches our understanding of C cycle processes well but makes it difficult to track model behaviors. It is also computationally expensive, limiting the ability to conduct comprehensive parametric sensitivity analyses. To overcome these challenges, we have developed a matrix approach, which reorganizes the C balance equations in the original ESM into one matrix equation without changing any modeled C cycle processes and mechanisms. We applied the matrix approach to the Community Land Model (CLM4.5) with vertically-resolved biogeochemistry. The matrix equation exactly reproduces litter and soil organic carbon (SOC) dynamics of the standard CLM4.5 across different spatial-temporal scales. The matrix approach enables effective diagnosis of system properties such as C residence time and attribution of global change impacts to relevant processes. We illustrated, for example, the impacts of CO 2 fertilization on litter and SOC dynamics can be easily decomposed into the relative contributions from C input, allocation of external C into different C pools, nitrogen regulation, altered soil environmental conditions, and vertical mixing along the soil profile. In addition, the matrix tool can accelerate model spin-up, permit thorough parametric sensitivity tests, enable pool-based data assimilation, and facilitate tracking and benchmarking of model behaviors. Overall, the matrix approach can make a broad range of future modeling activities more efficient and effective. © 2017 John Wiley & Sons Ltd.

Sensitivity of coronal loop sausage mode frequencies and decay rates to radial and longitudinal density inhomogeneities: a spectral approach

NASA Astrophysics Data System (ADS)

Cally, Paul S.; Xiong, Ming

2018-01-01

Fast sausage modes in solar magnetic coronal loops are only fully contained in unrealistically short dense loops. Otherwise they are leaky, losing energy to their surrounds as outgoing waves. This causes any oscillation to decay exponentially in time. Simultaneous observations of both period and decay rate therefore reveal the eigenfrequency of the observed mode, and potentially insight into the tubes’ nonuniform internal structure. In this article, a global spectral description of the oscillations is presented that results in an implicit matrix eigenvalue equation where the eigenvalues are associated predominantly with the diagonal terms of the matrix. The off-diagonal terms vanish identically if the tube is uniform. A linearized perturbation approach, applied with respect to a uniform reference model, is developed that makes the eigenvalues explicit. The implicit eigenvalue problem is easily solved numerically though, and it is shown that knowledge of the real and imaginary parts of the eigenfrequency is sufficient to determine the width and density contrast of a boundary layer over which the tubes’ enhanced internal densities drop to ambient values. Linearized density kernels are developed that show sensitivity only to the extreme outside of the loops for radial fundamental modes, especially for small density enhancements, with no sensitivity to the core. Higher radial harmonics do show some internal sensitivity, but these will be more difficult to observe. Only kink modes are sensitive to the tube centres. Variation in internal and external Alfvén speed along the loop is shown to have little effect on the fundamental dimensionless eigenfrequency, though the associated eigenfunction becomes more compact at the loop apex as stratification increases, or may even displace from the apex.

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

More on Chemical Reaction Balancing.

ERIC Educational Resources Information Center

Swinehart, D. F.

1985-01-01

A previous article stated that only the matrix method was powerful enough to balance a particular chemical equation. Shows how this equation can be balanced without using the matrix method. The approach taken involves writing partial mathematical reactions and redox half-reactions, and combining them to yield the final balanced reaction. (JN)

Matrix approach to uncertainty assessment and reduction for modeling terrestrial carbon cycle

NASA Astrophysics Data System (ADS)

Luo, Y.; Xia, J.; Ahlström, A.; Zhou, S.; Huang, Y.; Shi, Z.; Wang, Y.; Du, Z.; Lu, X.

2017-12-01

Terrestrial ecosystems absorb approximately 30% of the anthropogenic carbon dioxide emissions. This estimate has been deduced indirectly: combining analyses of atmospheric carbon dioxide concentrations with ocean observations to infer the net terrestrial carbon flux. In contrast, when knowledge about the terrestrial carbon cycle is integrated into different terrestrial carbon models they make widely different predictions. To improve the terrestrial carbon models, we have recently developed a matrix approach to uncertainty assessment and reduction. Specifically, the terrestrial carbon cycle has been commonly represented by a series of carbon balance equations to track carbon influxes into and effluxes out of individual pools in earth system models. This representation matches our understanding of carbon cycle processes well and can be reorganized into one matrix equation without changing any modeled carbon cycle processes and mechanisms. We have developed matrix equations of several global land C cycle models, including CLM3.5, 4.0 and 4.5, CABLE, LPJ-GUESS, and ORCHIDEE. Indeed, the matrix equation is generic and can be applied to other land carbon models. This matrix approach offers a suite of new diagnostic tools, such as the 3-dimensional (3-D) parameter space, traceability analysis, and variance decomposition, for uncertainty analysis. For example, predictions of carbon dynamics with complex land models can be placed in a 3-D parameter space (carbon input, residence time, and storage potential) as a common metric to measure how much model predictions are different. The latter can be traced to its source components by decomposing model predictions to a hierarchy of traceable components. Then, variance decomposition can help attribute the spread in predictions among multiple models to precisely identify sources of uncertainty. The highly uncertain components can be constrained by data as the matrix equation makes data assimilation computationally possible. We will illustrate various applications of this matrix approach to uncertainty assessment and reduction for terrestrial carbon cycle models.

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals.

PubMed

Zuehlsdorff, T J; Hine, N D M; Payne, M C; Haynes, P D

2015-11-28

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chvartatskyi, O. I., E-mail: alex.chvartatskyy@gmail.com; Sydorenko, Yu. M., E-mail: y-sydorenko@franko.lviv.ua

We introduce a new bidirectional generalization of (2+1)-dimensional k-constrained Kadomtsev-Petviashvili (KP) hierarchy ((2+1)-BDk-cKPH). This new hierarchy generalizes (2+1)-dimensional k-cKP hierarchy, (t{sub A}, τ{sub B}) and (γ{sub A}, σ{sub B}) matrix hierarchies. (2+1)-BDk-cKPH contains a new matrix (1+1)-k-constrained KP hierarchy. Some members of (2+1)-BDk-cKPH are also listed. In particular, it contains matrix generalizations of Davey-Stewartson (DS) systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik equation. (2+1)-BDk-cKPH also includes new matrix (2+1)-dimensional generalizations of the Yajima-Oikawa and Melnikov systems. Binary Darboux Transformation Dressing Method is also proposed for construction of exact solutions for equations from (2+1)-BDk-cKPH. As an example the exactmore » form of multi-soliton solutions for vector generalization of the DS system is given.« less

Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics, production version (SOUSSA-P 1.1). Volume 1: Theoretical manual. [Green function

NASA Technical Reports Server (NTRS)

Morino, L.

1980-01-01

Recent developments of the Green's function method and the computer program SOUSSA (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed and summarized. Applying the Green's function method to the fully unsteady (transient) potential equation yields an integro-differential-delay equation. With spatial discretization by the finite-element method, this equation is approximated by a set of differential-delay equations in time. Time solution by Laplace transform yields a matrix relating the velocity potential to the normal wash. Premultiplying and postmultiplying by the matrices relating generalized forces to the potential and the normal wash to the generalized coordinates one obtains the matrix of the generalized aerodynamic forces. The frequency and mode-shape dependence of this matrix makes the program SOUSSA useful for multiple frequency and repeated mode-shape evaluations.

Density reconstruction in multiparameter elastic full-waveform inversion

NASA Astrophysics Data System (ADS)

Sun, Min'ao; Yang, Jizhong; Dong, Liangguo; Liu, Yuzhu; Huang, Chao

2017-12-01

Elastic full-waveform inversion (EFWI) is a quantitative data fitting procedure that recovers multiple subsurface parameters from multicomponent seismic data. As density is involved in addition to P- and S-wave velocities, the multiparameter EFWI suffers from more serious tradeoffs. In addition, compared with P- and S-wave velocities, the misfit function is less sensitive to density perturbation. Thus, a robust density reconstruction remains a difficult problem in multiparameter EFWI. In this paper, we develop an improved scattering-integral-based truncated Gauss-Newton method to simultaneously recover P- and S-wave velocities and density in EFWI. In this method, the inverse Gauss-Newton Hessian has been estimated by iteratively solving the Gauss-Newton equation with a matrix-free conjugate gradient algorithm. Therefore, it is able to properly handle the parameter tradeoffs. To give a detailed illustration of the tradeoffs between P- and S-wave velocities and density in EFWI, wavefield-separated sensitivity kernels and the Gauss-Newton Hessian are numerically computed, and their distribution characteristics are analyzed. Numerical experiments on a canonical inclusion model and a modified SEG/EAGE Overthrust model have demonstrated that the proposed method can effectively mitigate the tradeoff effects, and improve multiparameter gradients. Thus, a high convergence rate and an accurate density reconstruction can be achieved.

The Principle of Energetic Consistency

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.

2009-01-01

A basic result in estimation theory is that the minimum variance estimate of the dynamical state, given the observations, is the conditional mean estimate. This result holds independently of the specifics of any dynamical or observation nonlinearity or stochasticity, requiring only that the probability density function of the state, conditioned on the observations, has two moments. For nonlinear dynamics that conserve a total energy, this general result implies the principle of energetic consistency: if the dynamical variables are taken to be the natural energy variables, then the sum of the total energy of the conditional mean and the trace of the conditional covariance matrix (the total variance) is constant between observations. Ensemble Kalman filtering methods are designed to approximate the evolution of the conditional mean and covariance matrix. For them the principle of energetic consistency holds independently of ensemble size, even with covariance localization. However, full Kalman filter experiments with advection dynamics have shown that a small amount of numerical dissipation can cause a large, state-dependent loss of total variance, to the detriment of filter performance. The principle of energetic consistency offers a simple way to test whether this spurious loss of variance limits ensemble filter performance in full-blown applications. The classical second-moment closure (third-moment discard) equations also satisfy the principle of energetic consistency, independently of the rank of the conditional covariance matrix. Low-rank approximation of these equations offers an energetically consistent, computationally viable alternative to ensemble filtering. Current formulations of long-window, weak-constraint, four-dimensional variational methods are designed to approximate the conditional mode rather than the conditional mean. Thus they neglect the nonlinear bias term in the second-moment closure equation for the conditional mean. The principle of energetic consistency implies that, to precisely the extent that growing modes are important in data assimilation, this term is also important.

Hierarchical Equation of Motion Investigation of Decoherence and Relaxation Dynamics in Nonequilibrium Transport through Interacting Quantum Dots

NASA Astrophysics Data System (ADS)

Hartle, Rainer; Cohen, Guy; Reichman, David R.; Millis, Andrew J.

2014-03-01

A recently developed hierarchical quantum master equation approach is used to investigate nonequilibrium electron transport through an interacting double quantum dot system in the regime where the inter-dot coupling is weaker than the coupling to the electrodes. The corresponding eigenstates provide tunneling paths that may interfere constructively or destructively, depending on the energy of the tunneling electrons. Electron-electron interactions are shown to quench these interference effects in bias-voltage dependent ways, leading, in particular, to negative differential resistance, population inversion and an enhanced broadening of resonances in the respective transport characteristics. Relaxation times are found to be very long, and to be correlated with very slow dynamics of the inter-dot coherences (off diagonal density matrix elements). The ability of the hierarchical quantum master equation approach to access very long time scales is crucial for the study of this physics. This work is supported by the National Science Foundation (NSF DMR-1006282 and NSF CHE-1213247), the Yad Hanadiv-Rothschild Foundation (via a Rothschild Fellowship for GC) and the Alexander von Humboldt Foundation (via a Feodor Lynen fellowship for RH).

An improved V-Lambda solution of the matrix Riccati equation

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Markley, F. Landis

1988-01-01

The authors present an improved algorithm for computing the V-Lambda solution of the matrix Riccati equation. The improvement is in the reduction of the computational load, results from the orthogonality of the eigenvector matrix that has to be solved for. The orthogonality constraint reduces the number of independent parameters which define the matrix from n-squared to n (n - 1)/2. The authors show how to specify the parameters, how to solve for them and how to form from them the needed eigenvector matrix. In the search for suitable parameters, the analogy between the present problem and the problem of attitude determination is exploited, resulting in the choice of Rodrigues parameters.

Detection of Matrix Crack Density of CFRP using an Electrical Potential Change Method with Multiple Probes

NASA Astrophysics Data System (ADS)

Todoroki, Akira; Omagari, Kazuomi

Carbon Fiber Reinforced Plastic (CFRP) laminates are adopted for fuel tank structures of next generation space rockets or automobiles. Matrix cracks may cause fuel leak or trigger fatigue damage. A monitoring system of the matrix crack density is required. The authors have developed an electrical resistance change method for the monitoring of delamination cracks in CFRP laminates. Reinforcement fibers are used as a self-sensing system. In the present study, the electric potential method is adopted for matrix crack density monitoring. Finite element analysis (FEA) was performed to investigate the possibility of monitoring matrix crack density using multiple electrodes mounted on a single surface of a specimen. The FEA reveals the matrix crack density increases electrical resistance for a target segment between electrodes. Experimental confirmation was also performed using cross-ply laminates. Eight electrodes were mounted on a single surface of a specimen using silver paste after polishing of the specimen surface with sandpaper. The two outermost electrodes applied electrical current, and the inner electrodes measured electric voltage changes. The slope of electrical resistance during reloading is revealed to be an appropriate index for the detection of matrix crack density.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

PubMed

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

Preserving the Helmholtz dispersion relation: One-way acoustic wave propagation using matrix square roots

NASA Astrophysics Data System (ADS)

Keefe, Laurence

2016-11-01

Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method

NASA Astrophysics Data System (ADS)

Volokitin, V.; Liniov, A.; Meyerov, I.; Hartmann, M.; Ivanchenko, M.; Hänggi, P.; Denisov, S.

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dim H =N ≲300 , while the direct long-time numerical integration of the master equation becomes increasingly problematic for N ≳400 , especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η1,η2,...,ηn} , one could propagate a quantum trajectory (with ηi's as norm thresholds) in a numerically exact way. By using a scalable N -particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N =2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method.

PubMed

Volokitin, V; Liniov, A; Meyerov, I; Hartmann, M; Ivanchenko, M; Hänggi, P; Denisov, S

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

A master equation for strongly interacting dipoles

NASA Astrophysics Data System (ADS)

Stokes, Adam; Nazir, Ahsan

2018-04-01

We consider a pair of dipoles such as Rydberg atoms for which direct electrostatic dipole–dipole interactions may be significantly larger than the coupling to transverse radiation. We derive a master equation using the Coulomb gauge, which naturally enables us to include the inter-dipole Coulomb energy within the system Hamiltonian rather than the interaction. In contrast, the standard master equation for a two-dipole system, which depends entirely on well-known gauge-invariant S-matrix elements, is usually derived using the multipolar gauge, wherein there is no explicit inter-dipole Coulomb interaction. We show using a generalised arbitrary-gauge light-matter Hamiltonian that this master equation is obtained in other gauges only if the inter-dipole Coulomb interaction is kept within the interaction Hamiltonian rather than the unperturbed part as in our derivation. Thus, our master equation depends on different S-matrix elements, which give separation-dependent corrections to the standard matrix elements describing resonant energy transfer and collective decay. The two master equations coincide in the large separation limit where static couplings are negligible. We provide an application of our master equation by finding separation-dependent corrections to the natural emission spectrum of the two-dipole system.

Renormalized dynamics of the Dean-Kawasaki model

NASA Astrophysics Data System (ADS)

Bidhoodi, Neeta; Das, Shankar P.

2015-07-01

We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ (x ,t ) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix Σ . The appropriate model for the renormalized dynamics involves an extended set of field variables {ρ ,θ } , linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of Σ which renormalizes the bare diffusion constant D0 to DR is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997), 10.1007/s002570050396]. DR sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of Σ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with DR=0 as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.

A new time dependent density functional algorithm for large systems and plasmons in metal clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baseggio, Oscar; Fronzoni, Giovanna; Stener, Mauro, E-mail: stener@univ.trieste.it

2015-07-14

A new algorithm to solve the Time Dependent Density Functional Theory (TDDFT) equations in the space of the density fitting auxiliary basis set has been developed and implemented. The method extracts the spectrum from the imaginary part of the polarizability at any given photon energy, avoiding the bottleneck of Davidson diagonalization. The original idea which made the present scheme very efficient consists in the simplification of the double sum over occupied-virtual pairs in the definition of the dielectric susceptibility, allowing an easy calculation of such matrix as a linear combination of constant matrices with photon energy dependent coefficients. The methodmore » has been applied to very different systems in nature and size (from H{sub 2} to [Au{sub 147}]{sup −}). In all cases, the maximum deviations found for the excitation energies with respect to the Amsterdam density functional code are below 0.2 eV. The new algorithm has the merit not only to calculate the spectrum at whichever photon energy but also to allow a deep analysis of the results, in terms of transition contribution maps, Jacob plasmon scaling factor, and induced density analysis, which have been all implemented.« less

In vitro dissolution kinetic study of theophylline from hydrophilic and hydrophobic matrices.

PubMed

Maswadeh, Hamzah M; Semreen, Mohammad H; Abdulhalim, Abdulatif A

2006-01-01

Oral dosage forms containing 300 mg theophylline in matrix type tablets, were prepared by direct compression method using two kinds of matrices, glycerylbehenate (hydrophobic), and (hydroxypropyl)methyl cellulose (hydrophilic). The in vitro release kinetics of these formulations were studied at pH 6.8 using the USP dissolution apparatus with the paddle assemble. The kinetics of the dissolution process were studied by analyzing the dissolution data using four kinetic equations, the zero-order equation, the first-order equation, the Higuchi square root equation and the Hixson-Crowell cube root law. The analysis of the dissolution kinetic data for the theophylline preparations in this study shows that it follows the first order kinetics and the release process involves erosion / diffusion and an alteration in the surface area and diameter of the matrix system, as well as in the diffusion path length from the matrix drug load during the dissolution process. This relation is best described by the use of both the first-order equation and the Hixson-Crowell cube root law.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chow, Edmond

Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

Algebraic methods are used to construct the exact solution P of the linear matrix equation PA + BP = - C, where A, B, and C are matrices with real entries. The emphasis of this equation is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The paper is divided into six sections which include the proof of the basic lemma, the Liapunov equation, and the computer implementation for the rational, integer and modular algorithms. Two numerical examples are given and the entire calculation process is depicted.

Modifying a numerical algorithm for solving the matrix equation X + AX T B = C

NASA Astrophysics Data System (ADS)

Vorontsov, Yu. O.

2013-06-01

Certain modifications are proposed for a numerical algorithm solving the matrix equation X + AX T B = C. By keeping the intermediate results in storage and repeatedly using them, it is possible to reduce the total complexity of the algorithm from O( n 4) to O( n 3) arithmetic operations.

Solving rational matrix equations in the state space with applications to computer-aided control-system design

NASA Technical Reports Server (NTRS)

Packard, A. K.; Sastry, S. S.

1986-01-01

A method of solving a class of linear matrix equations over various rings is proposed, using results from linear geometric control theory. An algorithm, successfully implemented, is presented, along with non-trivial numerical examples. Applications of the method to the algebraic control system design methodology are discussed.

Matrix Solution of Coupled Differential Equations and Looped Car Following Models

ERIC Educational Resources Information Center

McCartney, Mark

2008-01-01

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

Gradient-based stochastic estimation of the density matrix

NASA Astrophysics Data System (ADS)

Wang, Zhentao; Chern, Gia-Wei; Batista, Cristian D.; Barros, Kipton

2018-03-01

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. We introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S-(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

Chemical Equation Balancing.

ERIC Educational Resources Information Center

Blakley, G. R.

1982-01-01

Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

Adomian decomposition

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Jafari, Hossein

2005-01-01

Adomian decomposition method has been employed to obtain solutions of a system of fractional differential equations. Convergence of the method has been discussed with some illustrative examples. In particular, for the initial value problem: where A=[aij] is a real square matrix, the solution turns out to be , where E([alpha]1,...,[alpha]n),1 denotes multivariate Mittag-Leffler function defined for matrix arguments and Ai is the matrix having ith row as [ai1...ain], and all other entries are zero. Fractional oscillation and Bagley-Torvik equations are solved as illustrative examples.

Second level semi-degenerate fields in W_3 Toda theory: matrix element and differential equation

NASA Astrophysics Data System (ADS)

Belavin, Vladimir; Cao, Xiangyu; Estienne, Benoit; Santachiara, Raoul

2017-03-01

In a recent study we considered W_3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl_3 . We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.

A New Pipelined Systolic Array-Based Architecture for Matrix Inversion in FPGAs with Kalman Filter Case Study

NASA Astrophysics Data System (ADS)

Bigdeli, Abbas; Biglari-Abhari, Morteza; Salcic, Zoran; Tin Lai, Yat

2006-12-01

A new pipelined systolic array-based (PSA) architecture for matrix inversion is proposed. The pipelined systolic array (PSA) architecture is suitable for FPGA implementations as it efficiently uses available resources of an FPGA. It is scalable for different matrix size and as such allows employing parameterisation that makes it suitable for customisation for application-specific needs. This new architecture has an advantage of[InlineEquation not available: see fulltext.] processing element complexity, compared to the[InlineEquation not available: see fulltext.] in other systolic array structures, where the size of the input matrix is given by[InlineEquation not available: see fulltext.]. The use of the PSA architecture for Kalman filter as an implementation example, which requires different structures for different number of states, is illustrated. The resulting precision error is analysed and shown to be negligible.

Influence of the finite linewidth of the laser radiation spectrum on the shape of the coherent population trapping resonance line in an optically dense medium with a buffer gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barantsev, K. A., E-mail: kostmann@yandex.ru; Popov, E. N.; Litvinov, A. N., E-mail: andrey.litvinov@mail.ru

2015-11-15

The theory of coherent population trapping resonance is developed for the finite linewidth of the laser radiation spectrum in an optically dense medium of Λ atoms in a cell with a buffer gas. Equations are derived for the atomic density matrix and laser emission spectrum transfer in a cell with working and buffer gases at a finite temperature. The dependence of the quality factor of coherent population trapping resonance on the linewidth of the laser radiation spectrum is studied by measuring transmitted radiation and fluorescence signals.

Microscopic nonlinear relativistic quantum theory of absorption of powerful x-ray radiation in plasma.

PubMed

Avetissian, H K; Ghazaryan, A G; Matevosyan, H H; Mkrtchian, G F

2015-10-01

The microscopic quantum theory of plasma nonlinear interaction with the coherent shortwave electromagnetic radiation of arbitrary intensity is developed. The Liouville-von Neumann equation for the density matrix is solved analytically considering a wave field exactly and a scattering potential of plasma ions as a perturbation. With the help of this solution we calculate the nonlinear inverse-bremsstrahlung absorption rate for a grand canonical ensemble of electrons. The latter is studied in Maxwellian, as well as in degenerate quantum plasma for x-ray lasers at superhigh intensities and it is shown that one can achieve the efficient absorption coefficient in these cases.

Partition of volatile organic compounds from air and from water into plant cuticular matrix: An LFER analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Platts, J.A.; Abraham, M.H.

The partitioning of organic compounds between air and foliage and between water and foliage is of considerable environmental interest. The purpose of this work is to show that partitioning into the cuticular matrix of one particular species can be satisfactorily modeled by general equations the authors have previously developed and, hence, that the same general equations could be used to model partitioning into other plant materials of the same or different species. The general equations are linear free energy relationships that employ descriptors for polarity/polarizability, hydrogen bond acidity and basicity, dispersive effects, and volume. They have been applied to themore » partition of 62 very varied organic compounds between cuticular matrix of the tomato fruit, Lycopersicon esculentum, and either air (MX{sub a}) or water (MX{sub w}). Values of log MX{sub a} covering a range of 12.4 log units are correlated with a standard deviation of 0.232 log unit, and values of log MX{sub w} covering a range of 7.6 log unit are correlated with an SD of 0.236 log unit. Possibilities are discussed for the prediction of new air-plant cuticular matrix and water-plant cuticular matrix partition values on the basis of the equations developed.« less

A vector-dyadic development of the equations of motion for N-coupled flexible bodies and point masses. [spacecraft trajectories

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1975-01-01

The equations of motion for a system of coupled flexible bodies, rigid bodies, point masses, and symmetric wheels were derived. The equations were cast into a partitioned matrix form in which certain partitions became nontrivial when the effects of flexibility were treated. The equations are shown to contract to the coupled rigid body equations or expand to the coupled flexible body equations all within the same basic framework. Furthermore, the coefficient matrix always has the computationally desirable property of symmetry. Making use of the derived equations, a comparison was made between the equations which described a flexible body model and those which described a rigid body model of the same elastic appendage attached to an arbitrary coupled body system. From the comparison, equivalence relations were developed which defined how the two modeling approaches described identical dynamic effects.

[Evaluation of the Peusner's coefficients matrix for polymeric membrane and ternary non-electrolyte solutions].

PubMed

Jasik-Slęzak, Jolanta; Slęzak-Prochazka, Izabella; Slęzak, Andrzej

2014-01-01

A system of network forms of Kedem-Katchalsky (K-K) equations for ternary non-electrolyte solutions is made of eight matrix equations containing Peusner's coefficients R(ij), L(ij), H(ij), W(ij), K(ij), N(ij), S(ij) or P(ij) (i, j ∈ {1, 2, 3}). The equations are the result of symmetric or hybrid transformation of the classic form of K-K equations by the use of methods of Peusner's network thermodynamics (PNT). Calculating concentration dependences of the determinant of Peusner's coefficients matrixes R(ij), L(ij), H(ij), W(ij), S(ij), N(ij), K(ij) and P(ij) (i, j ∈ {1, 2, 3}). The material used in the experiment was a hemodialysis Nephrophan membrane with specified transport properties (L(p), σ, Ω) in aqueous glucose and ethanol solution. The method involved equations for determinants of the matrixes coefficients R(ij), L(ij), H(ij), W(ij), S(ij), N(ij), K(ij) or P(ij) (i, j ∈ {1, 2, 3}). The objective of calculations were dependences of determinants of Peusner's coeffcients matrixes R(ij), L(ij), H(ij), W(ij), S(ij), N(ij), K(ij) or P(ij) (i, j ∈ {1, 2, 3}) within the conditions of solution homogeneity upon an average concentration of one component of solution in the membrane (C1) with a determined value of the second component (C2). The method of calculating the determinants of Peusner's coeffcients matrixes R(ij), L(ij), H(ij), W(ij), S(ij), N(ij), K(ij) or P(ij) (i, j ∈ {1, 2, 3}) is a new tool that may be applicable in studies on membrane transport. Calculations showed that the coefficients are sensitive to concentration and composition of solutions separated by a polymeric membrane.

Surface Snow Density of East Antarctica Derived from In-Situ Observations

NASA Astrophysics Data System (ADS)

Tian, Y.; Zhang, S.; Du, W.; Chen, J.; Xie, H.; Tong, X.; Li, R.

2018-04-01

Models based on physical principles or semi-empirical parameterizations have used to compute the firn density, which is essential for the study of surface processes in the Antarctic ice sheet. However, parameterization of surface snow density is often challenged by the description of detailed local characterization. In this study we propose to generate a surface density map for East Antarctica from all the filed observations that are available. Considering that the observations are non-uniformly distributed around East Antarctica, obtained by different methods, and temporally inhomogeneous, the field observations are used to establish an initial density map with a grid size of 30 × 30 km2 in which the observations are averaged at a temporal scale of five years. We then construct an observation matrix with its columns as the map grids and rows as the temporal scale. If a site has an unknown density value for a period, we will set it to 0 in the matrix. In order to construct the main spatial and temple information of surface snow density matrix we adopt Empirical Orthogonal Function (EOF) method to decompose the observation matrix and only take first several lower-order modes, because these modes already contain most information of the observation matrix. However, there are a lot of zeros in the matrix and we solve it by using matrix completion algorithm, and then we derive the time series of surface snow density at each observation site. Finally, we can obtain the surface snow density by multiplying the modes interpolated by kriging with the corresponding amplitude of the modes. Comparative analysis have done between our surface snow density map and model results. The above details will be introduced in the paper.

A new Newton-like method for solving nonlinear equations.

PubMed

Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

2016-01-01

This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

Computer programs for the solution of systems of linear algebraic equations

NASA Technical Reports Server (NTRS)

Sequi, W. T.

1973-01-01

FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou Tao, E-mail: tzhou@lsec.cc.ac.c; Tang Tao, E-mail: ttang@hkbu.edu.h

2010-11-01

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy

NASA Astrophysics Data System (ADS)

Li, Chunxia; Li, Shi-Hao

2018-06-01

This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable hierarchy with the help of orthogonal polynomial theory and Toda-type equations. Starting from the symmetric reduction in Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the τ -function of the CKP hierarchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.

Effects of increased collagen-matrix density on the mechanical properties and in vivo absorbability of hydroxyapatite-collagen composites as artificial bone materials.

PubMed

Yunoki, Shunji; Sugiura, Hiroaki; Ikoma, Toshiyuki; Kondo, Eiji; Yasuda, Kazunori; Tanaka, Junzo

2011-02-01

The aim of this study was to evaluate the effects of increased collagen-matrix density on the mechanical properties and in vivo absorbability of porous hydroxyapatite (HAp)-collagen composites as artificial bone materials. Seven types of porous HAp-collagen composites were prepared from HAp nanocrystals and dense collagen fibrils. Their densities and HAp/collagen weight ratios ranged from 122 to 331 mg cm⁻³ and from 20/80 to 80/20, respectively. The flexural modulus and strength increased with an increase in density, reaching 2.46 ± 0.48 and 0.651 ± 0.103 MPa, respectively. The porous composites with a higher collagen-matrix density exhibited much higher mechanical properties at the same densities, suggesting that increasing the collagen-matrix density is an effective way of improving the mechanical properties. It was also suggested that other structural factors in addition to collagen-matrix density are required to achieve bone-like mechanical properties. The in vivo absorbability of the composites was investigated in bone defects of rabbit femurs, demonstrating that the absorption rate decreased with increases in the composite density. An exhaustive increase in density is probably limited by decreases in absorbability as artificial bones.

Beating the curse of dimension with accurate statistics for the Fokker-Planck equation in complex turbulent systems.

PubMed

Chen, Nan; Majda, Andrew J

2017-12-05

Solving the Fokker-Planck equation for high-dimensional complex dynamical systems is an important issue. Recently, the authors developed efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures, which contain many strong non-Gaussian features such as intermittency and fat-tailed probability density functions (PDFs). The algorithms involve a hybrid strategy with a small number of samples [Formula: see text], where a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious Gaussian kernel density estimation in the remaining low-dimensional subspace. In this article, two effective strategies are developed and incorporated into these algorithms. The first strategy involves a judicious block decomposition of the conditional covariance matrix such that the evolutions of different blocks have no interactions, which allows an extremely efficient parallel computation due to the small size of each individual block. The second strategy exploits statistical symmetry for a further reduction of [Formula: see text] The resulting algorithms can efficiently solve the Fokker-Planck equation with strongly non-Gaussian PDFs in much higher dimensions even with orders in the millions and thus beat the curse of dimension. The algorithms are applied to a [Formula: see text]-dimensional stochastic coupled FitzHugh-Nagumo model for excitable media. An accurate recovery of both the transient and equilibrium non-Gaussian PDFs requires only [Formula: see text] samples! In addition, the block decomposition facilitates the algorithms to efficiently capture the distinct non-Gaussian features at different locations in a [Formula: see text]-dimensional two-layer inhomogeneous Lorenz 96 model, using only [Formula: see text] samples. Copyright © 2017 the Author(s). Published by PNAS.

Acoustic 3D modeling by the method of integral equations

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2018-02-01

This paper presents a parallel algorithm for frequency-domain acoustic modeling by the method of integral equations (IE). The algorithm is applied to seismic simulation. The IE method reduces the size of the problem but leads to a dense system matrix. A tolerable memory consumption and numerical complexity were achieved by applying an iterative solver, accompanied by an effective matrix-vector multiplication operation, based on the fast Fourier transform (FFT). We demonstrate that, the IE system matrix is better conditioned than that of the finite-difference (FD) method, and discuss its relation to a specially preconditioned FD matrix. We considered several methods of matrix-vector multiplication for the free-space and layered host models. The developed algorithm and computer code were benchmarked against the FD time-domain solution. It was demonstrated that, the method could accurately calculate the seismic field for the models with sharp material boundaries and a point source and receiver located close to the free surface. We used OpenMP to speed up the matrix-vector multiplication, while MPI was used to speed up the solution of the system equations, and also for parallelizing across multiple sources. The practical examples and efficiency tests are presented as well.

Phenomenological QCD equation of state for massive neutron stars

DOE PAGES

Kojo, Toru; Powell, Philip D.; Song, Yifan; ...

2015-02-03

Here, we construct an equation of state for massive neutron stars based on quantum chromodynamics phenomenology. Our primary purpose is to delineate the relevant ingredients of equations of state that simultaneously have the required stiffness and satisfy constraints from thermodynamics and causality. These ingredients are (i) a repulsive density-density interaction, universal for all flavors, (ii) the color-magnetic interaction active from low to high densities, (iii) confining effects, which become increasingly important as the baryon density decreases, and (iv) nonperturbative gluons, which are not very sensitive to changes of the quark density. We use the following “3-window” description: At baryon densitiesmore » below about twice normal nuclear density, 2n 0, we use the Akmal-Pandharipande-Ravenhall (APR) equation of state, and at high densities, ≥(4–7)n 0, we use the three-flavor Nambu-Jona-Lasinio (NJL) model supplemented by vector and diquark interactions. In the transition density region, we smoothly interpolate the hadronic and quark equations of state in the chemical potential-pressure plane. Requiring that the equation of state approach APR at low densities, we find that the quark pressure in nonconfining models can be larger than the hadronic pressure, unlike in conventional equations of state. We show that consistent equations of state of stiffness sufficient to allow massive neutron stars are reasonably tightly constrained, suggesting that gluon dynamics remains nonperturbative even at baryon densities ~10n 0.« less

Direct Measurement of the Density Matrix of a Quantum System

NASA Astrophysics Data System (ADS)

Thekkadath, G. S.; Giner, L.; Chalich, Y.; Horton, M. J.; Banker, J.; Lundeen, J. S.

2016-09-01

One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.

Direct Measurement of the Density Matrix of a Quantum System.

PubMed

Thekkadath, G S; Giner, L; Chalich, Y; Horton, M J; Banker, J; Lundeen, J S

2016-09-16

One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.

Derivation of stiffness matrix in constitutive modeling of magnetorheological elastomer

NASA Astrophysics Data System (ADS)

Leng, D.; Sun, L.; Sun, J.; Lin, Y.

2013-02-01

Magnetorheological elastomers (MREs) are a class of smart materials whose mechanical properties change instantly by the application of a magnetic field. Based on the specially orthotropic, transversely isotropic stress-strain relationships and effective permeability model, the stiffness matrix of constitutive equations for deformable chain-like MRE is considered. To valid the components of shear modulus in this stiffness matrix, the magnetic-structural simulations with finite element method (FEM) are presented. An acceptable agreement is illustrated between analytical equations and numerical simulations. For the specified magnetic field, sphere particle radius, distance between adjacent particles in chains and volume fractions of ferrous particles, this constitutive equation is effective to engineering application to estimate the elastic behaviour of chain-like MRE in an external magnetic field.

Prompt charmonia production and polarization at the LHC in the NRQCD with kT-factorization. III. J /ψ meson

NASA Astrophysics Data System (ADS)

Baranov, S. P.; Lipatov, A. V.

2017-08-01

In the framework of the kT-factorization approach, the production and polarization of prompt J /ψ mesons at the LHC energies is studied. Our consideration is based on the nonrelativistic QCD formalism for bound states and off-shell amplitudes for hard partonic subprocesses. Both the direct production mechanism and feed-down contributions from χc and ψ (2 S ) decays are taken into account. The transverse momentum dependent (or unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. The nonperturbative color-octet matrix elements were first deduced from the fits to the latest CMS data on J /ψ transverse momentum distributions and then applied to describe the ATLAS and LHCb data on J /ψ production and polarization at √{s }=7 , 8 and 13 TeV. We perform an estimation of polarization parameters λθ, λϕ, and λθ ϕ which determine J /ψ spin density matrix and demonstrate that treating the soft gluon emission as a series of explicit color-electric dipole transitions within NRQCD leads to unpolarized J /ψ production at high transverse momenta, that is in qualitative agreement with the LHC data.

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

PubMed

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.

Relative Contribution of Matrix Structure, Patch Resources and Management to the Local Densities of Two Large Blue Butterfly Species

PubMed Central

Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal

2016-01-01

The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011–12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales. PMID:28005942

Relative Contribution of Matrix Structure, Patch Resources and Management to the Local Densities of Two Large Blue Butterfly Species.

PubMed

Kajzer-Bonk, Joanna; Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal

2016-01-01

The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011-12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales.

Water in the presence of inert Lennard-Jones obstacles

NASA Astrophysics Data System (ADS)

Kurtjak, Mario; Urbic, Tomaz

2014-04-01

Water confined by the presence of a 'sea' of inert obstacles was examined. In the article, freely mobile two-dimensional Mercedes-Benz (MB) water put to a disordered, but fixed, matrix of Lennard-Jones disks was studied by the Monte Carlo computer simulations. For the MB water molecules in the matrix of Lennard-Jones disks, we explored the structures, hydrogen-bond-network formation and thermodynamics as a function of temperature and size and density of matrix particles. We found that the structure of model water is perturbed by the presence of the obstacles. Density of confined water, which was in equilibrium with the bulk water, was smaller than the density of the bulk water and the temperature dependence of the density of absorbed water did not show the density anomaly in the studied temperature range. The behaviour observed as a consequence of confinement is similar to that of increasing temperature, which can for a matrix lead to a process similar to capillary evaporation. At the same occupancy of space, smaller matrix molecules cause higher destruction effect on the absorbed water molecules than the bigger ones. We have also tested the hypothesis that at low matrix densities the obstacles induce an increased ordering and 'hydrogen bonding' of the MB model molecules, relative to pure fluid, while at high densities the obstacles reduce MB water structuring, as they prevent the fluid to form good 'hydrogen-bonding' networks. However, for the size of matrix molecules similar to that of water, we did not observe this effect.

Leptonic CP phase determined by an equation involving PMNS matrix elements

NASA Astrophysics Data System (ADS)

Ke, Hong-Wei; Zhou, Jia-Hui; Li, Xue-Qian

2017-04-01

Several approximate equalities among the matrix elements of the Cabibbo-Kobayashi-Maskawa (CKM) and Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrices imply that hidden symmetries may exist and be common for both quark and neutrino sectors. The charge parity (CP) phase of the CKM matrix ({δ }{CKM}) is involved in these equalities and can be investigated when these equalities turn into several equations. As we substitute those experimentally measured values of the three mixing angles into the equations for quarks, it is noted that one of the equations which holds exactly has a solution {δ }{CKM}=({68.95}-1.15+1.15)^\\circ . That value accords with ({69.1}-3.85+2.02)^\\circ determined from available data. Generalizing the scenario to the lepton sector, the same equality determines the leptonic CP phase {δ }{PMNS} to be ({275.20}-1.15+1.15)^\\circ . Thus we predict the value of {δ }{PMNS} from the equation. So far there is no direct measurement on {δ }{PMNS}, but a recent analysis based on the neutrino oscillation data prefers a phase close to 270°.

Coupled bending-torsion steady-state response of pretwisted, nonuniform rotating beams using a transfer-matrix method

NASA Technical Reports Server (NTRS)

Gray, Carl E., Jr.

1988-01-01

Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with functionally graded interlayers.

PubMed

Guo, Xiao; Wei, Peijun; Lan, Man; Li, Li

2016-08-01

The effects of functionally graded interlayers on dispersion relations of elastic waves in a one-dimensional piezoelectric/piezomagnetic phononic crystal are studied in this paper. First, the state transfer equation of the functionally graded interlayer is derived from the motion equation by the reduction of order (from second order to first order). The transfer matrix of the functionally graded interlayer is obtained by solving the state transfer equation with the spatial-varying coefficient. Based on the transfer matrixes of the piezoelectric slab, the piezomagnetic slab and the functionally graded interlayers, the total transfer matrix of a single cell is obtained. Further, the Bloch theorem is used to obtain the resultant dispersion equations of in-plane and anti-plane Bloch waves. The dispersion equations are solved numerically and the numerical results are shown graphically. Five kinds of profiles of functionally graded interlayers between a piezoelectric slab and a piezomagnetic slab are considered. It is shown that the functionally graded interlayers have evident influences on the dispersion curves and the band gaps. Copyright © 2016 Elsevier B.V. All rights reserved.

Calculation of biochemical net reactions and pathways by using matrix operations.

PubMed Central

Alberty, R A

1996-01-01

Pathways for net biochemical reactions can be calculated by using a computer program that solves systems of linear equations. The coefficients in the linear equations are the stoichiometric numbers in the biochemical equations for the system. The solution of the system of linear equations is a vector of the stoichiometric numbers of the reactions in the pathway for the net reaction; this is referred to as the pathway vector. The pathway vector gives the number of times the various reactions have to occur to produce the desired net reaction. Net reactions may involve unknown numbers of ATP, ADP, and Pi molecules. The numbers of ATP, ADP, and Pi in a desired net reaction can be calculated in a two-step process. In the first step, the pathway is calculated by solving the system of linear equations for an abbreviated stoichiometric number matrix without ATP, ADP, Pi, NADred, and NADox. In the second step, the stoichiometric numbers in the desired net reaction, which includes ATP, ADP, Pi, NADred, and NADox, are obtained by multiplying the full stoichiometric number matrix by the calculated pathway vector. PMID:8804633

Proposed framework for thermomechanical life modeling of metal matrix composites

NASA Technical Reports Server (NTRS)

Halford, Gary R.; Lerch, Bradley A.; Saltsman, James F.

1993-01-01

The framework of a mechanics of materials model is proposed for thermomechanical fatigue (TMF) life prediction of unidirectional, continuous-fiber metal matrix composites (MMC's). Axially loaded MMC test samples are analyzed as structural components whose fatigue lives are governed by local stress-strain conditions resulting from combined interactions of the matrix, interfacial layer, and fiber constituents. The metallic matrix is identified as the vehicle for tracking fatigue crack initiation and propagation. The proposed framework has three major elements. First, TMF flow and failure characteristics of in situ matrix material are approximated from tests of unreinforced matrix material, and matrix TMF life prediction equations are numerically calibrated. The macrocrack initiation fatigue life of the matrix material is divided into microcrack initiation and microcrack propagation phases. Second, the influencing factors created by the presence of fibers and interfaces are analyzed, characterized, and documented in equation form. Some of the influences act on the microcrack initiation portion of the matrix fatigue life, others on the microcrack propagation life, while some affect both. Influencing factors include coefficient of thermal expansion mismatch strains, residual (mean) stresses, multiaxial stress states, off-axis fibers, internal stress concentrations, multiple initiation sites, nonuniform fiber spacing, fiber debonding, interfacial layers and cracking, fractured fibers, fiber deflections of crack fronts, fiber bridging of matrix cracks, and internal oxidation along internal interfaces. Equations exist for some, but not all, of the currently identified influencing factors. The third element is the inclusion of overriding influences such as maximum tensile strain limits of brittle fibers that could cause local fractures and ensuing catastrophic failure of surrounding matrix material. Some experimental data exist for assessing the plausibility of the proposed framework.

Three-Dimensional Effects of Crack Closure in Laminated Composite Plates Subjected to Bending Loads

DTIC Science & Technology

1994-06-01

Approved by: •UW. Kwon, Thesis Advisor wathe D.K~elleher, Chairman Department of Mechanical Engineering ii ABSTRACT Fracture is one of the dominant...5 A. OVERVIEW .......................................... 5 B. CONSTITUTIVE EQUATION .............................. 9 1. Isotropic...the elemental nodes. B. CONSTITUTIVE EQUATION The material property matrix [D] is a symmetric matrix which includes elasticity moduli and Poisson’s

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Predicting Fatigue Lives Of Metal-Matrix/Fiber Composites

NASA Technical Reports Server (NTRS)

Bartolotta, Paul A.

1994-01-01

Method of prediction of fatigue lives of intermetallic-matrix/fiber composite parts at high temperatures styled after method of universal slopes. It suffices to perform relatively small numbers of fatigue tests. Data from fatigue tests correlated with tensile-test data by fitting universal-slopes equation to both sets of data. Thereafter, universal-slopes equation used to predict fatigue lives from tensile properties.

Hybrid state vector methods for structural dynamic and aeroelastic boundary value problems

NASA Technical Reports Server (NTRS)

Lehman, L. L.

1982-01-01

A computational technique is developed that is suitable for performing preliminary design aeroelastic and structural dynamic analyses of large aspect ratio lifting surfaces. The method proves to be quite general and can be adapted to solving various two point boundary value problems. The solution method, which is applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. A mixed variational formulation is presented that conveniently yields a useful form for these state vector differential equations. Solutions to these equations are obtained by employing an integrating matrix method. The application of an integrating matrix provides a discretization of the differential equations that only requires solutions of standard linear matrix systems. It is demonstrated that matrix partitioning can be used to reduce the order of the required solutions. Results are presented for several example problems in structural dynamics and aeroelasticity to verify the technique and to demonstrate its use. These problems examine various types of loading and boundary conditions and include aeroelastic analyses of lifting surfaces constructed from anisotropic composite materials.

A momentum-space formulation without partial wave decomposition for scattering of two spin-half particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fachruddin, Imam, E-mail: imam.fachruddin@sci.ui.ac.id; Salam, Agus

2016-03-11

A new momentum-space formulation for scattering of two spin-half particles, both either identical or unidentical, is formulated. As basis states the free linear-momentum states are not expanded into the angular-momentum states, the system’s spin states are described by the product of the spin states of the two particles, and the system’s isospin states by the total isospin states of the two particles. We evaluate the Lippmann-Schwinger equations for the T-matrix elements in these basis states. The azimuthal behavior of the potential and of the T-matrix elements leads to a set of coupled integral equations for the T-matrix elements in twomore » variables only, which are the magnitude of the relative momentum and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved. A set of six spin operators to express any interaction of two spin-half particles is introduced. We show the spin-averaged differential cross section as being calculated in terms of the solution of the set of the integral equations.« less

Method for making 2-electron response reduced density matrices approximately N-representable

NASA Astrophysics Data System (ADS)

Lanssens, Caitlin; Ayers, Paul W.; Van Neck, Dimitri; De Baerdemacker, Stijn; Gunst, Klaas; Bultinck, Patrick

2018-02-01

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it fulfills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.

Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

NASA Astrophysics Data System (ADS)

Vogl, M.; Pankratov, O.; Shallcross, S.

2017-07-01

We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

Linear stability analysis of the Vlasov-Poisson equations in high density plasmas in the presence of crossed fields and density gradients

NASA Technical Reports Server (NTRS)

Kaup, D. J.; Hansen, P. J.; Choudhury, S. Roy; Thomas, Gary E.

1986-01-01

The equations for the single-particle orbits in a nonneutral high density plasma in the presence of inhomogeneous crossed fields are obtained. Using these orbits, the linearized Vlasov equation is solved as an expansion in the orbital radii in the presence of inhomogeneities and density gradients. A model distribution function is introduced whose cold-fluid limit is exactly the same as that used in many previous studies of the cold-fluid equations. This model function is used to reduce the linearized Vlasov-Poisson equations to a second-order ordinary differential equation for the linearized electrostatic potential whose eigenvalue is the perturbation frequency.

Kohn-Sham potentials from electron densities using a matrix representation within finite atomic orbital basis sets

NASA Astrophysics Data System (ADS)

Zhang, Xing; Carter, Emily A.

2018-01-01

We revisit the static response function-based Kohn-Sham (KS) inversion procedure for determining the KS effective potential that corresponds to a given target electron density within finite atomic orbital basis sets. Instead of expanding the potential in an auxiliary basis set, we directly update the potential in its matrix representation. Through numerical examples, we show that the reconstructed density rapidly converges to the target density. Preliminary results are presented to illustrate the possibility of obtaining a local potential in real space from the optimized potential in its matrix representation. We have further applied this matrix-based KS inversion approach to density functional embedding theory. A proof-of-concept study of a solvated proton transfer reaction demonstrates the method's promise.

Generating Nice Linear Systems for Matrix Gaussian Elimination

ERIC Educational Resources Information Center

Homewood, L. James

2004-01-01

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

METal matrix composite ANalyzer (METCAN): Theoretical manual

NASA Technical Reports Server (NTRS)

Murthy, P. L. N.; Chamis, C. C.

1993-01-01

This manuscript is intended to be a companion volume to the 'METCAN User's Manual' and the 'METAN Demonstration Manual.' The primary purpose of the manual is to give details pertaining to micromechanics and macromechanics equations of high temperature metal matrix composites that are programmed in the METCAN computer code. The subroutines which contain the programmed equations are also mentioned in order to facilitate any future changes or modifications that the user may intend to incorporate in the code. Assumptions and derivations leading to the micromechanics equations are briefly mentioned.

Solving periodic block tridiagonal systems using the Sherman-Morrison-Woodbury formula

NASA Technical Reports Server (NTRS)

Yarrow, Maurice

1989-01-01

Many algorithms for solving the Navier-Stokes equations require the solution of periodic block tridiagonal systems of equations. By applying a splitting to the matrix representing this system of equations, it may first be reduced to a block tridiagonal matrix plus an outer product of two block vectors. The Sherman-Morrison-Woodbury formula is then applied. The algorithm thus reduces a periodic banded system to a non-periodic banded system with additional right-hand sides and is of higher efficiency than standard Thomas algorithm/LU decompositions.

Linear and Nonlinear Optical Properties of Spherical Quantum Dots: Effects of Hydrogenic Impurity and Conduction Band Non-Parabolicity

NASA Astrophysics Data System (ADS)

Rezaei, G.; Vaseghi, B.; Doostimotlagh, N. A.

2012-03-01

Simultaneous effects of an on-center hydrogenic impurity and band edge non-parabolicity on intersubband optical absorption coefficients and refractive index changes of a typical GaAs/AlxGa1-x As spherical quantum dot are theoretically investigated, using the Luttinger—Kohn effective mass equation. So, electronic structure and optical properties of the system are studied by means of the matrix diagonalization technique and compact density matrix approach, respectively. Finally, effects of an impurity, band edge non-parabolicity, incident light intensity and the dot size on the linear, the third-order nonlinear and the total optical absorption coefficients and refractive index changes are investigated. Our results indicate that, the magnitudes of these optical quantities increase and their peaks shift to higher energies as the influences of the impurity and the band edge non-parabolicity are considered. Moreover, incident light intensity and the dot size have considerable effects on the optical absorption coefficients and refractive index changes.

Fully nonlocal inelastic scattering computations for spectroscopical transmission electron microscopy methods

NASA Astrophysics Data System (ADS)

Rusz, Ján; Lubk, Axel; Spiegelberg, Jakob; Tyutyunnikov, Dmitry

2017-12-01

The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major approaches to calculate inelastic scattering cross sections of fast electrons on crystals—Yoshioka-equations-based forward propagation and the reciprocal wave method—are founded in two conceptually differing schemes—a numerical forward integration of each inelastically scattered wave function, yielding the exit density matrix, and a computation of inelastic scattering matrix elements using elastically scattered initial and final states (double channeling). Here, we compare both approaches and show that the latter is computationally competitive to the former by exploiting analytical integration schemes over multiple excited states. Moreover, we show how to include full nonlocality of the inelastic scattering event, neglected in the forward propagation approaches, at no additional computing costs in the reciprocal wave method. Detailed simulations show in some cases significant errors due to the z -locality approximation and hence pitfalls in the interpretation of spectroscopical TEM results.

Acoustooptic linear algebra processors - Architectures, algorithms, and applications

NASA Technical Reports Server (NTRS)

Casasent, D.

1984-01-01

Architectures, algorithms, and applications for systolic processors are described with attention to the realization of parallel algorithms on various optical systolic array processors. Systolic processors for matrices with special structure and matrices of general structure, and the realization of matrix-vector, matrix-matrix, and triple-matrix products and such architectures are described. Parallel algorithms for direct and indirect solutions to systems of linear algebraic equations and their implementation on optical systolic processors are detailed with attention to the pipelining and flow of data and operations. Parallel algorithms and their optical realization for LU and QR matrix decomposition are specifically detailed. These represent the fundamental operations necessary in the implementation of least squares, eigenvalue, and SVD solutions. Specific applications (e.g., the solution of partial differential equations, adaptive noise cancellation, and optimal control) are described to typify the use of matrix processors in modern advanced signal processing.

A T Matrix Method Based upon Scalar Basis Functions

NASA Technical Reports Server (NTRS)

Mackowski, D.W.; Kahnert, F. M.; Mishchenko, Michael I.

2013-01-01

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

Simulation of naturally fractured reservoirs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saidi, A.M.

1983-11-01

A three-dimensional, three-phase reservoir simulator was developed to study the behavior of fully or partially fractured reservoirs. It is also demonstrated, that when a fractured reservoir is subject to a relatively large rate of pressure drop and/or it composed of relatively large blocks, the pseudo steady-state pressure concept gives large errors as compared with transient fromulation. In addition, when gravity drainage and imbibitum processes, which is the most important mechanism in the fractured reservoirs, are represented by a ''lumped parameter'' even larger errors can be produced in exchange flow between matrix and fractures. For these reasons, the matrix blocks aremore » gridded and the transfer between matrix and fractures are calculated using pressure and diffusion transient concept. In this way the gravity drainage is also calculated accurately. As the matrix-fracture exchange flow depends on the location of each matrix grid relative to the GOC and/or WOC in fracture, the exchange flow equation are derived and given for each possible case. The differential equation describing the flow of water, oil, and gas within the matrix and fracture system, each of which may contain six unknowns, are presented. The two sets of equations are solved implicitly for pressure water, and gas stauration in both matrix and fractures. The first twenty two years of the history of Haft Kel field was successfully matched with this model and the results are included.« less

On Schrödinger's bridge problem

NASA Astrophysics Data System (ADS)

Friedland, S.

2017-11-01

In the first part of this paper we generalize Georgiou-Pavon's result that a positive square matrix can be scaled uniquely to a column stochastic matrix which maps a given positive probability vector to another given positive probability vector. In the second part we prove that a positive quantum channel can be scaled to another positive quantum channel which maps a given positive definite density matrix to another given positive definite density matrix using Brouwer's fixed point theorem. This result proves the Georgiou-Pavon conjecture for two positive definite density matrices, made in their recent paper. We show that the fixed points are unique for certain pairs of positive definite density matrices. Bibliography: 15 titles.

Towards the development of micromechanics equations for ceramic matrix composites via fiber substructuring

NASA Technical Reports Server (NTRS)

Murthy, P. L. N.; Chamis, C. C.

1992-01-01

A generic unit cell model which includes a unique fiber substructuring concept is proposed for the development of micromechanics equations for continuous fiber reinforcement ceramic composites. The unit cell consists of three constituents: fiber, matrix, and an interphase. In the present approach, the unit cell is further subdivided into several slices and the equations of micromechanics are derived for each slice. These are subsequently integrated to obtain ply level properties. A stand alone computer code containing the micromechanics model as a module is currently being developed specifically for the analysis of ceramic matrix composites. Towards this development, equivalent ply property results for a SiC/Ti-15-3 composite with 0.5 fiber volume ratio are presented and compared with those obtained from customary micromechanics models to illustrate the concept. Also, comparisons with limited experimental data for the ceramic matrix composite, SiC/RBSN (Reaction Bonded Silicon Nitride) with a 0.3 fiber volume ratio are given to validate the concepts.

An efficient numerical method for the solution of the problem of elasticity for 3D-homogeneous elastic medium with cracks and inclusions

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices.

Carbon isotope composition of ambient CO2 and recycling: a matrix simulation model

USGS Publications Warehouse

da Silveira Lobo Sternberg, Leonel; DeAngelis, Donald L.

2002-01-01

The relationship between isotopic composition and concentration of ambient CO2 in a canopy and its associated convective boundary layer was modeled. The model divides the canopy and convective boundary layer into several layers. Photosynthesis, respiration, and exchange between each layer can be simulated by matrix equations. This simulation can be used to calculate recycling; defined here as the amount of respired CO2 re-fixed by photosynthesis relative to the total amount of respired CO2. At steady state the matrix equations can be solved for the canopy and convective boundary layer CO2 concentration and isotopic profile, which can be used to calculate a theoretical recycling index according to a previously developed equation. There is complete agreement between simulated and theoretical recycling indices for different exchange scenarios. Recycling indices from a simulation of gas exchange between a heterogeneous vegetation canopy and the troposphere also agreed with a more generalized form of the theoretical recycling equation developed here.

Equations of motion for a spectrum-generating algebra: Lipkin Meshkov Glick model

NASA Astrophysics Data System (ADS)

Rosensteel, G.; Rowe, D. J.; Ho, S. Y.

2008-01-01

For a spectrum-generating Lie algebra, a generalized equations-of-motion scheme determines numerical values of excitation energies and algebra matrix elements. In the approach to the infinite particle number limit or, more generally, whenever the dimension of the quantum state space is very large, the equations-of-motion method may achieve results that are impractical to obtain by diagonalization of the Hamiltonian matrix. To test the method's effectiveness, we apply it to the well-known Lipkin-Meshkov-Glick (LMG) model to find its low-energy spectrum and associated generator matrix elements in the eigenenergy basis. When the dimension of the LMG representation space is 106, computation time on a notebook computer is a few minutes. For a large particle number in the LMG model, the low-energy spectrum makes a quantum phase transition from a nondegenerate harmonic vibrator to a twofold degenerate harmonic oscillator. The equations-of-motion method computes critical exponents at the transition point.

Overview of Krylov subspace methods with applications to control problems

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

An overview of projection methods based on Krylov subspaces are given with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylov subspace methods is to generate a basis of the Krylov subspace Span and seek an approximate solution the the original problem from this subspace. Thus, the original matrix problem of size N is approximated by one of dimension m typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now just becoming popular for solving nonlinear equations. It is shown how they can be used to solve partial pole placement problems, Sylvester's equation, and Lyapunov's equation.

Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane-Emden type

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.; Youssri, Y. H.

2013-10-01

In this paper, we present a new second kind Chebyshev (S2KC) operational matrix of derivatives. With the aid of S2KC, an algorithm is described to obtain numerical solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems (IVPs). The idea of obtaining such solutions is essentially based on reducing the differential equation with its initial conditions to a system of algebraic equations. Two illustrative examples concern relevant physical problems (the Lane-Emden equations of the first and second kind) are discussed to demonstrate the validity and applicability of the suggested algorithm. Numerical results obtained are comparing favorably with the analytical known solutions.

Information loss in effective field theory: Entanglement and thermal entropies

NASA Astrophysics Data System (ADS)

Boyanovsky, Daniel

2018-03-01

Integrating out high energy degrees of freedom to yield a low energy effective field theory leads to a loss of information with a concomitant increase in entropy. We obtain the effective field theory of a light scalar field interacting with heavy fields after tracing out the heavy degrees of freedom from the time evolved density matrix. The initial density matrix describes the light field in its ground state and the heavy fields in equilibrium at a common temperature T . For T =0 , we obtain the reduced density matrix in a perturbative expansion; it reveals an emergent mixed state as a consequence of the entanglement between light and heavy fields. We obtain the effective action that determines the time evolution of the reduced density matrix for the light field in a nonperturbative Dyson resummation of one-loop correlations of the heavy fields. The Von-Neumann entanglement entropy associated with the reduced density matrix is obtained for the nonresonant and resonant cases in the asymptotic long time limit. In the nonresonant case the reduced density matrix displays an incipient thermalization albeit with a wave-vector, time and coupling dependent effective temperature as a consequence of memory of initial conditions. The entanglement entropy is time independent and is the thermal entropy for this effective, nonequilibrium temperature. In the resonant case the light field fully thermalizes with the heavy fields, the reduced density matrix loses memory of the initial conditions and the entanglement entropy becomes the thermal entropy of the light field. We discuss the relation between the entanglement entropy ultraviolet divergences and renormalization.

The influence of hyaluronic acid hydrogel crosslinking density and macromolecular diffusivity on human MSC chondrogenesis and hypertrophy.

PubMed

Bian, Liming; Hou, Chieh; Tous, Elena; Rai, Reena; Mauck, Robert L; Burdick, Jason A

2013-01-01

Hyaluronic acid (HA) hydrogels formed via photocrosslinking provide stable 3D hydrogel environments that support the chondrogenesis of mesenchymal stem cells (MSCs). Crosslinking density has a significant impact on the physical properties of hydrogels, including their mechanical stiffness and macromolecular diffusivity. Variations in the HA hydrogel crosslinking density can be obtained by either changes in the HA macromer concentration (1, 3, or 5% w/v at 15 min exposure) or the extent of reaction through light exposure time (5% w/v at 5, 10, or 15 min). In this work, increased crosslinking by either method resulted in an overall decrease in cartilage matrix content and more restricted matrix distribution. Increased crosslinking also promoted hypertrophic differentiation of the chondrogenically induced MSCs, resulting in more matrix calcification in vitro. For example, type X collagen expression in the high crosslinking density 5% 15 min group was ~156 and 285% higher when compared to the low crosslinking density 1% 15 min and 5% 5 min groups on day 42, respectively. Supplementation with inhibitors of the small GTPase pathway involved in cytoskeletal tension or myosin II had no effect on hypertrophic differentiation and matrix calcification, indicating that the differential response is unlikely to be related to force-sensing mechanotransduction mechanisms. When implanted subcutaneously in nude mice, higher crosslinking density again resulted in reduced cartilage matrix content, restricted matrix distribution, and increased matrix calcification. This study demonstrates that hydrogel properties mediated through alterations in crosslinking density must be considered in the context of the hypertrophic differentiation of chondrogenically induced MSCs. Copyright © 2012 Elsevier Ltd. All rights reserved.

Kinetic and spectral descriptions of autoionization phenomena associated with atomic processes in plasmas

NASA Astrophysics Data System (ADS)

Jacobs, Verne L.

2017-06-01

This investigation has been devoted to the theoretical description and computer modeling of atomic processes giving rise to radiative emission in energetic electron and ion beam interactions and in laboratory plasmas. We are also interested in the effects of directed electron and ion collisions and of anisotropic electric and magnetic fields. In the kinetic-theory description, we treat excitation, de-excitation, ionization, and recombination in electron and ion encounters with partially ionized atomic systems, including the indirect contributions from processes involving autoionizing resonances. These fundamental collisional and electromagnetic interactions also provide particle and photon transport mechanisms. From the spectral perspective, the analysis of atomic radiative emission can reveal detailed information on the physical properties in the plasma environment, such as non-equilibrium electron and charge-state distributions as well as electric and magnetic field distributions. In this investigation, a reduced-density-matrix formulation is developed for the microscopic description of atomic electromagnetic interactions in the presence of environmental (collisional and radiative) relaxation and decoherence processes. Our central objective is a fundamental microscopic description of atomic electromagnetic processes, in which both bound-state and autoionization-resonance phenomena can be treated in a unified and self-consistent manner. The time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix approach are developed in a unified and self-consistent manner. This is necessary for our ultimate goal of a systematic and self-consistent treatment of non-equilibrium (possibly coherent) atomic-state kinetics and high-resolution (possibly overlapping) spectral-line shapes. We thereby propose the introduction of a generalized collisional-radiative atomic-state kinetics model based on a reduced-density-matrix formulation. It will become apparent that the full atomic data needs for the precise modeling of extreme non-equilibrium plasma environments extend beyond the conventional radiative-transition-probability and collisional-cross-section data sets.

Entanglement between atomic thermal states and coherent or squeezed photons in a damping cavity

NASA Astrophysics Data System (ADS)

Yadollahi, F.; Safaiee, R.; Golshan, M. M.

2018-02-01

In the present study, the standard Jaynes-Cummings model, in a lossy cavity, is employed to characterize the entanglement between atoms and photons when the former is initially in a thermal state (mixed ensemble) while the latter is described by either coherent or squeezed distributions. The whole system is thus assumed to be in equilibrium with a heat reservoir at a finite temperature T, and the measure of negativity is used to determine the time evolution of atom-photon entanglement. To this end, the master equation for the density matrix, in the secular approximation, is solved and a partial transposition of the result is made. The degree of atom-photon entanglement is then numerically computed, through the negativity, as a function of time and temperature. To justify the behavior of atom-photon entanglement, moreover, we employ the so obtained total density matrix to compute and analyze the time evolution of the initial photonic coherent or squeezed probability distributions and the squeezing parameters. On more practical points, our results demonstrate that as the initial photon mean number increases, the atom-photon entanglement decays at a faster pace for the coherent distribution compared to the squeezed one. Moreover, it is shown that the degree of atom-photon entanglement is much higher and more stable for the squeezed distribution than that for the coherent one. Consequently, we conclude that the time intervals during which the atom-photon entanglement is distillable is longer for the squeezed distribution. It is also illustrated that as the temperature increases the rate of approaching separability is faster for the coherent initial distribution. The novel point of the present report is the calculation of dynamical density matrix (containing all physical information) for the combined system of atom-photon in a lossy cavity, as well as the corresponding negativity, at a finite temperature.

Energetic Consistency and Coupling of the Mean and Covariance Dynamics

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.

2008-01-01

The dynamical state of the ocean and atmosphere is taken to be a large dimensional random vector in a range of large-scale computational applications, including data assimilation, ensemble prediction, sensitivity analysis, and predictability studies. In each of these applications, numerical evolution of the covariance matrix of the random state plays a central role, because this matrix is used to quantify uncertainty in the state of the dynamical system. Since atmospheric and ocean dynamics are nonlinear, there is no closed evolution equation for the covariance matrix, nor for the mean state. Therefore approximate evolution equations must be used. This article studies theoretical properties of the evolution equations for the mean state and covariance matrix that arise in the second-moment closure approximation (third- and higher-order moment discard). This approximation was introduced by EPSTEIN [1969] in an early effort to introduce a stochastic element into deterministic weather forecasting, and was studied further by FLEMING [1971a,b], EPSTEIN and PITCHER [1972], and PITCHER [1977], also in the context of atmospheric predictability. It has since fallen into disuse, with a simpler one being used in current large-scale applications. The theoretical results of this article make a case that this approximation should be reconsidered for use in large-scale applications, however, because the second moment closure equations possess a property of energetic consistency that the approximate equations now in common use do not possess. A number of properties of solutions of the second-moment closure equations that result from this energetic consistency will be established.

Density Weighted FDF Equations for Simulations of Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2011-01-01

In this report, we briefly revisit the formulation of density weighted filtered density function (DW-FDF) for large eddy simulation (LES) of turbulent reacting flows, which was proposed by Jaberi et al. (Jaberi, F.A., Colucci, P.J., James, S., Givi, P. and Pope, S.B., Filtered mass density function for Large-eddy simulation of turbulent reacting flows, J. Fluid Mech., vol. 401, pp. 85-121, 1999). At first, we proceed the traditional derivation of the DW-FDF equations by using the fine grained probability density function (FG-PDF), then we explore another way of constructing the DW-FDF equations by starting directly from the compressible Navier-Stokes equations. We observe that the terms which are unclosed in the traditional DW-FDF equations are now closed in the newly constructed DW-FDF equations. This significant difference and its practical impact on the computational simulations may deserve further studies.

Semiclassical theory of sub-Doppler forces in an asymmetric magneto-optical trap with unequal laser detunings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noh, Heung-Ryoul; Jhe, Wonho

We present a semiclassical theory of the sub-Doppler forces in an asymmetric magneto-optical trap where the trap-laser frequencies are unequal to one another. To solve the optical Bloch equations, which contain explicit time dependence, unlike in the symmetric case of equal laser detunings, we have developed a convenient and efficient method to calculate the atomic forces at various oscillating frequencies for each atomic density matrix element. In particular, the theory provides a qualitative understanding of the array of sub-Doppler traps (SDTs) recently observed in such an asymmetric trap. We find that the distances between SDTs are proportional to the relativemore » detuning differences, in good agreement with experimental results. The theory presented here can be applied to a dynamic system with multiple laser frequencies involved; the number of coupled equations to solve is much reduced and the resulting numerical calculation can be performed rather simply and efficiently.« less

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

Theory of interaction-induced renormalization of Drude weight and plasmon frequency in chiral multilayer graphene

NASA Astrophysics Data System (ADS)

Li, Xiao; Tse, Wang-Kong

2017-02-01

We develop a theory for the optical conductivity of doped ABC-stacked multilayer graphene including the effects of electron-electron interactions. Applying the quantum kinetic formalism, we formulate a set of pseudospin Bloch equations that govern the dynamics of the nonequilibrium density matrix driven by an external ac electric field under the influence of Coulomb interactions. These equations reveal a dynamical mechanism that couples the Drude and interband responses arising from the chirality of pseudospin textures in multilayer graphene systems. We demonstrate that this results in an interaction-induced enhancement of the Drude weight and plasmon frequency strongly dependent on the pseudospin winding number. Using bilayer graphene as an example, we also study the influence of higher-energy bands and find that they contribute considerable renormalization effects not captured by a low-energy two-band description. We argue that this enhancement of Drude weight and plasmon frequency occurs generally in materials characterized by electronic chirality.

Critical behavior of dissipative two-dimensional spin lattices

NASA Astrophysics Data System (ADS)

Rota, R.; Storme, F.; Bartolo, N.; Fazio, R.; Ciuti, C.

2017-04-01

We explore critical properties of two-dimensional lattices of spins interacting via an anisotropic Heisenberg Hamiltonian that are subject to incoherent spin flips. We determine the steady-state solution of the master equation for the density matrix via the corner-space renormalization method. We investigate the finite-size scaling and critical exponent of the magnetic linear susceptibility associated with a dissipative ferromagnetic transition. We show that the von Neumann entropy increases across the critical point, revealing a strongly mixed character of the ferromagnetic phase. Entanglement is witnessed by the quantum Fisher information, which exhibits a critical behavior at the transition point, showing that quantum correlations play a crucial role in the transition.

Electromagnetically induced transparency in a multilayered spherical quantum dot with hydrogenic impurity

NASA Astrophysics Data System (ADS)

Pavlović, Vladan; Šušnjar, Marko; Petrović, Katarina; Stevanović, Ljiljana

2018-04-01

In this paper the effects of size, hydrostatic pressure and temperature on electromagnetically induced transparency, as well as on absorption and the dispersion properties of multilayered spherical quantum dot with hydrogenic impurity are theoretically investigated. Energy eigenvalues and wavefunctions of quantum systems in three-level and four-level configurations are calculated using the shooting method, while optical properties are obtained using the density matrix formalism and master equations. It is shown that peaks of the optical properties experience a blue-shift with increasing hydrostatic pressure and red-shift with increasing temperature. The changes of optical properties as a consequence of changes in barrier wells widths are non-monotonic, and these changes are discussed in detail.

Vector-valued Jack polynomials and wavefunctions on the torus

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2017-06-01

The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r 2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials taking values in modules of the symmetric group and the matrix solution of a system of linear differential equations one constructs novel eigenfunctions of the Hamiltonian. Like the usual wavefunctions each eigenfunction determines a symmetric probability density on the N-torus. The construction applies to any irreducible representation of the symmetric group. The methods depend on the theory of generalized Jack polynomials due to Griffeth, and the Yang-Baxter graph approach of Luque and the author.

Bulk-like-phonon polaritons in one-dimensional photonic superlattices

NASA Astrophysics Data System (ADS)

Gómez-Urrea, H. A.; Duque, C. A.; Mora-Ramos, M. E.

2017-05-01

We investigate the properties of a one-dimensional photonic superlattice made of alternating layers of air and wurtzite aluminum nitride. The Maxwell equations are solved for any admissible values of the angle of incidence by means of the transfer matrix formalism. The band structure of the frequency spectrum is obtained, as well as the density of states and transmittance associated to both the TM and TE modes. The dispersion relations indicate that for oblique incidence and TM modes there is a component of the electric field oriented along the growth direction of the structure that couples with the longitudinal optical phonon oscillations of the aluminum nitride thus leading to the appearance of longitudinal phonon polaritons in the system.

Decoherence dynamics of interacting qubits coupled to a bath of local optical phonons

NASA Astrophysics Data System (ADS)

Lone, Muzaffar Qadir; Yarlagadda, S.

2016-04-01

We study decoherence in an interacting qubit system described by infinite range Heisenberg model (IRHM) in a situation where the system is coupled to a bath of local optical phonons. Using perturbation theory in polaron frame of reference, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under nonadiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM upto leading orders of perturbation and thus has the same eigenstates as the IRHM. Using a quantum master equation with Markovian approximation of dynamical evolution, we show that the off-diagonal elements of the density matrix do not decay in the energy eigen basis of IRHM.

Carrier-Envelope Phase Effect on Atomic Excitation by Few-Cycle rf Pulses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Hebin; Welch, George R.; Sautenkov, Vladimir A.

2010-03-12

We present an experimental and theoretical study of the carrier-envelope phase effects on population transfer between two bound atomic states interacting with intense ultrashort pulses. Radio frequency pulses are used to transfer population among the ground state hyperfine levels in rubidium atoms. These pulses are only a few cycles in duration and have Rabi frequencies of the order of the carrier frequency. The phase difference between the carrier and the envelope of the pulses has a significant effect on the excitation of atomic coherence and population transfer. We provide a theoretical description of this phenomenon using density matrix equations. Wemore » discuss the implications and possible applications of our results.« less

Renormalization-group equations of neutrino masses and flavor mixing parameters in matter

NASA Astrophysics Data System (ADS)

Xing, Zhi-zhong; Zhou, Shun; Zhou, Ye-Ling

2018-05-01

We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter a≡ 2√{2}{G}F{N}_eE to be an arbitrary scale-like variable with N e being the net electron number density and E being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix V and the effective neutrino masses {\\tilde{m}}_i (for i = 1 , 2 , 3). Given the standard parametrization of V , the RGEs for {{\\tilde{θ}}_{12}, {\\tilde{θ}}_{13}, {\\tilde{θ}}_{23}, \\tilde{δ}} in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial μ- τ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of V are also obtained as a by-product.

Almost analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2017-11-01

We present an almost analytical new approach to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of solving this matrix eigenvalue problem purely numerically, which may suffer from the computational inaccuracy for big data, first, we consider a pair of integral and differential equations, which are related to the so-called prolate spheroidal wave functions (PSWF). For the PSWF differential equation, the pair of the eigenvectors (PSWF) and eigenvalues can be obtained from a relatively small number of analytical Legendre functions. Then, the eigenvalues in the PSWF integral equation are expressed in terms of functional values of the PSWF and the eigenvalues of the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data; ordinary irregular waves and rogue waves. We found that the present almost analytical method is better than the conventional data-independent Fourier representation and, also, the conventional direct numerical K-L representation in terms of both accuracy and computational cost. This work was supported by the National Research Foundation of Korea (NRF). (NRF-2017R1D1A1B03028299).

Development and evaluation of Ketoprofen sustained release matrix tablet using Hibiscus rosa-sinensis leaves mucilage.

PubMed

Kaleemullah, M; Jiyauddin, K; Thiban, E; Rasha, S; Al-Dhalli, S; Budiasih, S; Gamal, O E; Fadli, A; Eddy, Y

2017-07-01

Currently, the use of natural gums and mucilage is of increasing importance in pharmaceutical formulations as valuable drug excipient. Natural plant-based materials are economic, free of side effects, biocompatible and biodegradable. Therefore, Ketoprofen matrix tablets were formulated by employing Hibiscus rosa-sinensis leaves mucilage as natural polymer and HPMC (K100M) as a synthetic polymer to sustain the drug release from matrix system. Direct compression method was used to develop sustained released matrix tablets. The formulated matrix tablets were evaluated in terms of physical appearance, weight variation, thickness, diameter, hardness, friability and in vitro drug release. The difference between the natural and synthetic polymers was investigated concurrently. Matrix tablets developed from each formulation passed all standard physical evaluation tests. The dissolution studies of formulated tablets revealed sustained drug release up to 24 h compared to the reference drug Apo Keto® SR tablets. The dissolution data later were fitted into kinetic models such as zero order equation, first order equation, Higuchi equation, Hixson Crowell equation and Korsmeyer-Peppas equation to study the release of drugs from each formulation. The best formulations were selected based on the similarity factor ( f 2 ) value of 50% and more. Through the research, it is found that by increasing the polymers concentration, the rate of drug release decreased for both natural and synthetic polymers. The best formulation was found to be F3 which contained 40% Hibiscus rosa-sinensis mucilage polymer and showed comparable dissolution profile to the reference drug with f 2 value of 78.03%. The release kinetics of this formulation has shown to follow non-Fickian type which involved both diffusion and erosion mechanism. Additionally, the statistical results indicated that there was no significant difference (p > 0.05) between the F3 and reference drug in terms of MDT and T50% with p-values of 1.00 and 0.995 respectively.

Wave propagation through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces.

PubMed

Jiao, Fengyu; Wei, Peijun; Li, Yueqiu

2018-01-01

Reflection and transmission of plane waves through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces are studied in this paper. The secular equations in the flexoelectric piezoelectric material are first derived from the general governing equation. Different from the classical piezoelectric medium, there are five kinds of coupled elastic waves in the piezoelectric material with the microstructure effects taken into consideration. The state vectors are obtained by the summation of contributions from all possible partial waves. The state transfer equation of flexoelectric piezoelectric slab is derived from the motion equation by the reduction of order, and the transfer matrix of flexoelectric piezoelectric slab is obtained by solving the state transfer equation. By using the continuous conditions at the interface and the approach of partition matrix, we get the resultant algebraic equations in term of the transfer matrix from which the reflection and transmission coefficients can be calculated. The amplitude ratios and further the energy flux ratios of various waves are evaluated numerically. The numerical results are shown graphically and are validated by the energy conservation law. Based on these numerical results, the influences of two characteristic lengths of microstructure and the flexoelectric coefficients on the wave propagation are discussed. Copyright © 2017 Elsevier B.V. All rights reserved.

Modeling the Nonlinear, Strain Rate Dependent Deformation of Woven Ceramic Matrix Composites With Hydrostatic Stress Effects Included

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Carney, Kelly S.

2004-01-01

An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites with a plain weave fiber architecture. In the developed model, the differences in the tension and compression response have also been considered. State variable based viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear stiffness is independent of the stiffness in the normal directions. The developed equations have been implemented into a commercially available transient dynamic finite element code, LS-DYNA, through the use of user defined subroutines (UMATs). The tensile, compressive, and shear deformation of a representative plain weave woven ceramic matrix composite are computed and compared to experimental results. The computed values correlate well to the experimental data, demonstrating the ability of the model to accurately compute the deformation response of woven ceramic matrix composites.

Mesh-matrix analysis method for electromagnetic launchers

NASA Technical Reports Server (NTRS)

Elliott, David G.

1989-01-01

The mesh-matrix method is a procedure for calculating the current distribution in the conductors of electromagnetic launchers with coil or flat-plate geometry. Once the current distribution is known the launcher performance can be calculated. The method divides the conductors into parallel current paths, or meshes, and finds the current in each mesh by matrix inversion. The author presents procedures for writing equations for the current and voltage relations for a few meshes to serve as a pattern for writing the computer code. An available subroutine package provides routines for field and flux coefficients and equation solution.

Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix

DOE PAGES

Smallwood, D. O.

1996-01-01

It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.

Chosen interval methods for solving linear interval systems with special type of matrix

NASA Astrophysics Data System (ADS)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

Calculation of normal modes of the closed waveguides in general vector case

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Sevastianov, L. A.; Tiutiunnik, A. A.

2018-04-01

The article is devoted to the calculation of normal modes of the closed waveguides with an arbitrary filling ɛ, μ in the system of computer algebra Sage. Maxwell equations in the cylinder are reduced to the system of two bounded Helmholtz equations, the notion of weak solution of this system is given and then this system is investigated as a system of ordinary differential equations. The normal modes of this system are an eigenvectors of a matrix pencil. We suggest to calculate the matrix elements approximately and to truncate the matrix by usual way but further to solve the truncated eigenvalue problem exactly in the field of algebraic numbers. This approach allows to keep the symmetry of the initial problem and in particular the multiplicity of the eigenvalues. In the work would be presented some results of calculations.

Optical Control of Intersubband Absorption in a Multiple Quantum Well-Embedded Semiconductor Microcravity

NASA Technical Reports Server (NTRS)

Liu, Ansheng; Ning, Cun-Zheng

2000-01-01

Optical intersubband response of a multiple quantum well (MQW)-embedded microcavity driven by a coherent pump field is studied theoretically. The n-type doped MQW structure with three subbands in the conduction band is sandwiched between a semi-infinite medium and a distributed Bragg reflector (DBR). A strong pump field couples the two upper subbands and a weak field probes the two lower subbands. To describe the optical response of the MQW-embedded microcavity, we adopt a semi-classical nonlocal response theory. Taking into account the pump-probe interaction, we derive the probe-induced current density associated with intersubband transitions from the single-particle density-matrix formalism. By incorporating the current density into the Maxwell equation, we solve the probe local field exactly by means of Green's function technique and the transfer-matrix method. We obtain an exact expression for the probe absorption coefficient of the microcavity. For a GaAs/Al(sub x)Ga(sub 1-x)As MQW structure sandwiched between a GaAs/AlAs DBR and vacuum, we performed numerical calculations of the probe absorption spectra for different parameters such as pump intensity, pump detuning, and cavity length. We find that the probe spectrum is strongly dependent on these parameters. In particular, we find that the combination of the cavity effect and the Autler-Townes effect results in a triplet in the optical spectrum of the MQW system. The optical absorption peak value and its location can be feasibly controlled by varying the pump intensity and detuning.

Comparing direct and iterative equation solvers in a large structural analysis software system

NASA Technical Reports Server (NTRS)

Poole, E. L.

1991-01-01

Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.

Chandrasekhar-type algorithms for fast recursive estimation in linear systems with constant parameters

NASA Technical Reports Server (NTRS)

Choudhury, A. K.; Djalali, M.

1975-01-01

In this recursive method proposed, the gain matrix for the Kalman filter and the convariance of the state vector are computed not via the Riccati equation, but from certain other equations. These differential equations are of Chandrasekhar-type. The 'invariant imbedding' idea resulted in the reduction of the basic boundary value problem of transport theory to an equivalent initial value system, a significant computational advance. Initial value experience showed that there is some computational savings in the method and the loss of positive definiteness of the covariance matrix is less vulnerable.

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

QCDNUM: Fast QCD evolution and convolution

NASA Astrophysics Data System (ADS)

Botje, M.

2011-02-01

The QCDNUM program numerically solves the evolution equations for parton densities and fragmentation functions in perturbative QCD. Un-polarised parton densities can be evolved up to next-to-next-to-leading order in powers of the strong coupling constant, while polarised densities or fragmentation functions can be evolved up to next-to-leading order. Other types of evolution can be accessed by feeding alternative sets of evolution kernels into the program. A versatile convolution engine provides tools to compute parton luminosities, cross-sections in hadron-hadron scattering, and deep inelastic structure functions in the zero-mass scheme or in generalised mass schemes. Input to these calculations are either the QCDNUM evolved densities, or those read in from an external parton density repository. Included in the software distribution are packages to calculate zero-mass structure functions in un-polarised deep inelastic scattering, and heavy flavour contributions to these structure functions in the fixed flavour number scheme. Program summaryProgram title: QCDNUM version: 17.00 Catalogue identifier: AEHV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Public Licence No. of lines in distributed program, including test data, etc.: 45 736 No. of bytes in distributed program, including test data, etc.: 911 569 Distribution format: tar.gz Programming language: Fortran-77 Computer: All Operating system: All RAM: Typically 3 Mbytes Classification: 11.5 Nature of problem: Evolution of the strong coupling constant and parton densities, up to next-to-next-to-leading order in perturbative QCD. Computation of observable quantities by Mellin convolution of the evolved densities with partonic cross-sections. Solution method: Parametrisation of the parton densities as linear or quadratic splines on a discrete grid, and evolution of the spline coefficients by solving (coupled) triangular matrix equations with a forward substitution algorithm. Fast computation of convolution integrals as weighted sums of spline coefficients, with weights derived from user-given convolution kernels. Restrictions: Accuracy and speed are determined by the density of the evolution grid. Running time: Less than 10 ms on a 2 GHz Intel Core 2 Duo processor to evolve the gluon density and 12 quark densities at next-to-next-to-leading order over a large kinematic range.

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.; Gilat, Amos

2003-01-01

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

Unified Theory for Decoding the Signals from X-Ray Florescence and X-Ray Diffraction of Mixtures.

PubMed

Chung, Frank H

2017-05-01

For research and development or for solving technical problems, we often need to know the chemical composition of an unknown mixture, which is coded and stored in the signals of its X-ray fluorescence (XRF) and X-ray diffraction (XRD). X-ray fluorescence gives chemical elements, whereas XRD gives chemical compounds. The major problem in XRF and XRD analyses is the complex matrix effect. The conventional technique to deal with the matrix effect is to construct empirical calibration lines with standards for each element or compound sought, which is tedious and time-consuming. A unified theory of quantitative XRF analysis is presented here. The idea is to cancel the matrix effect mathematically. It turns out that the decoding equation for quantitative XRF analysis is identical to that for quantitative XRD analysis although the physics of XRD and XRF are fundamentally different. The XRD work has been published and practiced worldwide. The unified theory derives a new intensity-concentration equation of XRF, which is free from the matrix effect and valid for a wide range of concentrations. The linear decoding equation establishes a constant slope for each element sought, hence eliminating the work on calibration lines. The simple linear decoding equation has been verified by 18 experiments.

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor.

PubMed

Li, Yi; Chevillard, Laurent; Eyink, Gregory; Meneveau, Charles

2009-01-01

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.

A B-spline Galerkin method for the Dirac equation

NASA Astrophysics Data System (ADS)

Froese Fischer, Charlotte; Zatsarinny, Oleg

2009-06-01

The B-spline Galerkin method is first investigated for the simple eigenvalue problem, y=-λy, that can also be written as a pair of first-order equations y=λz, z=-λy. Expanding both y(r) and z(r) in the B basis results in many spurious solutions such as those observed for the Dirac equation. However, when y(r) is expanded in the B basis and z(r) in the dB/dr basis, solutions of the well-behaved second-order differential equation are obtained. From this analysis, we propose a stable method ( B,B) basis for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges Z and angular quantum numbers κ. When splines of the same order are used, many spurious solutions are found whereas none are found for splines of different order. Excellent agreement is obtained for the R-matrix and energies for bound states for low values of Z. For high Z, accuracy requires the use of a grid with many points near the nucleus. We demonstrate the accuracy of the bound-state wavefunctions by comparing integrals arising in hyperfine interaction matrix elements with exact analytic expressions. We also show that the Thomas-Reiche-Kuhn sum rule is not a good measure of the quality of the solutions obtained by the B-spline Galerkin method whereas the R-matrix is very sensitive to the appearance of pseudo-states.

SEAWAT Version 4: A Computer Program for Simulation of Multi-Species Solute and Heat Transport

USGS Publications Warehouse

Langevin, Christian D.; Thorne, Daniel T.; Dausman, Alyssa M.; Sukop, Michael C.; Guo, Weixing

2008-01-01

The SEAWAT program is a coupled version of MODFLOW and MT3DMS designed to simulate three-dimensional, variable-density, saturated ground-water flow. Flexible equations were added to the program to allow fluid density to be calculated as a function of one or more MT3DMS species. Fluid density may also be calculated as a function of fluid pressure. The effect of fluid viscosity variations on ground-water flow was included as an option. Fluid viscosity can be calculated as a function of one or more MT3DMS species, and the program includes additional functions for representing the dependence on temperature. Although MT3DMS and SEAWAT are not explicitly designed to simulate heat transport, temperature can be simulated as one of the species by entering appropriate transport coefficients. For example, the process of heat conduction is mathematically analogous to Fickian diffusion. Heat conduction can be represented in SEAWAT by assigning a thermal diffusivity for the temperature species (instead of a molecular diffusion coefficient for a solute species). Heat exchange with the solid matrix can be treated in a similar manner by using the mathematically equivalent process of solute sorption. By combining flexible equations for fluid density and viscosity with multi-species transport, SEAWAT Version 4 represents variable-density ground-water flow coupled with multi-species solute and heat transport. SEAWAT Version 4 is based on MODFLOW-2000 and MT3DMS and retains all of the functionality of SEAWAT-2000. SEAWAT Version 4 also supports new simulation options for coupling flow and transport, and for representing constant-head boundaries. In previous versions of SEAWAT, the flow equation was solved for every transport timestep, regardless of whether or not there was a large change in fluid density. A new option was implemented in SEAWAT Version 4 that allows users to control how often the flow field is updated. New options were also implemented for representing constant-head boundaries with the Time-Variant Constant-Head (CHD) Package. These options allow for increased flexibility when using CHD flow boundaries with the zero-dispersive flux solute boundaries implemented by MT3DMS at constant-head cells. This report contains revised input instructions for the MT3DMS Dispersion (DSP) Package, Variable-Density Flow (VDF) Package, Viscosity (VSC) Package, and CHD Package. The report concludes with seven cases of an example problem designed to highlight many of the new features.

Analysis of the release process of phenylpropanolamine hydrochloride from ethylcellulose matrix granules V. Release properties of ethylcellulose layered matrix granules.

PubMed

Fukui, Atsuko; Fujii, Ryuta; Yonezawa, Yorinobu; Sunada, Hisakazu

2008-04-01

In the pharmaceutical preparation of a controlled release drug, it is very important and necessary to understand the release properties. In previous papers, a combination of the square-root time law and cube-root law equations was confirmed to be a useful equation for qualitative treatment. It was also confirmed that the combination equation could analyze the release properties of layered granules as well as matrix granules. The drug release property from layered granules is different from that of matrix granules. A time lag occurs before release, and the entire release property of layered granules was analyzed using the combination of the square-root time law and cube-root law equations. It is considered that the analysis method is very useful and efficient for both matrix and layered granules. Comparing the granulation methods, it is easier to control the manufacturing process by tumbling granulation (method B) than by tumbling-fluidized bed granulation (method C). Ethylcellulose (EC) layered granulation by a fluidized bed granulator might be convenient for the preparation of controlled release dosage forms as compared with a tumbling granulator, because the layered granules prepared by the fluidized bed granulator can granulate and dry at the same time. The time required for drying by the fluidized bed granulator is shorter than that by the tumbling granulator, so the fluidized bed granulator is convenient for preparation of granules in handling and shorter processing time than the tumbling granulator. It was also suggested that the EC layered granules prepared by the fluidized bed granulator were suitable for a controlled release system as well as the EC matrix granules.

Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. III. Theory for the multilevel atom

NASA Astrophysics Data System (ADS)

Bommier, Véronique

2016-06-01

Context. We discuss the case of lines formed by scattering, which comprises both coherent and incoherent scattering. Both processes contribute to form the line profiles in the so-called second solar spectrum, which is the spectrum of the linear polarization of such lines observed close to the solar limb. However, most of the lines cannot be simply modeled with a two-level or two-term atom model, and we present a generalized formalism for this purpose. Aims: The aim is to obtain a formalism that is able to describe scattering in line centers (resonant scattering or incoherent scattering) and in far wings (Rayleigh/Raman scattering or coherent scattering) for a multilevel and multiline atom. Methods: The method is designed to overcome the Markov approximation, which is often performed in the atom-photon interaction description. The method was already presented in the two first papers of this series, but the final equations of those papers were for a two-level atom. Results: We present here the final equations generalized for the multilevel and multiline atom. We describe the main steps of the theoretical development, and, in particular, how we performed the series development to overcome the Markov approximation. Conclusions: The statistical equilibrium equations for the atomic density matrix and the radiative transfer equation coefficients are obtained with line profiles. The Doppler redistribution is also taken into account because we show that the statistical equilibrium equations must be solved for each atomic velocity class.

The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation

NASA Astrophysics Data System (ADS)

Zhang, Liangyin; Chen, Michael Z. Q.; Li, Chanying

2017-07-01

In this paper, two new pairs of dual continuous-time algebraic Riccati equations (CAREs) and dual discrete-time algebraic Riccati equations (DAREs) are proposed. The dual DAREs are first studied with some nonsingularity assumptions on the system matrix and the parameter matrix. Then, in the case of singular matrices, a generalised inverse is introduced to deal with the dual DARE problem. These dual AREs can easily lead us to an iterative procedure for finding the anti-stabilising solutions, especially to DARE, by means of that for the stabilising solutions. Furthermore, we provide the counterpart results on the set of all solutions to DARE inspired by the results for CARE. Two examples are presented to illustrate the theoretical results.

Density of Jatropha curcas Seed Oil and its Methyl Esters: Measurement and Estimations

NASA Astrophysics Data System (ADS)

Veny, Harumi; Baroutian, Saeid; Aroua, Mohamed Kheireddine; Hasan, Masitah; Raman, Abdul Aziz; Sulaiman, Nik Meriam Nik

2009-04-01

Density data as a function of temperature have been measured for Jatropha curcas seed oil, as well as biodiesel jatropha methyl esters at temperatures from above their melting points to 90 ° C. The data obtained were used to validate the method proposed by Spencer and Danner using a modified Rackett equation. The experimental and estimated density values using the modified Rackett equation gave almost identical values with average absolute percent deviations less than 0.03% for the jatropha oil and 0.04% for the jatropha methyl esters. The Janarthanan empirical equation was also employed to predict jatropha biodiesel densities. This equation performed equally well with average absolute percent deviations within 0.05%. Two simple linear equations for densities of jatropha oil and its methyl esters are also proposed in this study.

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuehlsdorff, T. J., E-mail: tjz21@cam.ac.uk; Payne, M. C.; Hine, N. D. M.

2015-11-28

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on amore » small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.« less

Quantum dissipation theory and applications to quantum transport and quantum measurement in mesoscopic systems

NASA Astrophysics Data System (ADS)

Cui, Ping

The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO) systems, and its closely related solvation mode transformation of system-bath coupling Hamiltonian in general. The exact QDT of DBO systems is also used to clarify the validity of conventional QDT formulations that involve Markovian approximation. In Chapter 3, we develop three nonequivalent but all complete second-order QDT (CS-QDT) formulations. Two of them are of the conventional prescriptions in terms of time-local dissipation and memory kernel, respectively. The third one is called the correlated driving-dissipation equations of motion (CODDE). This novel CS-QDT combines the merits of the former two for its advantages in both the application and numerical implementation aspects. Also highlighted is the importance of correlated driving-dissipation effects on the dynamics of the reduced system. In Chapter 4, we construct an exact QDT formalism via the calculus on path integrals. The new theory aims at the efficient evaluation of non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. By adopting exponential-like expansions for bath correlation function, hierarchical equations of motion formalism and continued fraction Liouville-space Green's function formalism are established. The latter will soon be used together with the Dyson equation technique for an efficient evaluation of non-perturbative reduced density matrix dynamics. The interplay between system-bath interaction strength, non-Markovian property, and the required level of hierarchy is also studied with the aid of simple spin-boson systems, together with the three proposed schemes to truncate the infinite hierarchy. In Chapter 5, we develop a nonperturbative theory of electron transfer (ET) in Debye solvents. The resulting exact and analytical rate expression is constructed on the basis of the aforementioned continued fraction Liouville-space Green's function formalism, together with the Dyson equation technique. Not only does it recover the celebrated Marcus' inversion and Kramers' turnover behaviors, the new theory also shows some distinct quantum solvation effects that can alter the ET mechanism. Moreover, the present theory predicts further for the ET reaction thermodynamics, such as equilibrium Gibbs free-energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. In Chapter 6, we discuss the constructed QDTs, in terms of their unified mathematical structure that supports a linear dynamics space, and thus facilitates their applications to various physical problems. The involving details are exemplified with the CODDE form of QDT. As the linear space is concerned, we identify the Schrodinger versus Heisenberg picture and the forward versus backward propagation of the reduced, dissipative Liouville dynamics. For applications we discuss the reduced linear response theory and the optimal control problems, in which the correlated effects of non-Markovian dissipation and field driving are shown to be important. In Chapter 7, we turn to quantum transport, i.e., electric current through molecular or mesoscopic systems under finite applied voltage. By viewing the nonequilibrium transport setup as a quantum open system, we develop a reduced-density-matrix approach to quantum transport. The resulting current is explicitly expressed in terms of the molecular reduced density matrix by tracing out the degrees of freedom of the electrodes at finite bias and temperature. We propose a conditional quantum master equation theory, which is an extension of the conventional (or unconditional) QDT by tracing out the well-defined bath subsets individually, instead of the entire bath degrees of freedom. Both the current and the noise spectrum can be conveniently analyzed in terms of the conditional reduced density matrix dynamics. By far, the QDT (including the conditional one) has only been exploited in second-order form. A self-consistent Born approximation for the system-electrode coupling is further proposed to recover all existing nonlinear current-voltage behaviors including the nonequilibrium Kondo effect. Transport theory based on the exact QDT formalism will be developed in future. In Chapter 8, we study the quantum measurement of a qubit with a quantum-point-contact detector. On the basis of a unified quantum master equation (a form of QDT), we study the measurement-induced relaxation and dephasing of the qubit. Our treatment pays particular attention on the detailed-balance relation, which is a consequence of properly accounting for the energy exchange between the qubit and detector during the measurement process. We also derive a conditional quantum master equation for quantum measurement in general, and study the readout characteristics of the qubit measurement. Our theory is applicable to the quantum measurement at arbitrary voltage and temperature. A number of remarkable new features are found and highlighted in concern with their possible relevance to future experiments. In Chapter 9, we discuss the further development of QDT, aiming at an efficient evaluation of many-electron systems. This will be carried out by reducing the many-particle (Fermion or Boson) QDT to a single-particle one by exploring, e.g. the Wick's contraction theorem. It also results in a time-dependent density functional theory (TDDFT) for transport through complex large-scale (e.g. molecules) systems. Primary results of the TDDFT-QDT are reported. In Chapter 10, we summary the thesis, and comment and remark on the future work on both the theoretical and application aspects of QDT.

Comparison of two Galerkin quadrature methods

DOE PAGES

Morel, Jim E.; Warsa, James; Franke, Brian C.; ...

2017-02-21

Here, we compare two methods for generating Galerkin quadratures. In method 1, the standard S N method is used to generate the moment-to-discrete matrix and the discrete-to-moment matrix is generated by inverting the moment-to-discrete matrix. This is a particular form of the original Galerkin quadrature method. In method 2, which we introduce here, the standard S N method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. With an N-point quadrature, method 1 has the advantage that it preserves N eigenvalues and N eigenvectors of the scattering operator in a pointwisemore » sense. With an N-point quadrature, method 2 has the advantage that it generates consistent angular moment equations from the corresponding S N equations while preserving N eigenvalues of the scattering operator. Our computational results indicate that these two methods are quite comparable for the test problem considered.« less

Comparison of two Galerkin quadrature methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morel, Jim E.; Warsa, James; Franke, Brian C.

Here, we compare two methods for generating Galerkin quadratures. In method 1, the standard S N method is used to generate the moment-to-discrete matrix and the discrete-to-moment matrix is generated by inverting the moment-to-discrete matrix. This is a particular form of the original Galerkin quadrature method. In method 2, which we introduce here, the standard S N method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. With an N-point quadrature, method 1 has the advantage that it preserves N eigenvalues and N eigenvectors of the scattering operator in a pointwisemore » sense. With an N-point quadrature, method 2 has the advantage that it generates consistent angular moment equations from the corresponding S N equations while preserving N eigenvalues of the scattering operator. Our computational results indicate that these two methods are quite comparable for the test problem considered.« less

The ab-initio density matrix renormalization group in practice.

PubMed

Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic

2015-01-21

The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

Catmull-Rom Curve Fitting and Interpolation Equations

ERIC Educational Resources Information Center

Jerome, Lawrence

2010-01-01

Computer graphics and animation experts have been using the Catmull-Rom smooth curve interpolation equations since 1974, but the vector and matrix equations can be derived and simplified using basic algebra, resulting in a simple set of linear equations with constant coefficients. A variety of uses of Catmull-Rom interpolation are demonstrated,…

Random-Effects Models for Meta-Analytic Structural Equation Modeling: Review, Issues, and Illustrations

ERIC Educational Resources Information Center

Cheung, Mike W.-L.; Cheung, Shu Fai

2016-01-01

Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…

Matrix algorithms for solving (in)homogeneous bound state equations

PubMed Central

Blank, M.; Krassnigg, A.

2011-01-01

In the functional approach to quantum chromodynamics, the properties of hadronic bound states are accessible via covariant integral equations, e.g. the Bethe–Salpeter equation for mesons. In particular, one has to deal with linear, homogeneous integral equations which, in sophisticated model setups, use numerical representations of the solutions of other integral equations as part of their input. Analogously, inhomogeneous equations can be constructed to obtain off-shell information in addition to bound-state masses and other properties obtained from the covariant analogue to a wave function of the bound state. These can be solved very efficiently using well-known matrix algorithms for eigenvalues (in the homogeneous case) and the solution of linear systems (in the inhomogeneous case). We demonstrate this by solving the homogeneous and inhomogeneous Bethe–Salpeter equations and find, e.g. that for the calculation of the mass spectrum it is as efficient or even advantageous to use the inhomogeneous equation as compared to the homogeneous. This is valuable insight, in particular for the study of baryons in a three-quark setup and more involved systems. PMID:21760640

Development of edge effects around experimental ecosystem hotspots is affected by edge density and matrix type

USDA-ARS?s Scientific Manuscript database

Ecological edge effects are sensitive to landscape context. In particular, edge effects can be altered by matrix type and by the presence of other nearby edges. We experimentally altered patch configurations in an African savanna to determine how edge density and matrix type influence edge effect de...

Theoretical and numerical aspects of fluid-saturated elasto-plastic soils

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ehlers, W.

1995-12-31

The theoretical and numerical treatment of fluid-saturated porous solid materials generally falls into the category of porous media models, which are described within the framework of the classical theory of mixtures extended by the concept of volume fractions (porous media theories). In particular, this concept allows for the description of saturated, unsaturated and empty porous matrix materials, thus offering a well-founded theoretical background for a lot of engineering problems occurring, for instance, in the fields of geomechanics (soil and rock mechanics as well as glacier and rock ice mechanics), oil producing industries, sintering technologies, biomechanics, etc. In the present contribution,more » theoretical and numerical studies are outlined to describe a two-phase material composed of an incompressible elasto-plastic soil matrix saturated by an incompressible viscous pore fluid. In this context, the phenomenon of phase incompressibility is well known as a microscopic effect not implying bulk incompressibility in the macro regime. This is seen from the fact that even if the material density functions of the individual constituents are constant during deformation, the corresponding bulk densities can still change through changes in the volume fractions. Within the framework of a pure mechanical theory, constitutive equations are given for both the solid and the fluid partial stress tensors and for the interaction force acting between the two materials. Concerning the porous soil matrix, the elastic properties are described by an elasticity law of Hookean type, while the plastic range is governed by a {open_quote}single surface{close_quote} yield function exhibiting a smooth and closed shape in the principal stress space together with a non-associated flow rule. The viscosity effects of the pore fluid are included in the fluid stress tensor and in the drag force.« less

Effects of the oceans on polar motion: Extended investigations

NASA Technical Reports Server (NTRS)

Dickman, Steven R.

1987-01-01

Matrix formulation of the tide equations (pole tide in nonglobal oceans); matrix formulation of the associated boundary conditions (constraints on the tide velocity at coastlines); and FORTRAN encoding of the tide equations excluding boundary conditions were completed. The need for supercomputer facilities was evident. Large versions of the programs were successfully run on the CYBER, submitting the jobs from SUNY through the BITNET network. The code was also restructured to include boundary constraints.

Implementation of Laminate Theory Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

2000-01-01

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were implemented into a mechanics of materials based micromechanics method. In the current work, the computation of the effective inelastic strain in the micromechanics model was modified to fully incorporate the Poisson effect. The micromechanics equations were also combined with classical laminate theory to enable the analysis of symmetric multilayered laminates subject to in-plane loading. A quasi-incremental trapezoidal integration method was implemented to integrate the constitutive equations within the laminate theory. Verification studies were conducted using an AS4/PEEK composite using a variety of laminate configurations and strain rates. The predicted results compared well with experimentally obtained values.

Fast computation of radiation pressure force exerted by multiple laser beams on red blood cell-like particles

NASA Astrophysics Data System (ADS)

Gou, Ming-Jiang; Yang, Ming-Lin; Sheng, Xin-Qing

2016-10-01

Mature red blood cells (RBC) do not contain huge complex nuclei and organelles, makes them can be approximately regarded as homogeneous medium particles. To compute the radiation pressure force (RPF) exerted by multiple laser beams on this kind of arbitrary shaped homogenous nano-particles, a fast electromagnetic optics method is demonstrated. In general, based on the Maxwell's equations, the matrix equation formed by the method of moment (MOM) has many right hand sides (RHS's) corresponding to the different laser beams. In order to accelerate computing the matrix equation, the algorithm conducts low-rank decomposition on the excitation matrix consisting of all RHS's to figure out the so-called skeleton laser beams by interpolative decomposition (ID). After the solutions corresponding to the skeletons are obtained, the desired responses can be reconstructed efficiently. Some numerical results are performed to validate the developed method.

The entrainment matrix of a superfluid nucleon mixture at finite temperatures

NASA Astrophysics Data System (ADS)

Leinson, Lev B.

2018-06-01

It is considered a closed system of non-linear equations for the entrainment matrix of a non-relativistic mixture of superfluid nucleons at arbitrary temperatures below the onset of neutron superfluidity, which takes into account the essential dependence of the superfluid energy gap in the nucleon spectra on the velocities of superfluid flows. It is assumed that the protons condense into the isotropic 1S0 state, and the neutrons are paired into the spin-triplet 3P2 state. It is derived an analytic solution to the non-linear equations for the entrainment matrix under temperatures just below the critical value for the neutron superfluidity onset. In general case of an arbitrary temperature of the superfluid mixture the non-linear equations are solved numerically and fitted by simple formulas convenient for a practical use with an arbitrary set of the Landau parameters.

How Should Equation Balancing Be Taught?

ERIC Educational Resources Information Center

Porter, Spencer K.

1985-01-01

Matrix methods and oxidation-number methods are currently advocated and used for balancing equations. This article shows how balancing equations can be introduced by a third method which is related to a fundamental principle, is easy to learn, and is powerful in its application. (JN)

Density matrix renormalization group with efficient dynamical electron correlation through range separation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hedegård, Erik Donovan, E-mail: erik.hedegard@phys.chem.ethz.ch; Knecht, Stefan; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

2015-06-14

We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems

NASA Astrophysics Data System (ADS)

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems.

PubMed

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

Gas Flux and Density Surrounding a Cylindrical Aperture in the Free Molecular Flow Regime

NASA Technical Reports Server (NTRS)

Soulas, George C.

2011-01-01

The equations for rigorously calculating the particle flux and density surrounding a cylindrical aperture in the free molecular flow regime are developed and presented. The fundamental equations for particle flux and density from a reservoir and a diffusely reflecting surface will initially be developed. Assumptions will include a Maxwell-Boltzmann speed distribution, equal particle and wall temperatures, and a linear flux distribution along the cylindrical aperture walls. With this information, the equations for axial flux and density surrounding a cylindrical aperture will be developed. The cylindrical aperture will be divided into multiple volumes and regions to rigorously determine the surrounding axial flux and density, and appropriate limits of integration will be determined. The results of these equations will then be evaluated. The linear wall flux distribution assumption will be assessed. The axial flux and density surrounding a cylindrical aperture with a thickness-to-radius ratio of 1.25 will be presented. Finally, the equations determined in this study will be verified using multiple methods.

Expansion of Tabulated Scattering Matrices in Generalized Spherical Functions

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Geogdzhayev, Igor V.; Yang, Ping

2016-01-01

An efficient way to solve the vector radiative transfer equation for plane-parallel turbid media is to Fourier-decompose it in azimuth. This methodology is typically based on the analytical computation of the Fourier components of the phase matrix and is predicated on the knowledge of the coefficients appearing in the expansion of the normalized scattering matrix in generalized spherical functions. Quite often the expansion coefficients have to be determined from tabulated values of the scattering matrix obtained from measurements or calculated by solving the Maxwell equations. In such cases one needs an efficient and accurate computer procedure converting a tabulated scattering matrix into the corresponding set of expansion coefficients. This short communication summarizes the theoretical basis of this procedure and serves as the user guide to a simple public-domain FORTRAN program.

New algorithms to compute the nearness symmetric solution of the matrix equation.

PubMed

Peng, Zhen-Yun; Fang, Yang-Zhi; Xiao, Xian-Wei; Du, Dan-Dan

2016-01-01

In this paper we consider the nearness symmetric solution of the matrix equation AXB = C to a given matrix [Formula: see text] in the sense of the Frobenius norm. By discussing equivalent form of the considered problem, we derive some necessary and sufficient conditions for the matrix [Formula: see text] is a solution of the considered problem. Based on the idea of the alternating variable minimization with multiplier method, we propose two iterative methods to compute the solution of the considered problem, and analyze the global convergence results of the proposed algorithms. Numerical results illustrate the proposed methods are more effective than the existing two methods proposed in Peng et al. (Appl Math Comput 160:763-777, 2005) and Peng (Int J Comput Math 87: 1820-1830, 2010).

Implementation of Fiber Substructuring Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

2001-01-01

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were incorporated into a mechanics of materials based micromechanics method. In the current work, the micromechanics method is revised such that the composite unit cell is divided into a number of slices. Micromechanics equations are then developed for each slice, with laminate theory applied to determine the elastic properties, effective stresses and effective inelastic strains for the unit cell. Verification studies are conducted using two representative polymer matrix composites with a nonlinear, strain rate dependent deformation response. The computed results compare well to experimentally obtained values.

Applying transfer matrix method to the estimation of the modal characteristics of the NASA Mini-Mass Truss

NASA Technical Reports Server (NTRS)

Shen, Ji-Yao; Taylor, Lawrence W., Jr.

1994-01-01

It is beneficial to use a distributed parameter model for large space structures because the approach minimizes the number of model parameters. Holzer's transfer matrix method provides a useful means to simplify and standardize the procedure for solving the system of partial differential equations. Any large space structures can be broken down into sub-structures with simple elastic and dynamical properties. For each single element, such as beam, tether, or rigid body, we can derive the corresponding transfer matrix. Combining these elements' matrices enables the solution of the global system equations. The characteristics equation can then be formed by satisfying the appropriate boundary conditions. Then natural frequencies and mode shapes can be determined by searching the roots of the characteristic equation at frequencies within the range of interest. This paper applies this methodology, and the maximum likelihood estimation method, to refine the modal characteristics of the NASA Mini-Mast Truss by successively matching the theoretical response to the test data of the truss. The method is being applied to more complex configurations.

Parallel scalability of Hartree-Fock calculations

NASA Astrophysics Data System (ADS)

Chow, Edmond; Liu, Xing; Smelyanskiy, Mikhail; Hammond, Jeff R.

2015-03-01

Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree-Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.

Assessment of two-dimensional induced accelerations from measured kinematic and kinetic data.

PubMed

Hof, A L; Otten, E

2005-11-01

A simple algorithm is presented to calculate the induced accelerations of body segments in human walking for the sagittal plane. The method essentially consists of setting up 2x4 force equations, 4 moment equations, 2x3 joint constraint equations and two constraints related to the foot-ground interaction. Data needed for the equations are, next to masses and moments of inertia, the positions of ankle, knee and hip. This set of equations is put in the form of an 18x18 matrix or 20x20 matrix, the solution of which can be found by inversion. By applying input vectors related to gravity, to centripetal accelerations or to muscle moments, the 'induced' accelerations and reaction forces related to these inputs can be found separately. The method was tested for walking in one subject. Good agreement was found with published results obtained by much more complicated three-dimensional forward dynamic models.

Transport features of nano-hydroxylapatite (n-HA) embedded silicone rubber (SR) systems: influence of SR/n-HA interaction, degree of reinforcement and morphology.

PubMed

M, Bindu; G, Unnikrishnan

2017-09-27

We report the transport characteristics of silicone rubber/nano-hydroxylapatite (SR/n-HA) systems at room temperature with reference to the effects of n-HA loading, morphology and penetrant nature, using toluene, xylene, ethyl acetate and butyl acetate in the liquid phase and methanol, ethanol, 1-propanol, 2-propanol and butanol in the vapour phase as probe molecules. The interaction between the n-HA particles and SR matrix has been confirmed by FTIR analysis. As the n-HA content in the SR matrix increased, the penetrant uptake has been found to decrease. The observations have been correlated with the density and void content of the systems. Scanning electron microscopy images have been found to be complementary to the observed transport features. The reinforcement effect of n-HA particles on the SR matrix has been verified by Kraus equation. Molecular mass between the cross links has been observed to decrease with an increase in n-HA loading. The results have been compared with affine, phantom network, parallel, series and Maxwell models. The transport data have been complemented by observations on biological fluid uptake with urea, d-glucose, KI, saline water, phosphate buffer and artificial urine as the media.

Notes on quantitative structure-properties relationships (QSPR) (1): A discussion on a QSPR dimensionality paradox (QSPR DP) and its quantum resolution.

PubMed

Carbó-Dorca, Ramon; Gallegos, Ana; Sánchez, Angel J

2009-05-01

Classical quantitative structure-properties relationship (QSPR) statistical techniques unavoidably present an inherent paradoxical computational context. They rely on the definition of a Gram matrix in descriptor spaces, which is used afterwards to reduce the original dimension via several possible kinds of algebraic manipulations. From there, effective models for the computation of unknown properties of known molecular structures are obtained. However, the reduced descriptor dimension causes linear dependence within the set of discrete vector molecular representations, leading to positive semi-definite Gram matrices in molecular spaces. To resolve this QSPR dimensionality paradox (QSPR DP) here is proposed to adopt as starting point the quantum QSPR (QQSPR) computational framework perspective, where density functions act as infinite dimensional descriptors. The fundamental QQSPR equation, deduced from employing quantum expectation value numerical evaluation, can be approximately solved in order to obtain models exempt of the QSPR DP. The substitution of the quantum similarity matrix by an empirical Gram matrix in molecular spaces, build up with the original non manipulated discrete molecular descriptor vectors, permits to obtain classical QSPR models with the same characteristics as in QQSPR, that is: possessing a certain degree of causality and explicitly independent of the descriptor dimension. 2008 Wiley Periodicals, Inc.

Quantum Dynamics in Biological Systems

NASA Astrophysics Data System (ADS)

Shim, Sangwoo

In the first part of this dissertation, recent efforts to understand quantum mechanical effects in biological systems are discussed. Especially, long-lived quantum coherences observed during the electronic energy transfer process in the Fenna-Matthews-Olson complex at physiological condition are studied extensively using theories of open quantum systems. In addition to the usual master equation based approaches, the effect of the protein structure is investigated in atomistic detail through the combined application of quantum chemistry and molecular dynamics simulations. To evaluate the thermalized reduced density matrix, a path-integral Monte Carlo method with a novel importance sampling approach is developed for excitons coupled to an arbitrary phonon bath at a finite temperature. In the second part of the thesis, simulations of molecular systems and applications to vibrational spectra are discussed. First, the quantum dynamics of a molecule is simulated by combining semiclassical initial value representation and density funcitonal theory with analytic derivatives. A computationally-tractable approximation to the sum-of-states formalism of Raman spectra is subsequently discussed.

SEDIDAT: A BASIC program for the collection and statistical analysis of particle settling velocity data

NASA Astrophysics Data System (ADS)

Wright, Robyn; Thornberg, Steven M.

SEDIDAT is a series of compiled IBM-BASIC (version 2.0) programs that direct the collection, statistical calculation, and graphic presentation of particle settling velocity and equivalent spherical diameter for samples analyzed using the settling tube technique. The programs follow a menu-driven format that is understood easily by students and scientists with little previous computer experience. Settling velocity is measured directly (cm,sec) and also converted into Chi units. Equivalent spherical diameter (reported in Phi units) is calculated using a modified Gibbs equation for different particle densities. Input parameters, such as water temperature, settling distance, particle density, run time, and Phi;Chi interval are changed easily at operator discretion. Optional output to a dot-matrix printer includes a summary of moment and graphic statistical parameters, a tabulation of individual and cumulative weight percents, a listing of major distribution modes, and cumulative and histogram plots of a raw time, settling velocity. Chi and Phi data.

Polystyrene Foam Products Equation of State as a Function of Porosity and Fill Gas

NASA Astrophysics Data System (ADS)

Mulford, R. N.; Swift, D. C.

2009-12-01

An accurate EOS for polystyrene foam is necessary for analysis of numerous experiments in shock compression, inertial confinement fusion, and astrophysics. Plastic to gas ratios vary between various samples of foam, according to the density and cell-size of the foam. A matrix of compositions has been investigated, allowing prediction of foam response as a function of the plastic-to-air ratio. The EOS code CHEETAH allows participation of the air in the decomposition reaction of the foam. Differences between air-filled, Ar-blown, and CO2-blown foams are investigated, to estimate the importance of allowing air to react with products of polystyrene decomposition. O2-blown foams are included in some comparisons, to amplify any consequences of reaction with oxygen in air. He-blown foams are included in some comparisons, to provide an extremum of density. Product pressures are slightly higher for oxygen-containing fill gases than for non-oxygen-containing fill gases. Examination of product species indicates that CO2 decomposes at high temperatures.

Darkness without dark matter and energy - generalized unimodular gravity

NASA Astrophysics Data System (ADS)

Barvinsky, A. O.; Kamenshchik, A. Yu.

2017-11-01

We suggest a Lorentz non-invariant generalization of the unimodular gravity theory, which is classically equivalent to general relativity with a locally inert (devoid of local degrees of freedom) perfect fluid having an equation of state with a constant parameter w. For the range of w near -1 this dark fluid can play the role of dark energy, while for w = 0 this dark dust admits spatial inhomogeneities and can be interpreted as dark matter. We discuss possible implications of this model in the cosmological initial conditions problem. In particular, this is the extension of known microcanonical density matrix predictions for the initial quantum state of the closed cosmology to the case of spatially open Universe, based on the imitation of the spatial curvature by the dark fluid density. We also briefly discuss quantization of this model necessarily involving the method of gauge systems with reducible constraints and the effect of this method on the treatment of recently! suggested mechanism of vacuum energy sequestering.

Current density characteristics in the studies of electromagnetically induced transparency in a GaAs/GaAlAs quantum well

NASA Astrophysics Data System (ADS)

Jayarubi, J.; Peter, A. John

2017-05-01

Confinement potential profiles due to conduction and valence bands are obtained in a Ga0.7Al0.3As/ GaAs/ Ga0.7Al0.3As using variation formulism. The free electron distribution is carried out. The confined energy eigenvalue and its corresponding wavefunctions of charge carriers are found using self-consistent method. The confined energies with the geometrical confinement are computed. The potentials due to charges are done by Poisson equation. The effects of dielectric mismatch between the GaAs and GaAlAs semiconductors are introduced in the effective potential expressions. Transfer matrix method is employed to obtain the respective energies. The transmission probability is obtained for a constant well size. The high current density characteristics as a function of applied voltage is investigated. This investigation on the electromagnetically induced transparency in the photonic material will exploit in fabricating novel nonlinear optical devices in future.

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Unsteady density-current equations for highly curved terrain

NASA Technical Reports Server (NTRS)

Sivakumaran, N. S.; Dressler, R. F.

1989-01-01

New nonlinear partial differential equations containing terrain curvature and its rate of change are derived that describe the flow of an atmospheric density current. Unlike the classical hydraulic-type equations for density currents, the new equations are valid for two-dimensional, gradually varied flow over highly curved terrain, hence suitable for computing unsteady (or steady) flows over arbitrary mountain/valley profiles. The model assumes the atmosphere above the density current exerts a known arbitrary variable pressure upon the unknown interface. Later this is specialized to the varying hydrostatic pressure of the atmosphere above. The new equations yield the variable velocity distribution, the interface position, and the pressure distribution that contains a centrifugal component, often significantly larger than its hydrostatic component. These partial differential equations are hyperbolic, and the characteristic equations and characteristic directions are derived. Using these to form a characteristic mesh, a hypothetical unsteady curved-flow problem is calculated, not based upon observed data, merely as an example to illustrate the simplicity of their application to unsteady flows over mountains.

A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.

2015-07-01

In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

NASA Technical Reports Server (NTRS)

Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James

1992-01-01

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Effect of atomic spontaneous decay on entanglement in the generalized Jaynes-Cummings model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hessian, H.A.; Obada, A.-S.F.; Mohamed, A.-B.A.

2010-03-15

Some aspects of the irreversible dynamics of a generalized Jaynes-Cummings model are addressed. By working in the dressed-state representation, it is possible to split the dynamics of the entanglement and coherence. The exact solution of the master equation in the case of a high-Q cavity with atomic decay is found. Effects of the atomic spontaneous decay on the temporal evolution of partial entropies of the atom or the field and the total entropy as a quantitative measure entanglement are elucidated. The degree of entanglement, through the sum of the negative eigenvalues of the partially transposed density matrix and the negativemore » mutual information has been studied and compared with other measures.« less

Kerr nonlinearity and nonlinear absorption coefficient in a four-level M-model cylindrical quantum dot under the phenomenon of electromagnetically induced transparency

NASA Astrophysics Data System (ADS)

Behroozian, B.; Askari, H. R.

2018-07-01

The Kerr nonlinearity and the nonlinear absorption coefficient in a four-level M-model of a GaAs cylindrical quantum dot (QD) with parabolic potential under electromagnetically induced transparency are investigated. By solving the density matrix equations in the steady-state, the third order susceptibility is obtained. Then, by using the real and imaginary parts of third order susceptibility, the Kerr nonlinearity and the nonlinear absorption coefficient, respectively, for this system are computed. The effects of the radius and height of the cylindrical QD are then investigated. In addition, the effects of the control laser fields on the Kerr nonlinearity and the nonlinear absorption coefficient are investigated.

Vibrational and vibronic coherences in the dynamics of the FMO complex

NASA Astrophysics Data System (ADS)

Liu, Xiaomeng; Kühn, Oliver

2016-12-01

The coupled exciton-vibrational dynamics of a seven site Frenkel exciton model of the Fenna-Matthews-Olson (FMO) complex is investigated using a Quantum Master Equation approach. Thereby, one vibrational mode per monomer is treated explicitly as being part of the relevant system. Emphasis is put on the comparison of this model with that of a purely excitonic relevant system. Further, the effects of two different approximations to the exciton-vibrational basis are investigated, namely the one- and two-particle description. Analysis of the vibronic and vibrational density matrix in the site basis points to the importance of on- and inter-site coherences for the exciton transfer. Here, one- and two-particle approximations give rise to qualitatively different results.

Ramsey scheme for coherent population resonance detection in the optically dense medium

NASA Astrophysics Data System (ADS)

Barantsev, Konstantin; Litvinov, Andrey; Popov, Evgeniy

2018-04-01

This work is devoted to a theoretical investigation of the Ramsey method of detection of the coherent population trapping resonance in cold atomic clouds taking into account collective effects caused by finite optical depth of the considered clouds. The interaction of atoms with pulsed laser radiation is described in the formalism of density matrix by means of Maxwell-Bloch set of equations. The Ramsey signal of coherent population trapping resonance was calculated for the radiation passed through the medium and analyzed for different length of the atomic cloud. Also the population of excited level was calculated in dependence on the two-photon detuning and coordinate along the main optical axis. The light shift of sidebands and appearance of additional harmonics were discovered.

Approximate methods for the fast computation of EPR and ST-EPR spectra. V. Application of the perturbation approach to the problem of anisotropic motion

NASA Astrophysics Data System (ADS)

Robinson, B. H.; Dalton, L. R.

1981-01-01

The modulation perturbation treatment of Galloway and Dalton is applied to the solution of the stochastic Liouville equation for the spin density matrix which incorporates an anisotropic rotational diffusion operator. Pseudosecular and saturation terms of the spin hamiltonian are explicitly considered as is the interaction of the electron spins with the applied Zeeman modulation field. The modulation perturbation treatment results in a factor of four improvement in computational speed relative to inversion of the full supermatrix with little or no loss of computational accuracy. The theoretical simulations of EPR and ST-EPR spectra are in nearly quantitative agreement with experimental spectra taken under high resolution conditions.

Glueball spectra from a matrix model of pure Yang-Mills theory

NASA Astrophysics Data System (ADS)

Acharyya, Nirmalendu; Balachandran, A. P.; Pandey, Mahul; Sanyal, Sambuddha; Vaidya, Sachindeo

2018-05-01

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang-Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang-Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

Multi-cut solutions in Chern-Simons matrix models

NASA Astrophysics Data System (ADS)

Morita, Takeshi; Sugiyama, Kento

2018-04-01

We elaborate the Chern-Simons (CS) matrix models at large N. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hayes, S. L.; Harp, J. M.; Chichester, H. J. M.

Research and development activities on metallic fuels in the US are focused on their potential use for actinide transmutation in future sodium fast reactors. As part of this application, there is a desire to demonstrate a multifold increase in burnup potential. A number of metallic fuel design innovations are under investigation with a view toward significantly increasing the burnup potential of metallic fuels, since higher discharge burnups equate to lower potential actinide losses during recycle. Promising innovations under investigation include: 1) lowering the fuel smeared density in order to accommodate the additional swelling expected as burnups increase, 2) utilizing anmore » annular fuel geometry for better geometrical stability at low smeared densities, as well as the potential to eliminate the need for a sodium bond, and 3) minor alloy additions to immobilize lanthanide fission products inside the metallic fuel matrix and prevent their transport to the cladding resulting in fuel-cladding chemical interaction. This paper presents results from these efforts to advance metallic fuel technology in support of high burnup and actinide transmutation objectives. Highlights include examples of fabrication of low smeared density annular metallic fuels, experiments to identify alloy additions effective in immobilizing lanthanide fission products, and early postirradiation examinations of annular metallic fuels having low smeared densities and palladium additions for fission product immobilization.« less

Ensemble Averaged Probability Density Function (APDF) for Compressible Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2012-01-01

In this paper, we present a concept of the averaged probability density function (APDF) for studying compressible turbulent reacting flows. The APDF is defined as an ensemble average of the fine grained probability density function (FG-PDF) with a mass density weighting. It can be used to exactly deduce the mass density weighted, ensemble averaged turbulent mean variables. The transport equation for APDF can be derived in two ways. One is the traditional way that starts from the transport equation of FG-PDF, in which the compressible Navier- Stokes equations are embedded. The resulting transport equation of APDF is then in a traditional form that contains conditional means of all terms from the right hand side of the Navier-Stokes equations except for the chemical reaction term. These conditional means are new unknown quantities that need to be modeled. Another way of deriving the transport equation of APDF is to start directly from the ensemble averaged Navier-Stokes equations. The resulting transport equation of APDF derived from this approach appears in a closed form without any need for additional modeling. The methodology of ensemble averaging presented in this paper can be extended to other averaging procedures: for example, the Reynolds time averaging for statistically steady flow and the Reynolds spatial averaging for statistically homogeneous flow. It can also be extended to a time or spatial filtering procedure to construct the filtered density function (FDF) for the large eddy simulation (LES) of compressible turbulent reacting flows.

Solution of the Orr-Sommerfeld equation for the Blausius boundary-layer documentation of program ORRBL and a test case

NASA Technical Reports Server (NTRS)

Biringen, S.; Danabasoglu, G.

1988-01-01

A Chebyshev matrix collocation method is outlined for the solution of the Orr-Sommerfeld equation for the Blausius boundary layer. User information is provided for FORTRAN program ORRBL which solves the equation by the QR method.

Meta-Analytic Structural Equation Modeling (MASEM): Comparison of the Multivariate Methods

ERIC Educational Resources Information Center

Zhang, Ying

2011-01-01

Meta-analytic Structural Equation Modeling (MASEM) has drawn interest from many researchers recently. In doing MASEM, researchers usually first synthesize correlation matrices across studies using meta-analysis techniques and then analyze the pooled correlation matrix using structural equation modeling techniques. Several multivariate methods of…

Associative Flow Rule Used to Include Hydrostatic Stress Effects in Analysis of Strain-Rate-Dependent Deformation of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.

2004-01-01

designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and the strain-rate dependence of the composite response are due primarily to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. By applying micromechanics techniques along with given fiber properties, one can also determine the effects of the hydrostatic stresses in the polymer on the overall composite deformation response. First efforts to account for the hydrostatic stress effects in the composite deformation applied purely empirical methods that relied on composite-level data. In later efforts, to allow polymer properties to be characterized solely on the basis of polymer data, researchers at the NASA Glenn Research Center developed equations to model the polymers that were based on a non-associative flow rule, and efforts to use these equations to simulate the deformation of representative polymer materials were reasonably successful. However, these equations were found to have difficulty in correctly analyzing the multiaxial stress states found in the polymer matrix constituent of a composite material. To correct these difficulties, and to allow for the accurate simulation of the nonlinear strain-rate-dependent deformation analysis of polymer matrix composites, in the efforts reported here Glenn researchers reformulated the polymer constitutive equations from basic principles using the concept of an associative flow rule. These revised equations were characterized and validated in an experimental program carried out through a university grant with the Ohio State University, wherein tensile and shear deformation data were obtained for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. Tensile deformation data also were obtained over a variety of strain rates and fiber orientation angles for a representative polymer matrix composite composed using the polymer.

A Concise Introduction to Quantum Mechanics

NASA Astrophysics Data System (ADS)

Swanson, Mark S.

2018-02-01

Assuming a background in basic classical physics, multivariable calculus, and differential equations, A Concise Introduction to Quantum Mechanics provides a self-contained presentation of the mathematics and physics of quantum mechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric effect, and electron diffraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyze the system consisting of a particle confined to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schrödinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. The general properties of the Schrödinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic field. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.

Nonequilibrium, steady-state electron transport with N-representable density matrices from the anti-Hermitian contracted Schrödinger equation

NASA Astrophysics Data System (ADS)

Rothman, Adam E.; Mazziotti, David A.

2010-03-01

We study molecular conductivity for a one-electron, bath-molecule-bath model Hamiltonian. The primary quantum-mechanical variable is the one-electron reduced density matrix (1-RDM). By identifying similarities between the steady-state Liouville equation and the anti-Hermitian contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. A 75, 022505 (2007)], we develop a way of enforcing nonequilibrium, steady-state behavior in a time-independent theory. Our results illustrate the relationship between current and voltage in molecular junctions assuming that the total number of electrons under consideration can be fixed across all driving potentials. The impetus for this work is a recent study by Subotnik et al. that also uses the 1-RDM to study molecular conductivity under different assumptions regarding the total number of electrons [J. E. Subotnik et al., J. Chem. Phys. 130, 144105 (2009)]. Unlike calculations in the previous study, our calculations result in 1-RDMs that are fully N-representable. The present work maintains N-representability through a bath-bath mixing that is related to a time-independent relaxation of the baths in the absence of the molecule, as governed by the ACSE. A lack of N-representability can be important since it corresponds to occupying energy states in the molecule or baths with more than one electron or hole (the absence of an electron) in violation of the Pauli principle. For this reason the present work may serve as an important, albeit preliminary, step in designing a 2-RDM/ACSE method for studying steady-state molecular conductivity with an explicit treatment of electron correlation.

A density functional approach to ferrogels

NASA Astrophysics Data System (ADS)

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.

Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

NASA Astrophysics Data System (ADS)

Zhou, Xin

1990-03-01

For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.

Horizontal density-gradient effects on simulation of flow and transport in the Potomac Estuary

USGS Publications Warehouse

Schaffranek, Raymond W.; Baltzer, Robert A.; ,

1990-01-01

A two-dimensional, depth-integrated, hydrodynamic/transport model of the Potomac Estuary between Indian Head and Morgantown, Md., has been extended to include treatment of baroclinic forcing due to horizontal density gradients. The finite-difference model numerically integrates equations of mass and momentum conservation in conjunction with a transport equation for heat, salt, and constituent fluxes. Lateral and longitudinal density gradients are determined from salinity distributions computed from the convection-diffusion equation and an equation of state that expresses density as a function of temperature and salinity; thus, the hydrodynamic and transport computations are directly coupled. Horizontal density variations are shown to contribute significantly to momentum fluxes determined in the hydrodynamic computation. These fluxes lead to enchanced tidal pumping, and consequently greater dispersion, as is evidenced by numerical simulations. Density gradient effects on tidal propagation and transport behavior are discussed and demonstrated.

Simplified equation for Young's modulus of CNT reinforced concrete

NASA Astrophysics Data System (ADS)

Chandran, RameshBabu; Gifty Honeyta A, Maria

2017-12-01

This research investigation focuses on finite element modeling of carbon nanotube (CNT) reinforced concrete matrix for three grades of concrete namely M40, M60 and M120. Representative volume element (RVE) was adopted and one-eighth model depicting the CNT reinforced concrete matrix was simulated using FEA software ANSYS17.2. Adopting random orientation of CNTs, with nine fibre volume fractions from 0.1% to 0.9%, finite element modeling simulations replicated exactly the CNT reinforced concrete matrix. Upon evaluations of the model, the longitudinal and transverse Young's modulus of elasticity of the CNT reinforced concrete was arrived. The graphical plots between various fibre volume fractions and the concrete grade revealed simplified equation for estimating the young's modulus. It also exploited the fact that the concrete grade does not have significant impact in CNT reinforced concrete matrix.

Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra by quantum separation of variables

NASA Astrophysics Data System (ADS)

Pezelier, Baptiste

2018-02-01

In this proceeding, we recall the notion of quantum integrable systems on a lattice and then introduce the Sklyanin’s Separation of Variables method. We sum up the main results for the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazanov-Stroganov Lax operator. These results apply as well to the spectral analysis of the lattice sine-Gordon model with open boundary conditions. The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations. We state an equivalent characterization as the set of solutions to a Baxter’s like T-Q functional equation, allowing us to rewrite the transfer matrix eigenstates in an algebraic Bethe ansatz form.

Decomposed direct matrix inversion for fast non-cartesian SENSE reconstructions.

PubMed

Qian, Yongxian; Zhang, Zhenghui; Wang, Yi; Boada, Fernando E

2006-08-01

A new k-space direct matrix inversion (DMI) method is proposed here to accelerate non-Cartesian SENSE reconstructions. In this method a global k-space matrix equation is established on basic MRI principles, and the inverse of the global encoding matrix is found from a set of local matrix equations by taking advantage of the small extension of k-space coil maps. The DMI algorithm's efficiency is achieved by reloading the precalculated global inverse when the coil maps and trajectories remain unchanged, such as in dynamic studies. Phantom and human subject experiments were performed on a 1.5T scanner with a standard four-channel phased-array cardiac coil. Interleaved spiral trajectories were used to collect fully sampled and undersampled 3D raw data. The equivalence of the global k-space matrix equation to its image-space version, was verified via conjugate gradient (CG) iterative algorithms on a 2x undersampled phantom and numerical-model data sets. When applied to the 2x undersampled phantom and human-subject raw data, the decomposed DMI method produced images with small errors (< or = 3.9%) relative to the reference images obtained from the fully-sampled data, at a rate of 2 s per slice (excluding 4 min for precalculating the global inverse at an image size of 256 x 256). The DMI method may be useful for noise evaluations in parallel coil designs, dynamic MRI, and 3D sodium MRI with fixed coils and trajectories. Copyright 2006 Wiley-Liss, Inc.

Towards a multiconfigurational method of increments

NASA Astrophysics Data System (ADS)

Fertitta, E.; Koch, D.; Paulus, B.; Barcza, G.; Legeza, Ö.

2018-06-01

The method of increments (MoI) allows one to successfully calculate cohesive energies of bulk materials with high accuracy, but it encounters difficulties when calculating dissociation curves. The reason is that its standard formalism is based on a single Hartree-Fock (HF) configuration whose orbitals are localised and used for the many-body expansion. In situations where HF does not allow a size-consistent description of the dissociation, the MoI cannot be guaranteed to yield proper results either. Herein, we address the problem by employing a size-consistent multiconfigurational reference for the MoI formalism. This leads to a matrix equation where a coupling derived by the reference itself is employed. In principle, such an approach allows one to evaluate approximate values for the ground as well as excited states energies. While the latter are accurate close to the avoided crossing only, the ground state results are very promising for the whole dissociation curve, as shown by the comparison with density matrix renormalisation group benchmarks. We tested this two-state constant-coupling MoI on beryllium rings of different sizes and studied the error introduced by the constant coupling.

A Transfer Hamiltonian Model for Devices Based on Quantum Dot Arrays

PubMed Central

Illera, S.; Prades, J. D.; Cirera, A.; Cornet, A.

2015-01-01

We present a model of electron transport through a random distribution of interacting quantum dots embedded in a dielectric matrix to simulate realistic devices. The method underlying the model depends only on fundamental parameters of the system and it is based on the Transfer Hamiltonian approach. A set of noncoherent rate equations can be written and the interaction between the quantum dots and between the quantum dots and the electrodes is introduced by transition rates and capacitive couplings. A realistic modelization of the capacitive couplings, the transmission coefficients, the electron/hole tunneling currents, and the density of states of each quantum dot have been taken into account. The effects of the local potential are computed within the self-consistent field regime. While the description of the theoretical framework is kept as general as possible, two specific prototypical devices, an arbitrary array of quantum dots embedded in a matrix insulator and a transistor device based on quantum dots, are used to illustrate the kind of unique insight that numerical simulations based on the theory are able to provide. PMID:25879055

An approximate stationary solution for multi-allele neutral diffusion with low mutation rates.

PubMed

Burden, Conrad J; Tang, Yurong

2016-12-01

We address the problem of determining the stationary distribution of the multi-allelic, neutral-evolution Wright-Fisher model in the diffusion limit. A full solution to this problem for an arbitrary K×K mutation rate matrix involves solving for the stationary solution of a forward Kolmogorov equation over a (K-1)-dimensional simplex, and remains intractable. In most practical situations mutations rates are slow on the scale of the diffusion limit and the solution is heavily concentrated on the corners and edges of the simplex. In this paper we present a practical approximate solution for slow mutation rates in the form of a set of line densities along the edges of the simplex. The method of solution relies on parameterising the general non-reversible rate matrix as the sum of a reversible part and a set of (K-1)(K-2)/2 independent terms corresponding to fluxes of probability along closed paths around faces of the simplex. The solution is potentially a first step in estimating non-reversible evolutionary rate matrices from observed allele frequency spectra. Copyright © 2016 Elsevier Inc. All rights reserved.

A transfer hamiltonian model for devices based on quantum dot arrays.

PubMed

Illera, S; Prades, J D; Cirera, A; Cornet, A

2015-01-01

We present a model of electron transport through a random distribution of interacting quantum dots embedded in a dielectric matrix to simulate realistic devices. The method underlying the model depends only on fundamental parameters of the system and it is based on the Transfer Hamiltonian approach. A set of noncoherent rate equations can be written and the interaction between the quantum dots and between the quantum dots and the electrodes is introduced by transition rates and capacitive couplings. A realistic modelization of the capacitive couplings, the transmission coefficients, the electron/hole tunneling currents, and the density of states of each quantum dot have been taken into account. The effects of the local potential are computed within the self-consistent field regime. While the description of the theoretical framework is kept as general as possible, two specific prototypical devices, an arbitrary array of quantum dots embedded in a matrix insulator and a transistor device based on quantum dots, are used to illustrate the kind of unique insight that numerical simulations based on the theory are able to provide.

Imaging diffusive media using time-independent and time-harmonic sources: dependence of image quality on imaging algorithms, target volume, weight matrix, and view angles

NASA Astrophysics Data System (ADS)

Chang, Jenghwa; Aronson, Raphael; Graber, Harry L.; Barbour, Randall L.

1995-05-01

We present results examining the dependence of image quality for imaging in dense scattering media as influenced by the choice of parameters pertaining to the physical measurement and factors influencing the efficiency of the computation. The former includes the density of the weight matrix as affected by the target volume, view angle, and source condition. The latter includes the density of the weight matrix and type of algorithm used. These were examined by solving a one-step linear perturbation equation derived from the transport equation using three different algorithms: POCS, CGD, and SART algorithms with contraints. THe above were explored by evaluating four different 3D cylindrical phantom media: a homogeneous medium, an media containing a single black rod on the axis, a single black rod parallel to the axis, and thirteen black rods arrayed in the shape of an 'X'. Solutions to the forward problem were computed using Monte Carlo methods for an impulse source, from which was calculated time- independent and time harmonic detector responses. The influence of target volume on image quality and computational efficiency was studied by computing solution to three types of reconstructions: 1) 3D reconstruction, which considered each voxel individually, 2) 2D reconstruction, which assumed that symmetry along the cylinder axis was know a proiri, 3) 2D limited reconstruction, which assumed that only those voxels in the plane of the detectors contribute information to the detecot readings. The effect of view angle was explored by comparing computed images obtained from a single source, whose position was varied, as well as for the type of tomographic measurement scheme used (i.e., radial scan versus transaxial scan). The former condition was also examined for the dependence of the above on choice of source condition [ i.e., cw (2D reconstructions) versus time-harmonic (2D limited reconstructions) source]. The efficiency of the computational effort was explored, principally, by conducting a weight matrix 'threshold titration' study. This involved computing the ratio of each matrix element to the maximum element of its row and setting this to zero if the ratio was less than a preselected threshold. Results obtained showed that all three types of reconstructions provided good image quality. The 3D reconstruction outperformed the other two reconstructions. The time required for 2D and 2D limited reconstruction is much less (< 10%) than that for the 3D reconstruction. The 'threshold titration' study shows that artifacts were present when the threshold was 5% or higher, and no significant differences of image quality were observed when the thresholds were less tha 1%, in which case 38% (21,849 of 57,600) of the total weight elements were set to zero. Restricting the view angle produced degradation in image quality, but, in all cases, clearly recognizable images were obtained.

Strain Rate Dependent Deformation and Strength Modeling of a Polymer Matrix Composite Utilizing a Micromechanics Approach. Degree awarded by Cincinnati Univ.

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

1999-01-01

Potential gas turbine applications will expose polymer matrix composites to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under extreme conditions. Specifically, analytical methods designed for these applications must have the capability of properly capturing the strain rate sensitivities and nonlinearities that are present in the material response. The Ramaswamy-Stouffer constitutive equations, originally developed to analyze the viscoplastic deformation of metals, have been modified to simulate the nonlinear deformation response of ductile, crystalline polymers. The constitutive model is characterized and correlated for two representative ductile polymers. Fiberite 977-2 and PEEK, and the computed results correlate well with experimental values. The polymer constitutive equations are implemented in a mechanics of materials based composite micromechanics model to predict the nonlinear, rate dependent deformation response of a composite ply. Uniform stress and uniform strain assumptions are applied to compute the effective stresses of a composite unit cell from the applied strains. The micromechanics equations are successfully verified for two polymer matrix composites. IM7/977-2 and AS4/PEEK. The ultimate strength of a composite ply is predicted with the Hashin failure criteria that were implemented in the composite micromechanics model. The failure stresses of the two composite material systems are accurately predicted for a variety of fiber orientations and strain rates. The composite deformation model is implemented in LS-DYNA, a commercially available transient dynamic explicit finite element code. The matrix constitutive equations are converted into an incremental form, and the model is implemented into LS-DYNA through the use of a user defined material subroutine. The deformation response of a bulk polymer and a polymer matrix composite are predicted by finite element analyses. The results compare reasonably well to experimental values, with some discrepancies. The discrepancies are at least partially caused by the method used to integrate the rate equations in the polymer constitutive model.

Parallel algorithms for computation of the manipulator inertia matrix

NASA Technical Reports Server (NTRS)

Amin-Javaheri, Masoud; Orin, David E.

1989-01-01

The development of an O(log2N) parallel algorithm for the manipulator inertia matrix is presented. It is based on the most efficient serial algorithm which uses the composite rigid body method. Recursive doubling is used to reformulate the linear recurrence equations which are required to compute the diagonal elements of the matrix. It results in O(log2N) levels of computation. Computation of the off-diagonal elements involves N linear recurrences of varying-size and a new method, which avoids redundant computation of position and orientation transforms for the manipulator, is developed. The O(log2N) algorithm is presented in both equation and graphic forms which clearly show the parallelism inherent in the algorithm.

Unified theory of quantized electrons, phonons, and photons out of equilibrium: A simplified ab initio approach based on the generalized Baym-Kadanoff ansatz

NASA Astrophysics Data System (ADS)

de Melo, Pedro Miguel M. C.; Marini, Andrea

2016-04-01

We present a full ab initio description of the coupled out-of-equilibrium dynamics of photons, phonons, and electrons. In the present approach, the quantized nature of the electromagnetic field as well as of the nuclear oscillations is fully taken into account. The result is a set of integrodifferential equations, written on the Keldysh contour, for the Green's functions of electrons, phonons, and photons where the different kinds of interactions are merged together. We then concentrate on the electronic dynamics in order to reduce the problem to a computationally feasible approach. By using the generalized Baym-Kadanoff ansatz and the completed collision approximation, we introduce a series of efficient but controllable approximations. In this way, we reduce all equations to a set of decoupled equations for the density matrix that describe all kinds of static and dynamical correlations. The final result is a coherent, general, and inclusive scheme to calculate several physical quantities: carrier dynamics, transient photoabsorption, and light emission, all of which include, at the same time, electron-electron, electron-phonon, and electron-photon interactions. We further discuss how all these observables can be easily calculated within the present scheme using a fully atomistic ab initio approach.

Mathematical model of water transport in Bacon and alkaline matrix-type hydrogen-oxygen fuel cells

NASA Technical Reports Server (NTRS)

Prokopius, P. R.; Easter, R. W.

1972-01-01

Based on general mass continuity and diffusive transport equations, a mathematical model was developed that simulates the transport of water in Bacon and alkaline-matrix fuel cells. The derived model was validated by using it to analytically reproduce various Bacon and matrix-cell experimental water transport transients.

Empirical data and the variance-covariance matrix for the 1969 Smithsonian Standard Earth (2)

NASA Technical Reports Server (NTRS)

Gaposchkin, E. M.

1972-01-01

The empirical data used in the 1969 Smithsonian Standard Earth (2) are presented. The variance-covariance matrix, or the normal equations, used for correlation analysis, are considered. The format and contents of the matrix, available on magnetic tape, are described and a sample printout is given.

Research on numerical algorithms for large space structures

NASA Technical Reports Server (NTRS)

Denman, E. D.

1981-01-01

Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.

Multi-Dimensional Asymptotically Stable 4th Order Accurate Schemes for the Diffusion Equation

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Ditkowski, Adi

1996-01-01

An algorithm is presented which solves the multi-dimensional diffusion equation on co mplex shapes to 4th-order accuracy and is asymptotically stable in time. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty like terms. Numerical examples in 2-D show that the method is effective even where standard schemes, stable by traditional definitions fail.

Aspects of the inverse problem for the Toda chain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kozlowski, K. K., E-mail: karol.kozlowski@u-bourgogne.fr

We generalize Babelon's approach to equations in dual variables so as to be able to treat new types of operators which we build out of the sub-constituents of the model's monodromy matrix. Further, we also apply Sklyanin's recent monodromy matrix identities so as to obtain equations in dual variables for yet other operators. The schemes discussed in this paper appear to be universal and thus, in principle, applicable to many models solvable through the quantum separation of variables.

Exact differential equation for the density and ionization energy of a many-particle system

NASA Technical Reports Server (NTRS)

Levy, M.; Perdew, J. P.; Sahni, V.

1984-01-01

The present investigation is concerned with relations studied by Hohenberg and Kohn (1964) and Kohn and Sham (1965). The properties of a ground-state many-electron system are determined by the electron density. The correct differential equation for the density, as dictated by density-functional theory, is presented. It is found that the ground-state density n of a many-electron system obeys a Schroedinger-like differential equation which may be solved by standard Kohn-Sham programs. Results are connected to the traditional exact Kohn-Sham theory. It is pointed out that the results of the current investigations are readily extended to spin-density functional theory.

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Godfrey, Andrew G.

1993-01-01

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Energy density functional on a microscopic basis

NASA Astrophysics Data System (ADS)

Baldo, M.; Robledo, L.; Schuck, P.; Viñas, X.

2010-06-01

In recent years impressive progress has been made in the development of highly accurate energy density functionals, which allow us to treat medium-heavy nuclei. In this approach one tries to describe not only the ground state but also the first relevant excited states. In general, higher accuracy requires a larger set of parameters, which must be carefully chosen to avoid redundancy. Following this line of development, it is unavoidable that the connection of the functional with the bare nucleon-nucleon interaction becomes more and more elusive. In principle, the construction of a density functional from a density matrix expansion based on the effective nucleon-nucleon interaction is possible, and indeed the approach has been followed by few authors. However, to what extent a density functional based on such a microscopic approach can reach the accuracy of the fully phenomenological ones remains an open question. A related question is to establish which part of a functional can be actually derived by a microscopic approach and which part, in contrast, must be left as purely phenomenological. In this paper we discuss the main problems that are encountered when the microscopic approach is followed. To this purpose we will use the method we have recently introduced to illustrate the different aspects of these problems. In particular we will discuss the possible connection of the density functional with the nuclear matter equation of state and the distinct features of finite-size effect typical of nuclei.

A split band-Cholesky equation solving strategy for finite element analysis of transient field problems. [in fluid mechanics

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1978-01-01

The paper describes the split-Cholesky strategy for banded matrices arising from the large systems of equations in certain fluid mechanics problems. The basic idea is that for a banded matrix the computation can be carried out in pieces, with only a small portion of the matrix residing in core. Mesh considerations are discussed by demonstrating the manner in which the assembly of finite element equations proceeds for linear trial functions on a triangular mesh. The FORTRAN code which implements the out-of-core decomposition strategy for banded symmetric positive definite matrices (mass matrices) of a coupled initial value problem is given.

Geometry of Lax pairs: Particle motion and Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2013-01-01

A geometric formulation of the Lax pair equation on a curved manifold is studied using the phase-space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well-known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting a hidden symmetry of Killing-Yano tensors.

Matrix Sturm-Liouville equation with a Bessel-type singularity on a finite interval

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia

2017-03-01

The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.

Split Octonion Reformulation for Electromagnetic Chiral Media of Massive Dyons

NASA Astrophysics Data System (ADS)

Chanyal, B. C.

2017-12-01

In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2×2 Zorn’s vector matrix realization of split-octonion and its dual Euclidean spaces, we represent the unified structure of split octonionic electric and magnetic induction vectors for chiral media. As such, in present paper, we describe the chiral parameter and pairing constants in terms of split octonionic matrix representation of Drude-Born-Fedorov constitutive relations. We have expressed a split octonionic electromagnetic field vector for chiral media, which exhibits the unified field structure of electric and magnetic chiral fields of dyons. The beauty of split octonionic representation of Zorn vector matrix realization is that, the every scalar and vector components have its own meaning in the generalized chiral electromagnetism of dyons. Correspondingly, we obtained the alternative form of generalized Proca-Maxwell’s equations of massive dyons in chiral media. Furthermore, the continuity equations, Poynting theorem and wave propagation for generalized electromagnetic fields of chiral media of massive dyons are established by split octonionic form of Zorn vector matrix algebra.

Incorporation of Mean Stress Effects into the Micromechanical Analysis of the High Strain Rate Response of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.; Gilat, Amos

2002-01-01

The results presented here are part of an ongoing research program, to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. A micromechanics approach is employed in this work, in which state variable constitutive equations originally developed for metals have been modified to model the deformation of the polymer matrix, and a strength of materials based micromechanics method is used to predict the effective response of the composite. In the analysis of the inelastic deformation of the polymer matrix, the definitions of the effective stress and effective inelastic strain have been modified in order to account for the effect of hydrostatic stresses, which are significant in polymers. Two representative polymers, a toughened epoxy and a brittle epoxy, are characterized through the use of data from tensile and shear tests across a variety of strain rates. Results computed by using the developed constitutive equations correlate well with data generated via experiments. The procedure used to incorporate the constitutive equations within a micromechanics method is presented, and sample calculations of the deformation response of a composite for various fiber orientations and strain rates are discussed.

Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

PubMed

Schuss, Z; Nadler, B; Eisenberg, R S

2001-09-01

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time averages over long times of the motion of a quasiparticle that diffuses with the same diffusion coefficient as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.

Quantitative (31)P NMR spectroscopy and (1)H MRI measurements of bone mineral and matrix density differentiate metabolic bone diseases in rat models.

PubMed

Cao, Haihui; Nazarian, Ara; Ackerman, Jerome L; Snyder, Brian D; Rosenberg, Andrew E; Nazarian, Rosalynn M; Hrovat, Mirko I; Dai, Guangping; Mintzopoulos, Dionyssios; Wu, Yaotang

2010-06-01

In this study, bone mineral density (BMD) of normal (CON), ovariectomized (OVX), and partially nephrectomized (NFR) rats was measured by (31)P NMR spectroscopy; bone matrix density was measured by (1)H water- and fat-suppressed projection imaging (WASPI); and the extent of bone mineralization (EBM) was obtained by the ratio of BMD/bone matrix density. The capability of these MR methods to distinguish the bone composition of the CON, OVX, and NFR groups was evaluated against chemical analysis (gravimetry). For cortical bone specimens, BMD of the CON and OVX groups was not significantly different; BMD of the NFR group was 22.1% (by (31)P NMR) and 17.5% (by gravimetry) lower than CON. For trabecular bone specimens, BMD of the OVX group was 40.5% (by (31)P NMR) and 24.6% (by gravimetry) lower than CON; BMD of the NFR group was 26.8% (by (31)P NMR) and 21.5% (by gravimetry) lower than CON. No significant change of cortical bone matrix density between CON and OVX was observed by WASPI or gravimetry; NFR cortical bone matrix density was 10.3% (by WASPI) and 13.9% (by gravimetry) lower than CON. OVX trabecular bone matrix density was 38.0% (by WASPI) and 30.8% (by gravimetry) lower than CON, while no significant change in NFR trabecular bone matrix density was observed by either method. The EBMs of OVX cortical and trabecular specimens were slightly higher than CON but not significantly different from CON. Importantly, EBMs of NFR cortical and trabecular specimens were 12.4% and 26.3% lower than CON by (31)P NMR/WASPI, respectively, and 4.0% and 11.9% lower by gravimetry. Histopathology showed evidence of osteoporosis in the OVX group and severe secondary hyperparathyroidism (renal osteodystrophy) in the NFR group. These results demonstrate that the combined (31)P NMR/WASPI method is capable of discerning the difference in EBM between animals with osteoporosis and those with impaired bone mineralization. Copyright 2010 Elsevier Inc. All rights reserved.

Radiation reabsorption in a laser-produced plasma

NASA Astrophysics Data System (ADS)

Brunner, W.; John, R. W.; Paul, H.; Steudel, H.

1988-11-01

Taking into account the emission and absorption of resonance radiation in a recombining laser-produced plasma of intermediate density, the system of rate equations for the population densities coupled with the radiative transfer equation is approximately treated. In the case of spatially varying absorption, an approximate form of the rate equation determining the population density of the upper resonance level is derived. By applying this relation to an axially symmetric plasma, a simple formula that describes the effect of radiation reabsorption on the spatial behavior of the population density is obtained.

Applications of Black Scholes Complexity Concepts to Combat Modelling

DTIC Science & Technology

2009-03-01

Lauren, G C McIntosh, N D Perry and J Moffat, Chaos 17, 2007. 4 Lanchester Models of Warfare Volumes 1 and 2, J G Taylor, Operations Research Society...transformation matrix A Lanchester Equation solution parameter bi Dependent model variables b(x,t) Variable variance rate B Lanchester Equation solution...distribution. The similarity between this equation and the Lanchester Equations (equation 1) is clear. This suggests an obvious solution to the question of

Autonomous Navigation of a Satellite Cluster

DTIC Science & Technology

1990-12-01

satellite’s velocity are determined by the Clohessy - Wiltshire equations I (these equations will be introduced in the next section) and take the form: (8:80...transition matrix, is based upon the Clohessy - Wiltshire equations of motion. These equations describe "the relative motion of two satellites when one is in a...discovery warranted a re-examination of the solutions to the Clohessy - Wiltshire equations. If the solutions for satellite #1 and #2 are subtracted

Generalized isobaric multiplet mass equation and its application to the Nolen-Schiffer anomaly

NASA Astrophysics Data System (ADS)

Dong, J. M.; Zhang, Y. H.; Zuo, W.; Gu, J. Z.; Wang, L. J.; Sun, Y.

2018-02-01

The Wigner isobaric multiplet mass equation (IMME) is the most fundamental prediction in nuclear physics with the concept of isospin. However, it was deduced based on the Wigner-Eckart theorem with the assumption that all charge-violating interactions can be written as tensors of rank two. In the present work, the charge-symmetry breaking (CSB) and charge-independent breaking (CIB) components of the nucleon-nucleon force, which contribute to the effective interaction in nuclear medium, are established in the framework of Brueckner theory with AV18 and AV14 bare interactions. Because such charge-violating components can no longer be expressed as an irreducible tensor due to density dependence, its matrix element cannot be analytically reduced by the Wigner-Eckart theorem. With an alternative approach, we derive a generalized IMME (GIMME) that modifies the coefficients of the original IMME. As the first application of GIMME, we study the long-standing question of the origin of the Nolen-Schiffer anomaly (NSA) found in the Coulomb displacement energy of mirror nuclei. We find that the naturally emerged CSB term in GIMME is largely responsible for explaining the NSA.

Steady bipartite coherence induced by non-equilibrium environment

NASA Astrophysics Data System (ADS)

Huangfu, Yong; Jing, Jun

2018-01-01

We study the steady state of two coupled two-level atoms interacting with a non-equilibrium environment that consists of two heat baths at different temperatures. Specifically, we analyze four cases with respect to the configuration about the interactions between atoms and heat baths. Using secular approximation, the conventional master equation usually neglects steady-state coherence, even when the system is coupled with a non-equilibrium environment. When employing the master equation with no secular approximation, we find that the system coherence in our model, denoted by the off-diagonal terms in the reduced density matrix spanned by the eigenvectors of the system Hamiltonian, would survive after a long-time decoherence evolution. The absolute value of residual coherence in the system relies on different configurations of interaction channels between the system and the heat baths. We find that a large steady quantum coherence term can be achieved when the two atoms are resonant. The absolute value of quantum coherence decreases in the presence of additional atom-bath interaction channels. Our work sheds new light on the mechanism of steady-state coherence in microscopic quantum systems in non-equilibrium environments.

A multichannel model for the self-consistent analysis of coherent transport in graphene nanoribbons.

PubMed

Mencarelli, Davide; Pierantoni, Luca; Farina, Marco; Di Donato, Andrea; Rozzi, Tullio

2011-08-23

In this contribution, we analyze the multichannel coherent transport in graphene nanoribbons (GNRs) by a scattering matrix approach. We consider the transport properties of GNR devices of a very general form, involving multiple bands and multiple leads. The 2D quantum transport over the whole GNR surface, described by the Schrödinger equation, is strongly nonlinear as it implies calculation of self-generated and externally applied electrostatic potentials, solutions of the 3D Poisson equation. The surface charge density is computed as a balance of carriers traveling through the channel at all of the allowed energies. Moreover, formation of bound charges corresponding to a discrete modal spectrum is observed and included in the model. We provide simulation examples by considering GNR configurations typical for transistor devices and GNR protrusions that find an interesting application as cold cathodes for X-ray generation. With reference to the latter case, a unified model is required in order to couple charge transport and charge emission. However, to a first approximation, these could be considered as independent problems, as in the example. © 2011 American Chemical Society

Cavity-coupled double-quantum dot at finite bias: Analogy with lasers and beyond

NASA Astrophysics Data System (ADS)

Kulkarni, Manas; Cotlet, Ovidiu; Türeci, Hakan E.

2014-09-01

We present a theoretical and experimental study of photonic and electronic transport properties of a voltage biased InAs semiconductor double quantum dot (DQD) that is dipole coupled to a superconducting transmission line resonator. We obtain the master equation for the reduced density matrix of the coupled system of cavity photons and DQD electrons accounting systematically for both the presence of phonons and the effect of leads at finite voltage bias. We subsequently derive analytical expressions for transmission, phase response, photon number, and the nonequilibrium steady-state electron current. We show that the coupled system under finite bias realizes an unconventional version of a single-atom laser and analyze the spectrum and the statistics of the photon flux leaving the cavity. In the transmission mode, the system behaves as a saturable single-atom amplifier for the incoming photon flux. Finally, we show that the back action of the photon emission on the steady-state current can be substantial. Our analytical results are compared to exact master equation results establishing regimes of validity of various analytical models. We compare our findings to available experimental measurements.

Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

NASA Astrophysics Data System (ADS)

Semenov, Alexander; Babikov, Dmitri

2013-11-01

We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complex-valued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by real-valued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the body-fixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

Detecting Damage in Ceramic Matrix Composites Using Electrical Resistance

NASA Technical Reports Server (NTRS)

Smith, Craig E.; Gyekenyesi, Andrew

2011-01-01

The majority of damage in SiC/SiC ceramic matrix composites subjected to monotonic tensile loads is in the form of distributed matrix cracks. These cracks initiate near stress concentrations, such as 90 deg fiber tows or large matrix pores and continue to accumulate with additional stress until matrix crack saturation is achieved. Such damage is difficult to detect with conventional nondestructive evaluation techniques (immersion ultrasonics, x-ray, etc.). Monitoring a specimen.s electrical resistance change provides an indirect approach for monitoring matrix crack density. Sylramic-iBN fiber- reinforced SiC composites with a melt infiltrated (MI) matrix were tensile tested at room temperature. Results showed an increase in resistance of more than 500% prior to fracture, which can be detected either in situ or post-damage. A relationship between resistance change and matrix crack density was also determined.

Detecting Cracks in Ceramic Matrix Composites by Electrical Resistance

NASA Technical Reports Server (NTRS)

Smith, Craig; Gyekenyesi, Andrew

2011-01-01

The majority of damage in SiC/SiC ceramic matrix composites subjected to monotonic tensile loads is in the form of distributed matrix cracks. These cracks initiate near stress concentrations, such as 90o fiber tows or large matrix pores and continue to accumulate with additional stress until matrix crack saturation is achieved. Such damage is difficult to detect with conventional nondestructive evaluation techniques (immersion ultrasonics, x-ray, etc.). Monitoring a specimen.s electrical resistance change provides an indirect approach for monitoring matrix crack density. Sylramic-iBN fiber- reinforced SiC composites with a melt infiltrated (MI) matrix were tensile tested at room temperature. Results showed an increase in resistance of more than 500% prior to fracture, which can be detected either in situ or post-damage. A relationship between resistance change and matrix crack density was also determined.

Fundamental Flux Equations for Fracture-Matrix Interactions with Linear Diffusion

NASA Astrophysics Data System (ADS)

Oldenburg, C. M.; Zhou, Q.; Rutqvist, J.; Birkholzer, J. T.

2017-12-01

The conventional dual-continuum models are only applicable for late-time behavior of pressure propagation in fractured rock, while discrete-fracture-network models may explicitly deal with matrix blocks at high computational expense. To address these issues, we developed a unified-form diffusive flux equation for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular matrix blocks (squares, cubes, rectangles, and rectangular parallelepipeds) by partitioning the entire dimensionless-time domain (Zhou et al., 2017a, b). For each matrix block, this flux equation consists of the early-time solution up until a switch-over time after which the late-time solution is applied to create continuity from early to late time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the coefficients dependent on dimensionless area-to-volume ratio and aspect ratios for rectangular blocks. For the late-time solutions, one exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic blocks. The time-partitioning method was also used for calculating pressure/concentration/temperature distribution within a matrix block. The approximate solution contains an error-function solution for early times and an exponential solution for late times, with relative errors less than 0.003. These solutions form the kernel of multirate and multidimensional hydraulic, solute and thermal diffusion in fractured reservoirs.

The ESS and replicator equation in matrix games under time constraints.

PubMed

Garay, József; Cressman, Ross; Móri, Tamás F; Varga, Tamás

2018-06-01

Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model. Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games.

A computational method for solving stochastic Itô–Volterra integral equations based on stochastic operational matrix for generalized hat basis functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

2014-08-01

In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Itô–Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0,T] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by forward substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O(1/(n{sup 2}) ). Further, in order to show themore » accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method.« less

An efficient algorithm using matrix methods to solve wind tunnel force-balance equations

NASA Technical Reports Server (NTRS)

Smith, D. L.

1972-01-01

An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.

Investigation of Elliptical Cooling Channels for a Naval Electromagnetic Railgun

DTIC Science & Technology

2005-05-09

Numerical Recipes in C : The Art of Scientific Computing, Second Edition. Cambridge: Cambridge University Press, 1992. Ramanujan , S. Ramanujan’s...by Midshipman 1/ c Elizabeth R. Kealey, Class of 2005 United States Naval Academy Annapolis, MD ___________________________________ (signature...system 55 10 Equation 46: Fourier number 55 Equation 47: General heat equation with coefficients a, b, c , and d 55 Equation 48: Tridiagonal matrix

Satellite Formation Design for Space Based Radar Applications

DTIC Science & Technology

2007-07-30

communications. While the Clohessy - Wiltshire Hills (CWH) equations have been in existence for sometime, it is more recently that they have been... Clohessy - Wiltshire equations. To get the state transition matrix for relative position and velocity, these differential equations are integrated to...Practical Guidance Methodology for Relative Motion of LEO Spacecraft Based on the Clohessy - Wiltshire Equations,” AAS Paper 04-252, AAS/AIAA Space

Low-Density Parity-Check Code Design Techniques to Simplify Encoding

NASA Astrophysics Data System (ADS)

Perez, J. M.; Andrews, K.

2007-11-01

This work describes a method for encoding low-density parity-check (LDPC) codes based on the accumulate-repeat-4-jagged-accumulate (AR4JA) scheme, using the low-density parity-check matrix H instead of the dense generator matrix G. The use of the H matrix to encode allows a significant reduction in memory consumption and provides the encoder design a great flexibility. Also described are new hardware-efficient codes, based on the same kind of protographs, which require less memory storage and area, allowing at the same time a reduction in the encoding delay.

Variational optimization algorithms for uniform matrix product states

NASA Astrophysics Data System (ADS)

Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T.; Verstraete, F.; Haegeman, J.

2018-01-01

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

An improved model of fission gas atom transport in irradiated uranium dioxide

NASA Astrophysics Data System (ADS)

Shea, J. H.

2018-04-01

The hitherto standard approach to predicting fission gas release has been a pure diffusion gas atom transport model based upon Fick's law. An additional mechanism has subsequently been identified from experimental data at high burnup and has been summarised in an empirical model that is considered to embody a so-called fuel matrix 'saturation' phenomenon whereby the fuel matrix has become saturated with fission gas so that the continued addition of extra fission gas atoms results in their expulsion from the fuel matrix into the fuel rod plenum. The present paper proposes a different approach by constructing an enhanced fission gas transport law consisting of two components: 1) Fick's law and 2) a so-called drift term. The new transport law can be shown to be effectively identical in its predictions to the 'saturation' approach and is more readily physically justifiable. The method introduces a generalisation of the standard diffusion equation which is dubbed the Drift Diffusion Equation. According to the magnitude of a dimensionless Péclet number, P, the new equation can vary from pure diffusion to pure drift, which latter represents a collective motion of the fission gas atoms through the fuel matrix at a translational velocity. Comparison is made between the saturation and enhanced transport approaches. Because of its dependence on P, the Drift Diffusion Equation is shown to be more effective at managing the transition from one type of limiting transport phenomenon to the other. Thus it can adapt appropriately according to the reactor operation.

Computational complexities and storage requirements of some Riccati equation solvers

NASA Technical Reports Server (NTRS)

Utku, Senol; Garba, John A.; Ramesh, A. V.

1989-01-01

The linear optimal control problem of an nth-order time-invariant dynamic system with a quadratic performance functional is usually solved by the Hamilton-Jacobi approach. This leads to the solution of the differential matrix Riccati equation with a terminal condition. The bulk of the computation for the optimal control problem is related to the solution of this equation. There are various algorithms in the literature for solving the matrix Riccati equation. However, computational complexities and storage requirements as a function of numbers of state variables, control variables, and sensors are not available for all these algorithms. In this work, the computational complexities and storage requirements for some of these algorithms are given. These expressions show the immensity of the computational requirements of the algorithms in solving the Riccati equation for large-order systems such as the control of highly flexible space structures. The expressions are also needed to compute the speedup and efficiency of any implementation of these algorithms on concurrent machines.

On Rank and Nullity

ERIC Educational Resources Information Center

Dobbs, David E.

2012-01-01

This note explains how Emil Artin's proof that row rank equals column rank for a matrix with entries in a field leads naturally to the formula for the nullity of a matrix and also to an algorithm for solving any system of linear equations in any number of variables. This material could be used in any course on matrix theory or linear algebra.

Multigrid Equation Solvers for Large Scale Nonlinear Finite Element Simulations

DTIC Science & Technology

1999-01-01

purpose of the second partitioning phase , on each SMP, is to minimize the communication within the SMP; even if a multi - threaded matrix vector product...8.7 Comparison of model with experimental data for send phase of matrix vector product on ne grid...140 8.4 Matrix vector product phase times : : : : : : : : : : : : : : : : : : : : : : : 145 9.1 Flat and

The use of an analytic Hamiltonian matrix for solving the hydrogenic atom

NASA Astrophysics Data System (ADS)

Bhatti, Mohammad

2001-10-01

The non-relativistic Hamiltonian corresponding to the Shrodinger equation is converted into analytic Hamiltonian matrix using the kth order B-splines functions. The Galerkin method is applied to the solution of the Shrodinger equation for bound states of hydrogen-like systems. The program Mathematica is used to create analytic matrix elements and exact integration is performed over the knot-sequence of B-splines and the resulting generalized eigenvalue problem is solved on a specified numerical grid. The complete basis set and the energy spectrum is obtained for the coulomb potential for hydrogenic systems with Z less than 100 with B-splines of order eight. Another application is given to test the Thomas-Reiche-Kuhn sum rule for the hydrogenic systems.

A Chess-Like Game for Teaching Engineering Students to Solve Large System of Simultaneous Linear Equations

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Mohammed, Ahmed Ali; Kadiam, Subhash

2010-01-01

Solving large (and sparse) system of simultaneous linear equations has been (and continues to be) a major challenging problem for many real-world engineering/science applications [1-2]. For many practical/large-scale problems, the sparse, Symmetrical and Positive Definite (SPD) system of linear equations can be conveniently represented in matrix notation as [A] {x} = {b} , where the square coefficient matrix [A] and the Right-Hand-Side (RHS) vector {b} are known. The unknown solution vector {x} can be efficiently solved by the following step-by-step procedures [1-2]: Reordering phase, Matrix Factorization phase, Forward solution phase, and Backward solution phase. In this research work, a Game-Based Learning (GBL) approach has been developed to help engineering students to understand crucial details about matrix reordering and factorization phases. A "chess-like" game has been developed and can be played by either a single player, or two players. Through this "chess-like" open-ended game, the players/learners will not only understand the key concepts involved in reordering algorithms (based on existing algorithms), but also have the opportunities to "discover new algorithms" which are better than existing algorithms. Implementing the proposed "chess-like" game for matrix reordering and factorization phases can be enhanced by FLASH [3] computer environments, where computer simulation with animated human voice, sound effects, visual/graphical/colorful displays of matrix tables, score (or monetary) awards for the best game players, etc. can all be exploited. Preliminary demonstrations of the developed GBL approach can be viewed by anyone who has access to the internet web-site [4]!

On the cross-stream spectral method for the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Zorumski, William E.; Hodge, Steven L.

1993-01-01

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

Low-density resin impregnated ceramic article and method for making the same

NASA Technical Reports Server (NTRS)

Tran, Huy K. (Inventor); Henline, William D. (Inventor); Hsu, Ming-ta S. (Inventor); Rasky, Daniel J. (Inventor); Riccitiello, Salvatore R. (Inventor)

1997-01-01

A low-density resin impregnated ceramic article advantageously employed as a structural ceramic ablator comprising a matrix of ceramic fibers. The fibers of the ceramic matrix are coated with an organic resin film. The organic resin can be a thermoplastic resin or a cured thermosetting resin. In one embodiment, the resin is uniformly distributed within the ceramic article. In a second embodiment, the resin is distributed so as to provide a density gradient along at least one direction of the ceramic article. The resin impregnated ceramic article is prepared by providing a matrix of ceramic fibers; immersing the matrix of ceramic fibers in a solution of a solvent and an organic resin infiltrant; and removing the solvent to form a resin film on the ceramic fibers.

Optimizing finite element predictions of local subchondral bone structural stiffness using neural network-derived density-modulus relationships for proximal tibial subchondral cortical and trabecular bone.

PubMed

Nazemi, S Majid; Amini, Morteza; Kontulainen, Saija A; Milner, Jaques S; Holdsworth, David W; Masri, Bassam A; Wilson, David R; Johnston, James D

2017-01-01

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain. However, it is unclear what density-modulus equation(s) should be applied with subchondral cortical and subchondral trabecular bone when constructing finite element models of the tibia. Using a novel approach applying neural networks, optimization, and back-calculation against in situ experimental testing results, the objective of this study was to identify subchondral-specific equations that optimized finite element predictions of local structural stiffness at the proximal tibial subchondral surface. Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using multiple density-modulus equations (93 total variations) then mapped to corresponding finite element models. For each variation, root mean squared error was calculated between finite element prediction and in situ measured stiffness at 47 indentation sites. Resulting errors were used to train an artificial neural network, which provided an unlimited number of model variations, with corresponding error, for predicting stiffness at the subchondral bone surface. Nelder-Mead optimization was used to identify optimum density-modulus equations for predicting stiffness. Finite element modeling predicted 81% of experimental stiffness variance (with 10.5% error) using optimized equations for subchondral cortical and trabecular bone differentiated with a 0.5g/cm 3 density. In comparison with published density-modulus relationships, optimized equations offered improved predictions of local subchondral structural stiffness. Further research is needed with anisotropy inclusion, a smaller voxel size and de-blurring algorithms to improve predictions. Copyright © 2016 Elsevier Ltd. All rights reserved.

The physics of polarization

NASA Astrophysics Data System (ADS)

Landi Degl'Innocenti, Egidio

This course is intended to give a description of the basic physical concepts which underlie the study and the interpretation of polarization phenomena. Apart from a brief historical introduction (Sect. 1), the course is organized in three parts. A first part (Sects. 2 - 6) covers the most relevant facts about the polarization phenomena that are typically encountered in laboratory applications and in everyday life. In Sect. 2, the modern description of polarization in terms of the Stokes parameters is recalled, whereas Sect. 3 is devoted to introduce the basic tools of laboratory polarimetry, such as the Jones calculus and the Mueller matrices. The polarization phenomena which are met in the reflection and refraction of a beam of radiation at the separation surface between two dielectrics, or between a dielectric and a metal, are recalled in Sect. 4. Finally, Sect. 5 gives an introduction to the phenomena of dichroism and of anomalous dispersion and Sect. 6 summarizes the polarization phenomena that are commonly encountered in everyday life. The second part of this course (Sects. 7-14) deals with the description, within the formalism of classical physics, of the spectro-polarimetric properties of the radiation emitted by accelerated charges. Such properties are derived by taking as starting point the Liénard and Wiechert equations that are recalled and discussed in Sect. 7 both in the general case and in the non-relativistic approximation. The results are developed to find the percentage polarization, the radiation diagram, the cross-section and the spectral characteristics of the radiation emitted in different phenomena particularly relevant from the astrophysical point of view. The emission of a linear antenna is derived in Sect. 8. The other Sections are devoted to Thomson scattering (Sect. 9), Rayleigh scattering (Sect. 10), Mie scattering (Sect. 11), bremsstrahlung radiation (Sect. 12), cyclotron radiation (Sect. 13), and synchrotron radiation (Sect. 14). Finally, the third part (Sects. 15-19) is devoted to give a sketch of the theory of the generation and transfer of polarized radiation in spectral lines. After a general introduction to the argument (Sect. 15), the concepts of density-matrix and of atomic polarization are illustrated in Sect. 16. In Sect. 17, a parallelism is established, within the framework of the theory of stellar atmospheres, between the usual formalism, which neglects polarization phenomena, and the more involved formalism needed for the interpretation of spectro-polarimetric observations. Some consequences of the radiative transfer equations for polarized radiation, pointing to the importance of dichroism phenomena in establishing the amplification condition via stimulated emission, are discussed in Sect. 18. The last section (Sect. 19) is devoted to introduce the problem of finding a self-consistent solution of the radiative transfer equations for polarized radiation and of the statistical equilibrium equations for the density matrix (non-LTE of the 2nd kind).

A high-order spatial filter for a cubed-sphere spectral element model

NASA Astrophysics Data System (ADS)

Kang, Hyun-Gyu; Cheong, Hyeong-Bin

2017-04-01

A high-order spatial filter is developed for the spectral-element-method dynamical core on the cubed-sphere grid which employs the Gauss-Lobatto Lagrange interpolating polynomials (GLLIP) as orthogonal basis functions. The filter equation is the high-order Helmholtz equation which corresponds to the implicit time-differencing of a diffusion equation employing the high-order Laplacian. The Laplacian operator is discretized within a cell which is a building block of the cubed sphere grid and consists of the Gauss-Lobatto grid. When discretizing a high-order Laplacian, due to the requirement of C0 continuity along the cell boundaries the grid-points in neighboring cells should be used for the target cell: The number of neighboring cells is nearly quadratically proportional to the filter order. Discrete Helmholtz equation yields a huge-sized and highly sparse matrix equation whose size is N*N with N the number of total grid points on the globe. The number of nonzero entries is also almost in quadratic proportion to the filter order. Filtering is accomplished by solving the huge-matrix equation. While requiring a significant computing time, the solution of global matrix provides the filtered field free of discontinuity along the cell boundaries. To achieve the computational efficiency and the accuracy at the same time, the solution of the matrix equation was obtained by only accounting for the finite number of adjacent cells. This is called as a local-domain filter. It was shown that to remove the numerical noise near the grid-scale, inclusion of 5*5 cells for the local-domain filter was found sufficient, giving the same accuracy as that obtained by global domain solution while reducing the computing time to a considerably lower level. The high-order filter was evaluated using the standard test cases including the baroclinic instability of the zonal flow. Results indicated that the filter performs better on the removal of grid-scale numerical noises than the explicit high-order viscosity. It was also presented that the filter can be easily implemented on the distributed-memory parallel computers with a desirable scalability.

Calculating the True and Observed Rates of Complex Heterogeneous Catalytic Reactions

NASA Astrophysics Data System (ADS)

Avetisov, A. K.; Zyskin, A. G.

2018-06-01

Equations of the theory of steady-state complex reactions are considered in matrix form. A set of stage stationarity equations is given, and an algorithm is described for deriving the canonic set of stationarity equations with appropriate corrections for the existence of fast stages in a mechanism. A formula for calculating the number of key compounds is presented. The applicability of the Gibbs rule to estimating the number of independent compounds in a complex reaction is analyzed. Some matrix equations relating the rates of dependent and key substances are derived. They are used as a basis to determine the general diffusion stoichiometry relationships between temperature, the concentrations of dependent reaction participants, and the concentrations of key reaction participants in a catalyst grain. An algorithm is described for calculating heat and mass transfer in a catalyst grain with respect to arbitrary complex heterogeneous catalytic reactions.

Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques.

PubMed

Han, Seungsuk; Yarkony, David R

2011-05-07

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.

Two-Layer Viscous Shallow-Water Equations and Conservation Laws

NASA Astrophysics Data System (ADS)

Kanayama, Hiroshi; Dan, Hiroshi

In our previous papers, the two-layer viscous shallow-water equations were derived from the three-dimensional Navier-Stokes equations under the hydrostatic assumption. Also, it was noted that the combination of upper and lower equations in the two-layer model produces the classical one-layer equations if the density of each layer is the same. Then, the two-layer equations were approximated by a finite element method which followed our numerical scheme established for the one-layer model in 1978. Also, it was numerically demonstrated that the interfacial instability generated when the densities are the same can be eliminated by providing a sufficient density difference. In this paper, we newly show that conservation laws are still valid in the two-layer model. Also, we show results of a new physical experiment for the interfacial instability.

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

NASA Technical Reports Server (NTRS)

Winget, J. M.; Hughes, T. J. R.

1985-01-01

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations

DOE PAGES

Shao, Xuan-Min

2016-04-12

The fundamental electromagnetic equations used by lightning researchers were introduced in a seminal paper by Uman, McLain, and Krider in 1975. However, these equations were derived for an infinitely thin, one-dimensional source current, and not for a general three-dimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a three-dimensional, time-dependent current density distribution based on Jefimenko's original electric and magnetic equations. To do this, we derive the Jefimenko electric field equation into a new form that depends only on the time-dependent current density similar to that of Uman, McLain, and Krider,more » rather than on both the charge and current densities in its original form. The original Jefimenko magnetic field equation depends only on current, so no further derivation is needed. We show that the equations of Uman, McLain, and Krider can be readily obtained from the generalized equations if a one-dimensional source current is considered. For the purpose of practical applications, we discuss computational implementation of the new equations and present electric field calculations for a three-dimensional, conical-shape discharge.« less

Effect of an atom on a quantum guided field in a weakly driven fiber-Bragg-grating cavity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Le Kien, Fam; Hakuta, K.

2010-02-15

We study the interaction of an atom with a quantum guided field in a weakly driven fiber-Bragg-grating (FBG) cavity. We present an effective Hamiltonian and derive the density-matrix equations for the combined atom-cavity system. We calculate the mean photon number, the second-order photon correlation function, and the atomic excited-state population. We show that due to the confinement of the guided cavity field in the fiber cross-section plane and in the space between the FBG mirrors, the presence of the atom in the FBG cavity can significantly affect the mean photon number and the photon statistics even though the cavity finessemore » is moderate, the cavity is long, and the probe field is weak.« less

Active mode-locking of mid-infrared quantum cascade lasers with short gain recovery time.

PubMed

Wang, Yongrui; Belyanin, Alexey

2015-02-23

We investigate the dynamics of actively modulated mid-infrared quantum cascade lasers (QCLs) using space- and time-domain simulations of coupled density matrix and Maxwell equations with resonant tunneling current taken into account. We show that it is possible to achieve active mode locking and stable generation of picosecond pulses in high performance QCLs with a vertical laser transition and a short gain recovery time by bias modulation of a short section of a monolithic Fabry-Perot cavity. In fact, active mode locking in QCLs with a short gain recovery time turns out to be more robust to the variation of parameters as compared to previously studied lasers with a long gain recovery time. We investigate the effects of spatial hole burning and phase locking on the laser output.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang, Zhoufei; Ouyang, Xiaolong; Gong, Zhihao

An extended hierarchy equation of motion (HEOM) is proposed and applied to study the dynamics of the spin-boson model. In this approach, a complete set of orthonormal functions are used to expand an arbitrary bath correlation function. As a result, a complete dynamic basis set is constructed by including the system reduced density matrix and auxiliary fields composed of these expansion functions, where the extended HEOM is derived for the time derivative of each element. The reliability of the extended HEOM is demonstrated by comparison with the stochastic Hamiltonian approach under room-temperature classical ohmic and sub-ohmic noises and the multilayermore » multiconfiguration time-dependent Hartree theory under zero-temperature quantum ohmic noise. Upon increasing the order in the hierarchical expansion, the result obtained from the extended HOEM systematically converges to the numerically exact answer.« less

Exchange-Induced Relaxation in the Presence of a Fictitious Field

PubMed Central

Sorce, Dennis J.; Mangia, Silvia; Liimatainen, Timo; Garwood, Michael; Michaeli, Shalom

2014-01-01

In the present study we derive a solution for two site fast exchange-induced relaxation in the presence of a fictitious magnetic field as generated by amplitude and frequency modulated RF pulses. This solution provides a means to analyze data obtained from relaxation experiments with the method called RAFFn (Relaxation Along a Fictitious Field of rank n), in which a fictitious field is created in a coordinate frame undergoing multi-fold rotation about n axes (rank n). The RAFF2 technique is relevant to MRI relaxation methods that provide good contrast enhancement for tumor detection. The relaxation equations for n = 2 are derived for the fast exchange regime using density matrix formalism. The method of derivation can be further extended to obtain solutions for n > 2. PMID:24911888

Autoionizing states driven by stochastic electromagnetic fields

NASA Astrophysics Data System (ADS)

Mouloudakis, G.; Lambropoulos, P.

2018-01-01

We have examined the profile of an isolated autoionizing resonance driven by a pulse of short duration and moderately strong field. The analysis has been based on stochastic differential equations governing the time evolution of the density matrix under a stochastic field. Having focused our quantitative analysis on the 2{{s}}2{{p}}({}1{{P}}) resonance of helium, we have investigated the role of field fluctuations and of the duration of the pulse. We report surprisingly strong distortion of the profile, even for peak intensity below the strong field limit. Our results demonstrate the intricate connection between intensity and pulse duration, with the latter appearing to be the determining influence, even for a seemingly short pulse of 50 fs. Further effects that would arise under much shorter pulses are discussed.

Development of a poly(dimethylacrylamide) based matrix material for solid phase high density peptide array synthesis employing a laser based material transfer

NASA Astrophysics Data System (ADS)

Ridder, Barbara; Foertsch, Tobias C.; Welle, Alexander; Mattes, Daniela S.; von Bojnicic-Kninski, Clemens M.; Loeffler, Felix F.; Nesterov-Mueller, Alexander; Meier, Michael A. R.; Breitling, Frank

2016-12-01

Poly(dimethylacrylamide) (PDMA) based matrix materials were developed for laser-based in situ solid phase peptide synthesis to produce high density arrays. In this specific array synthesis approach, amino acid derivatives are embedded into a matrix material, serving as a ;solid; solvent material at room temperature. Then, a laser pulse transfers this mixture to the target position on a synthesis slide, where the peptide array is synthesized. Upon heating above the glass transition temperature of the matrix material, it softens, allowing diffusion of the amino acid derivatives to the synthesis surface and serving as a solvent for peptide bond formation. Here, we synthesized PDMA six-arm star polymers, offering the desired matrix material properties, using atom transfer radical polymerization. With the synthesized polymers as matrix material, we structured and synthesized arrays with combinatorial laser transfer. With densities of up to 20,000 peptide spots per cm2, the resolution could be increased compared to the commercially available standard matrix material. Time-of-Flight Secondary Ion Mass Spectrometry experiments revealed the penetration behavior of an amino acid derivative into the prepared acceptor synthesis surface and the effectiveness of the washing protocols.

Decay of correlations between cross-polarized electromagnetic waves in a two-dimensional random medium.

PubMed

Gorodnichev, E E

2018-04-01

The problem of multiple scattering of polarized light in a two-dimensional medium composed of fiberlike inhomogeneities is studied. The attenuation lengths for the density matrix elements are calculated. For a highly absorbing medium it is found that, as the sample thickness increases, the intensity of waves polarized along the fibers decays faster than the other density matrix elements. With further increase in the sample thickness, the off-diagonal elements which are responsible for correlations between the cross-polarized waves disappear. In the asymptotic limit of very thick samples the scattered light proves to be polarized perpendicular to the fibers. The difference in the attenuation lengths between the density matrix elements results in a nonmonotonic depth dependence of the degree of polarization. In the opposite case of a weakly absorbing medium, the off-diagonal element of the density matrix and, correspondingly, the correlations between the cross-polarized fields are shown to decay faster than the intensity of waves polarized along and perpendicular to the fibers.

Joint refinement model for the spin resolved one-electron reduced density matrix of YTiO3 using magnetic structure factors and magnetic Compton profiles data.

PubMed

Gueddida, Saber; Yan, Zeyin; Kibalin, Iurii; Voufack, Ariste Bolivard; Claiser, Nicolas; Souhassou, Mohamed; Lecomte, Claude; Gillon, Béatrice; Gillet, Jean-Michel

2018-04-28

In this paper, we propose a simple cluster model with limited basis sets to reproduce the unpaired electron distributions in a YTiO 3 ferromagnetic crystal. The spin-resolved one-electron-reduced density matrix is reconstructed simultaneously from theoretical magnetic structure factors and directional magnetic Compton profiles using our joint refinement algorithm. This algorithm is guided by the rescaling of basis functions and the adjustment of the spin population matrix. The resulting spin electron density in both position and momentum spaces from the joint refinement model is in agreement with theoretical and experimental results. Benefits brought from magnetic Compton profiles to the entire spin density matrix are illustrated. We studied the magnetic properties of the YTiO 3 crystal along the Ti-O 1 -Ti bonding. We found that the basis functions are mostly rescaled by means of magnetic Compton profiles, while the molecular occupation numbers are mainly modified by the magnetic structure factors.

A Depth-Averaged 2-D Simulation for Coastal Barrier Breaching Processes

DTIC Science & Technology

2011-05-01

including bed change and variable flow density in the flow continuity and momentum equations. The model adopts the HLL approximate Riemann solver to handle...flow density in the flow continuity and momentum equations. The model adopts the HLL approximate Riemann solver to handle the mixed-regime flows near...18 547 Keulegan equation or the Bernoulli equation, and the breach morphological change is determined using simplified sediment transport models

Inertially Stabilized Platforms for SATCOM On-The-Move Applications: A Hybrid Open/Closed-Loop Antenna Pointing Strategy

DTIC Science & Technology

2008-06-01

Photo courtesy of www.mathworks.com. Next, Equation (3.16) translates the aircraft disturbance rates through the de - sired local azimuth and elevation...Hessian matrix of the assumed quadratic cost function [34–36]. Equation (4.11) exactly de - termines the minimum of a quadratic function in a single...according to: Bkpk = −gk (4.21) Bk+1 = Bk +Qk (4.22) where Bk in some way approximates Gk from (4.12), and Qk is an update matrix de - pendent upon xk

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: Application to solvatochromic shift calculations

NASA Astrophysics Data System (ADS)

Minezawa, Noriyuki; Kato, Shigeki

2007-02-01

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to "solute" water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: application to solvatochromic shift calculations.

PubMed

Minezawa, Noriyuki; Kato, Shigeki

2007-02-07

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to "solute" water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.

Effect of bidispersity in grafted chain length on grafted chain conformations and potential of mean force between polymer grafted nanoparticles in a homopolymer matrix.

PubMed

Nair, Nitish; Wentzel, Nathaniel; Jayaraman, Arthi

2011-05-21

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Further comparison of the PMF for bidisperse and monodisperse polymer grafted particles in a homopolymer matrix at varying parameters shows that the effects of matrix chain length, matrix packing fraction, grafting density, and particle curvature on the PMF between bidisperse polymer grafted particles are similar to those seen between monodisperse polymer grafted particles. © 2011 American Institute of Physics.

Cosmology with galaxy cluster phase spaces

NASA Astrophysics Data System (ADS)

Stark, Alejo; Miller, Christopher J.; Huterer, Dragan

2017-07-01

We present a novel approach to constrain accelerating cosmologies with galaxy cluster phase spaces. With the Fisher matrix formalism we forecast constraints on the cosmological parameters that describe the cosmological expansion history. We find that our probe has the potential of providing constraints comparable to, or even stronger than, those from other cosmological probes. More specifically, with 1000 (100) clusters uniformly distributed in the redshift range 0 ≤z ≤0.8 , after applying a conservative 80% mass scatter prior on each cluster and marginalizing over all other parameters, we forecast 1 σ constraints on the dark energy equation of state w and matter density parameter ΩM of σw=0.138 (0.431 ) and σΩM=0.007(0.025 ) in a flat universe. Assuming 40% mass scatter and adding a prior on the Hubble constant we can achieve a constraint on the Chevallier-Polarski-Linder parametrization of the dark energy equation of state parameters w0 and wa with 100 clusters in the same redshift range: σw 0=0.191 and σwa=2.712. Dropping the assumption of flatness and assuming w =-1 we also attain competitive constraints on the matter and dark energy density parameters: σΩ M=0.101 and σΩ Λ=0.197 for 100 clusters uniformly distributed in the range 0 ≤z ≤0.8 after applying a prior on the Hubble constant. We also discuss various observational strategies for tightening constraints in both the near and far future.

The Nonlinear Steepest Descent Method to Long-Time Asymptotics of the Coupled Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Liu, Huan

2018-04-01

The Riemann-Hilbert problem for the coupled nonlinear Schrödinger equation is formulated on the basis of the corresponding 3× 3 matrix spectral problem. Using the nonlinear steepest descent method, we obtain leading-order asymptotics for the Cauchy problem of the coupled nonlinear Schrödinger equation.

Development, implementation, and test results on integrated optics switching matrix

NASA Technical Reports Server (NTRS)

Rutz, E.

1982-01-01

A small integrated optics switching matrix, which was developed, implemented, and tested, indicates high performance. The matrix serves as a model for the design of larger switching matrices. The larger integrated optics switching matrix should form the integral part of a switching center with high data rate throughput of up to 300 megabits per second. The switching matrix technique can accomplish the design goals of low crosstalk and low distortion. About 50 illustrations help explain and depict the many phases of the integrated optics switching matrix. Many equations used to explain and calculate the experimental data are also included.