Self-dual geometry of generalized Hermitian surfaces

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

Arsen'eva, O E; Kirichenko, V F

Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian RK-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chenmore » problem in this class of Hermitian surfaces.« less

On the time-reversal symmetry in pseudo-Hermitian systems

NASA Astrophysics Data System (ADS)

Choutri, B.; Cherbal, O.; Ighezou, F. Z.; Trifonov, D. A.

2014-11-01

In a recent paper [M. Sato, K. Hasebe, K. Esaki, and M. Kohmoto, Prog. Theor. Phys. 127, 937 (2012)] Sato and his collaborators established a generalization of the Kramers degeneracy structure to pseudo-Hermitian Hamiltonian systems, admitting even time-reversal symmetry, T2=1. This extension is achieved using the mathematical structure of split-quaternions instead of quaternions, usually adopted in the case of Hermitian Hamiltonians with odd time-reversal symmetry, T2=-1. Here we find that the metric operator for the pseudo-Hermitian Hamiltonian H that allows the realization of the generalized Kramers degeneracy is necessarily indefinite. We show that such H with real spectrum also possesses odd antilinear symmetry induced from the existing odd time-reversal symmetry of its Hermitian counterpart h, so that the generalized Kramers degeneracy of H is in fact crypto-Hermitian Kramers degeneracy. We study in greater detail a new example of the pseudo-Hermitian split-quaternionic four-level Hamiltonian system, which admits an indefinite metric operator and time-reversal symmetry and, as a consequence, a generalized Kramers degeneracy structure. We provide a complete solution of the eigenvalue problem, construct pseudo-Hermitian ladder operators closing the normal and abnormal pseudo-fermionic algebras, and show that this system fulfills a crypto-Hermitian degeneracy.

Solving general gauge theories on inner product spaces

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

1995-02-01

By means of a generalized quartet mechanism we show in a model independent way that a BRST quantization on an inner product space leads to physical states of the form ph> = exp [ Q, ψ]ph> 0 where Q is the nilpotent BRST operator, ψ a hermitian fermionic gauge-fixing operator, and ph> o BRST invariant states determined by a hermitian set of BRST doublets in involution. ph> 0 does not belong to an inner product space although ph> does. Since the BRST quartets are split into two sets of hermitian BRST doublets there are two choices for ph> 0 and the corresponding ψ. When applied to general, both irreducible and reducible, gauge theories of arbitrary rank within the BFV formulation we find that ph> 0 are trivial BRST invariant states which only depend on the matter variables for one set of solutions, and for the other set ph> 0 are solutions of a Dirac quantization. This generalizes previous Lie group solutions obtained by means of a bigrading.

Asymmetric scattering by non-Hermitian potentials

NASA Astrophysics Data System (ADS)

Ruschhaupt, A.; Dowdall, T.; Simón, M. A.; Muga, J. G.

2017-10-01

The scattering of quantum particles by non-Hermitian (generally non-local) potentials in one dimension may result in asymmetric transmission and/or reflection from left and right incidence. After extending the concept of symmetry for non-Hermitian potentials, eight generalized symmetries based on the discrete Klein's four-group (formed by parity, time reversal, their product, and unity) are found. Together with generalized unitarity relations they determine selection rules for the possible and/or forbidden scattering asymmetries. Six basic device types are identified when the scattering coefficients (squared moduli of scattering amplitudes) adopt zero/one values, and transmission and/or reflection are asymmetric. They can pictorically be described as a one-way mirror, a one-way barrier (a Maxwell pressure demon), one-way (transmission or reflection) filters, a mirror with unidirectional transmission, and a transparent, one-way reflector. We design potentials for these devices and also demonstrate that the behavior of the scattering coefficients can be extended to a broad range of incident momenta.

Quantum Transport and Non-Hermiticity on Flat-Band Lattices

NASA Astrophysics Data System (ADS)

Park, Hee Chul; Ryu, Jung-Wan; Myoung, Nojoon

2018-04-01

We investigate quantum transport in a flat-band lattice induced in a twisted cross-stitch lattice with Hermitian or non-Hermitian potentials, with a combination of parity and time-reversal symmetry invariant. In the given system, the transmission probability demonstrates a resonant behavior on the real part of the energy bands. Both of the potentials break the parity symmetry, which lifts the degeneracy of the flat and dispersive bands. In addition, non-Hermiticity conserving PT-symmetry induces a transition between the unbroken and broken PT-symmetric phases through exceptional points in momentum space. Characteristics of non-Hermitian and Hermitian bandgaps are distinguishable: The non-Hermitian bandgap is induced by separation toward complex energy, while the Hermitian bandgap is caused by the expelling of available states into real energy. Deviation of the two bandgaps follows as a function of the quartic power of the induced potential. It is notable that non-Hermiticity plays an important role in the mechanism of generating a bandgap distinguishable from a Hermitian bandgap.

Non-Hermitian optics in atomic systems

NASA Astrophysics Data System (ADS)

Zhang, Zhaoyang; Ma, Danmeng; Sheng, Jiteng; Zhang, Yiqi; Zhang, Yanpeng; Xiao, Min

2018-04-01

A wide class of non-Hermitian Hamiltonians can possess entirely real eigenvalues when they have parity-time (PT) symmetric potentials. Recently, this family of non-Hermitian systems has attracted considerable attention in diverse areas of physics due to their extraordinary properties, especially in optical systems based on solid-state materials, such as coupled gain-loss waveguides and microcavities. Considering the desired refractive index can be effectively manipulated through atomic coherence, it is important to realize such non-Hermitian optical potentials and further investigate their distinct properties in atomic systems. In this paper, we review the recent theoretical and experimental progress of non-Hermitian optics with coherently prepared multi-level atomic configurations. The realizations of (anti-) PT symmetry with different schemes have extensively demonstrated the special optical properties of non-Hermitian optical systems with atomic coherence.

Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges

NASA Astrophysics Data System (ADS)

Cerjan, Alexander; Xiao, Meng; Yuan, Luqi; Fan, Shanhui

2018-02-01

We provide a systematic study of non-Hermitian topologically charged systems. Starting from a Hermitian Hamiltonian supporting Weyl points with arbitrary topological charge, adding a non-Hermitian perturbation transforms the Weyl points to one-dimensional exceptional contours. We analytically prove that the topological charge is preserved on the exceptional contours. In contrast to Hermitian systems, the addition of gain and loss allows for a new class of topological phase transition: when two oppositely charged exceptional contours touch, the topological charge can dissipate without opening a gap. These effects can be demonstrated in realistic photonics and acoustics systems.

Possible treatment of the ghost states in the Lee-Wick standard model

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

Shalaby, Abouzeid M.; Physics Department, Faculty of Science, Qassim University

2009-07-15

In this work, we employ the techniques used to cure the indefinite norm problem in pseudo-Hermitian Hamiltonians to show that the ghost states in a higher derivative scalar field theory are not real ghosts. For the model under investigation, an imaginary auxiliary field is introduced to have an equivalent non-Hermitian two-field scalar theory. We were able to calculate exactly the positive definite metric operator {eta} for the quantum mechanical as well as the quantum field versions of the theory. While the equivalent Hamiltonian is non-Hermitian in a Hilbert space characterized by the Dirac sense inner product, it is, however, amore » Hermitian in a Hilbert space endowed with the inner product . The main feature of the latter Hilbert space is that the propagator has the correct sign (no Lee-Wick fields). Moreover, the calculated metric operator diagonalizes the Hamiltonian in the two fields (no mixing). We found that the Hermiticity of the calculated metric operator to lead to the constrain M>2m for the two Higgs masses, in agreement with other calculations in the literature. Besides, our mass formulas coincide with those obtained in other works (obtained by a very different regime but with the existence of ghost states), which means that our positive normed Hamiltonian form preserves the mass spectra.« less

Application of parametric equations of motion to study the laser induced multiphoton dissociation of H2+ in intense laser field.

PubMed

Kalita, Dhruba J; Rao, Akshay; Rajvanshi, Ishir; Gupta, Ashish K

2011-06-14

We have applied parametric equations of motion (PEM) to study photodissociation dynamics of H(2)(+). The resonances are extracted using smooth exterior scaling method. This is the first application of PEM to non-Hermitian Hamiltonian that includes resonances and the continuum. Here, we have studied how the different resonance states behave with respect to the change in field amplitude. The advantage of this method is that one can easily trace the different states that are changing as the field parameter changes.

Non-Hermitian bidirectional robust transport

NASA Astrophysics Data System (ADS)

Longhi, Stefano

2017-01-01

Transport of quantum or classical waves in open systems is known to be strongly affected by non-Hermitian terms that arise from an effective description of system-environment interaction. A simple and paradigmatic example of non-Hermitian transport, originally introduced by Hatano and Nelson two decades ago [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996), 10.1103/PhysRevLett.77.570], is the hopping dynamics of a quantum particle on a one-dimensional tight-binding lattice in the presence of an imaginary vectorial potential. The imaginary gauge field can prevent Anderson localization via non-Hermitian delocalization, opening up a mobility region and realizing robust transport immune to disorder and backscattering. Like for robust transport of topologically protected edge states in quantum Hall and topological insulator systems, non-Hermitian robust transport in the Hatano-Nelson model is unidirectional. However, there is not any physical impediment to observe robust bidirectional non-Hermitian transport. Here it is shown that in a quasi-one-dimensional zigzag lattice, with non-Hermitian (imaginary) hopping amplitudes and a synthetic gauge field, robust transport immune to backscattering can occur bidirectionally along the lattice.

A Relaxation Method for Nonlocal and Non-Hermitian Operators

NASA Astrophysics Data System (ADS)

Lagaris, I. E.; Papageorgiou, D. G.; Braun, M.; Sofianos, S. A.

1996-06-01

We present a grid method to solve the time dependent Schrödinger equation (TDSE). It uses the Crank-Nicholson scheme to propagate the wavefunction forward in time and finite differences to approximate the derivative operators. The resulting sparse linear system is solved by the symmetric successive overrelaxation iterative technique. The method handles local and nonlocal interactions and Hamiltonians that correspond to either Hermitian or to non-Hermitian matrices with real eigenvalues. We test the method by solving the TDSE in the imaginary time domain, thus converting the time propagation to asymptotic relaxation. Benchmark problems solved are both in one and two dimensions, with local, nonlocal, Hermitian and non-Hermitian Hamiltonians.

Non-Hermitian photonics based on parity-time symmetry

NASA Astrophysics Data System (ADS)

Feng, Liang; El-Ganainy, Ramy; Ge, Li

2017-12-01

Nearly one century after the birth of quantum mechanics, parity-time symmetry is revolutionizing and extending quantum theories to include a unique family of non-Hermitian Hamiltonians. While conceptually striking, experimental demonstration of parity-time symmetry remains unexplored in quantum electronic systems. The flexibility of photonics allows for creating and superposing non-Hermitian eigenstates with ease using optical gain and loss, which makes it an ideal platform to explore various non-Hermitian quantum symmetry paradigms for novel device functionalities. Such explorations that employ classical photonic platforms not only deepen our understanding of fundamental quantum physics but also facilitate technological breakthroughs for photonic applications. Research into non-Hermitian photonics therefore advances and benefits both fields simultaneously.

Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts

NASA Astrophysics Data System (ADS)

Noble, J. H.; Lubasch, M.; Stevens, J.; Jentschura, U. D.

2017-12-01

We describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices, A ̲ =A̲T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product 〈 u ̲ , v ̲ 〉 ∗ =∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generalized Householder transformations (first step). An iterative, generalized QL decomposition of the tridiagonal matrix employing an implicit shift converges toward diagonal form (second step). The QL algorithm employs iterative deflation techniques when a machine-precision zero is encountered "prematurely" on the super-/sub-diagonal. The algorithm allows for a reliable and computationally efficient computation of resonance and antiresonance energies which emerge from complex-scaled Hamiltonians, and for the numerical determination of the real energy eigenvalues of pseudo-Hermitian and PT-symmetric Hamilton matrices. Numerical reference values are provided.

Quantum catastrophes: a case study

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2012-11-01

The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e. made Hermitian via an ad hoc choice of the inner product in the physical Hilbert space of quantum bound states (i.e. via an ad hoc construction of the operator Θ called the metric). The name quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e. to the scenario in which we leave the domain D along such a path that at the boundary of D, an N-plet of bound-state energies degenerates and, subsequently, complexifies. At any fixed N ⩾ 2, this process is simulated via an N × N benchmark effective matrix Hamiltonian H. It is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.

Edge states at the interface of non-Hermitian systems

NASA Astrophysics Data System (ADS)

Yuce, C.

2018-04-01

Topological edge states appear at the interface of two topologically distinct Hermitian insulators. We study the extension of this idea to non-Hermitian systems. We consider P T -symmetric and topologically distinct non-Hermitian insulators with real spectra and study topological edge states at the interface of them. We show that P T symmetry is spontaneously broken at the interface during the topological phase transition. Therefore, topological edge states with complex energy eigenvalues appear at the interface. We apply our idea to a complex extension of the Su-Schrieffer-Heeger model.

Disappearing Q operator

NASA Astrophysics Data System (ADS)

Jones, H. F.; Rivers, R. J.

2007-01-01

In the Schrödinger formulation of non-Hermitian quantum theories a positive-definite metric operator η≡e-Q must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent Hermitian theory, by means of a similarity transformation. If, however, quantum mechanics is formulated in terms of functional integrals, we show that the Q operator makes only a subliminal appearance and is not needed for the calculation of expectation values. Instead, the relation to the Hermitian theory is encoded via the external source j(t). These points are illustrated and amplified for two non-Hermitian quantum theories: the Swanson model, a non-Hermitian transform of the simple harmonic oscillator, and the wrong-sign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator.

Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force

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

Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems ontomore » non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.« less

Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force

DOE PAGES

Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

2016-08-26

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems ontomore » non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.« less

A non-Hermitian analysis of strongly correlated quantum systems

NASA Astrophysics Data System (ADS)

Nakamura, Yuichi; Hatano, Naomichi

2006-03-01

We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. Hatano and Nelson[1] applied this technique to non-interacting random electron systems. They related a non-Hermitian critical point to the inverse localization length of the Hermitian systems. We here conjecture that we can obtain in the same way the correlation length of Hermitian interacting non-random systems[2]. We show for the Hubbard model and the antiferromagnetic XXZ model in one dimension that the non-Hermitian critical point of the ground state, where the energy gap vanishes, is equal to the inverse correlation length. We also show that the conjecture is consistent with numerical results for S=1/2 frustrated quantum spin chains with the nearest- and next-nearest-neighbor interactions including the Majumdar-Ghosh model[3]. [1] N. Hatano and D. R. Nelson, PRL 77 (1996) 570; PRB 56 (1997) 8651. [2] Y. Nakamura and N. Hatano, Physica B, accepted. [3] C. K. Majumdar and D. K. Ghosh, J. Phys. C3 (1970) 911; J. Math. Phys. 10 (1969) 1388, 1399.

Quantum physics with non-Hermitian operators Quantum physics with non-Hermitian operators

NASA Astrophysics Data System (ADS)

Bender, Carl; Fring, Andreas; Günther, Uwe; Jones, Hugh

2012-11-01

The main motivation behind the call for this special issue was to gather recent results, developments and open problems in quantum physics with non-Hermitian operators. There have been previous special issues in this journal [1, 2] and elsewhere on this subject. The intention of this issue is to reflect the current state of this rapidly-developing field. It has therefore been open to all contributions containing new results on non-Hermitian theories that are explicitly PT-symmetric and/or pseudo-Hermitian or quasi-Hermitian. In the last decade these types of systems have proved to be viable self-consistent physical theories with well defined unitary time-evolution and real spectra. As the large number of responses demonstrates, this is a rapidly evolving field of research. A consensus has been reached regarding most of the fundamental problems, and the general ideas and techniques are now readily being employed in many areas of physics. Nonetheless, this issue still contains some treatments of a more general nature regarding the spectral analysis of these models, in particular, the physics of the exceptional points, the breaking of the PT-symmetry, an interpretation of negative energies and the consistent implementation of the WKB analysis. This issue also contains a treatment of a scattering theory associated with these types of systems, weak measurements, coherent states, decoherence, unbounded metric operators and the inclusion of domain issues to obtain well defined self-adjoint theories. Contributions in the form of applications of the general ideas include: studies of classical shock-waves and tunnelling, supersymmetric models, spin chain models, models with ring structure, random matrix models, the Pauli equation, the nonlinear Schrödinger equation, quasi-exactly solvable models, integrable models such as the Calogero model, Bose-Einstein condensates, thermodynamics, nonlinear oligomers, quantum catastrophes, the Landau-Zener problem and pseudo-Fermions. Applications close to experimental realization are proposed in optics, including short light pulse models, waveguides and laser systems, and also in electronics. We hope that this issue will become a valuable reference and inspiration for the broader scientific community working in mathematical and theoretical physics. References [1] Fring A, Jones H F and Znojil M (ed) 2008 J. Phys. A: Math. Theor. 41 240301 [2] Geyer H, Heiss D and Znojil M (ed) 2006 J. Phys. A: Math. Gen. 39 9963

Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

NASA Astrophysics Data System (ADS)

Graefe, E. M.; Korsch, H. J.; Rush, A.

2016-07-01

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and PT-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.

Metric versus observable operator representation, higher spin models

NASA Astrophysics Data System (ADS)

Fring, Andreas; Frith, Thomas

2018-02-01

We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on how to employ the time-dependent Dyson relation and the quasi-Hermiticity relation to solve time-dependent Hermitian Hamiltonian systems. By solving both equations separately we argue here that it is in general easier to solve the former. We solve the mutually related time-dependent Schrödinger equation for a Hermitian and non-Hermitian spin 1/2, 1 and 3/2 model with time-independent and time-dependent metric, respectively. In all models the overdetermined coupled system of equations for the Dyson map can be decoupled algebraic manipulations and reduces to simple linear differential equations and an equation that can be converted into the non-linear Ermakov-Pinney equation.

Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems

NASA Astrophysics Data System (ADS)

Yin, Chuanhao; Jiang, Hui; Li, Linhu; Lü, Rong; Chen, Shu

2018-05-01

We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems are integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number ν of a non-Hermitian system is equal to half of the summation of two winding numbers ν1 and ν2 associated with two exceptional points, respectively. The winding numbers ν1 and ν2 represent the times of the real part of the Hamiltonian in momentum space encircling the exceptional points and can only take integers. We further find that the difference of ν1 and ν2 is related to the second winding number or energy vorticity. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of left and right zero-mode edge states is closely related to the winding number ν1 and ν2.

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1991-01-01

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Non-Hermitian physics and PT symmetry

NASA Astrophysics Data System (ADS)

El-Ganainy, Ramy; Makris, Konstantinos G.; Khajavikhan, Mercedeh; Musslimani, Ziad H.; Rotter, Stefan; Christodoulides, Demetrios N.

2018-01-01

In recent years, notions drawn from non-Hermitian physics and parity-time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments.

Sensitivity analysis and approximation methods for general eigenvalue problems

NASA Technical Reports Server (NTRS)

Murthy, D. V.; Haftka, R. T.

1986-01-01

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Nonlinear and non-Hermitian optical systems applied to the development of filters and optical sensors

NASA Astrophysics Data System (ADS)

Amaro de Faria Júnior, A. C.

2015-09-01

In this work we present a method of investigation of nonlinear optical beams generated from non-Hermitian optical systems1 . This method can be applied in the development of optical filters and optical sensors to process, analyze and choose the passband of the propagation modes of an optical pulse from an non-Hermitian optical system. Non-Hermitian optical systems can be used to develop optical fiber sensors that suppress certain propagation modes of optical pulses that eventually behave as quantum noise. Such systems are described by the Nonlinear Schrödinger-like Equation with Parity-Time (PT) Symmetric Optical Potentials. There are optical fiber sensors that due to high laser intensity and frequency can produce quantum noise, such as Raman and Brillouin scattering. However, the optical fiber, for example, can be designed so that its geometry suppress certain propagation modes of the beam. We apply some results of non- Hermitian optical systems with PT symmetry to simulate optical lattice by a appropriate potential function, which among other applications, can naturally suppress certain propagation modes of an optical beam propagating through a waveguide. In other words, the optical system is modeled by a potential function in the Nonlinear Schrödinger-like Equation that one relates with the geometric aspects of the wave guides and with the optical beam interacting with the waveguide material. The paper is organized as follows: sections 1 and 2 present a brief description about nonlinear optical systems and non-Hermitian optical systems with PT symmetry. Section 3 presents a description of the dynamics of nonlinear optical pulses propagating through optical networks described by a optical potential non-Hermitian. Sections 4 and 5 present a general description of this non-Hermitian optical systems and how to get them from a more general model. Section 6 presents some conclusions and comment and the final section presents the references. Begin the abstract two lines below author names and addresses.

Special issue on quantum physics with non-Hermitian operators Special issue on quantum physics with non-Hermitian operators

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Fring, Andreas; Guenther, Uwe; Jones, Hugh F.

2012-01-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to quantum physics with non-Hermitian operators. The main motivation behind this special issue is to gather together recent results, developments and open problems in this rapidly evolving field of research in a single comprehensive volume. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will be open to all contributions containing new results on non-Hermitian theories which are explicitly PT-symmetric and/or pseudo-Hermitian or quasi-Hermitian. The main novelties in the past years in this area have been many experimental observations, realizations, and applications of PT symmetric Hamiltonians in optics and microwave cavities. We especially invite contributions on the theoretical interpretations of these recent PT-symmetric experiments and on theoretical proposals for new experiments. Editorial policy The Guest Editors for this issue are Carl Bender, Andreas Fring, Uwe Guenther and Hugh Jones. The areas and topics for this issue include, but are not limited to: spectral problems novel properties of complex optical potentials PT-symmetry related threshold lasers and spectral singularities construction of metric operators scattering theory supersymmetric theories Lie algebraic and Krein-space methods random matrix models classical and semi-classical models exceptional points in model systems operator theoretic approaches microwave cavities aspects of integrability and exact solvability field theories with indefinite metric All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The deadline for contributed papers will be 31 March 2012. This deadline will allow the special issue to appear before the end of November 2012. There is a nominal page limit of 15 printed pages per contribution (invited review papers can be longer). For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and Theoretical may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via authors.iop.org/, or by email to jphysa@iop.org, quoting 'JPhysA Special issue on quantum physics with non-Hermitian operators'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on quantum physics with non-Hermitian operators Special issue on quantum physics with non-Hermitian operators

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Fring, Andreas; Guenther, Uwe; Jones, Hugh F.

2012-01-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to quantum physics with non-Hermitian operators. The main motivation behind this special issue is to gather together recent results, developments and open problems in this rapidly evolving field of research in a single comprehensive volume. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will be open to all contributions containing new results on non-Hermitian theories which are explicitly PT-symmetric and/or pseudo-Hermitian or quasi-Hermitian. The main novelties in the past years in this area have been many experimental observations, realizations, and applications of PT symmetric Hamiltonians in optics and microwave cavities. We especially invite contributions on the theoretical interpretations of these recent PT-symmetric experiments and on theoretical proposals for new experiments. Editorial policy The Guest Editors for this issue are Carl Bender, Andreas Fring, Uwe Guenther and Hugh Jones. The areas and topics for this issue include, but are not limited to: spectral problems novel properties of complex optical potentials PT-symmetry related threshold lasers and spectral singularities construction of metric operators scattering theory supersymmetric theories Lie algebraic and Krein-space methods random matrix models classical and semi-classical models exceptional points in model systems operator theoretic approaches microwave cavities aspects of integrability and exact solvability field theories with indefinite metric All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The deadline for contributed papers will be 31 March 2012. This deadline will allow the special issue to appear before the end of November 2012. There is a nominal page limit of 15 printed pages per contribution (invited review papers can be longer). For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and Theoretical may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via authors.iop.org, or by email to jphysa@iop.org, quoting 'JPhysA Special issue on quantum physics with non-Hermitian operators'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Topological Band Theory for Non-Hermitian Hamiltonians

NASA Astrophysics Data System (ADS)

Shen, Huitao; Zhen, Bo; Fu, Liang

2018-04-01

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.

Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2013-10-01

The Euclidean action with acceleration has been analyzed in Ref. 1, and referred to henceforth as Paper I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation and destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.

Topologically protected bound states in photonic parity-time-symmetric crystals.

PubMed

Weimann, S; Kremer, M; Plotnik, Y; Lumer, Y; Nolte, S; Makris, K G; Segev, M; Rechtsman, M C; Szameit, A

2017-04-01

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

An inclusive SUSY approach to position dependent mass systems

NASA Astrophysics Data System (ADS)

Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.

2018-06-01

The supersymmetry (SUSY) formalism for a position dependent mass problem with a more general ordering is yet to be formulated. In this paper, we present an unified SUSY approach for PDM problems of any ordering. Highlighting all non-Hermitian Hamiltonians of PDM problems are of quasi-Hermitian nature, the SUSY operators of these problems are constructed using similarity transformation. The methodology that we propose here is applicable for even more general cases where the kinetic energy term is represented by linear combination of infinite number of possible orderings. We illustrate the method with an example, namely Mathews-Lakshmanan (ML) oscillator. Our results show that the latter system is shape invariant for all possible orderings. We derive eigenvalues and eigenvectors of this nonlinear oscillator for all possible orderings including Hermitian and non-Hermitian ones.

Disappearing Q operator

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

Jones, H. F.; Rivers, R. J.

In the Schroedinger formulation of non-Hermitian quantum theories a positive-definite metric operator {eta}{identical_to}e{sup -Q} must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent Hermitian theory, by means of a similarity transformation. If, however, quantum mechanics is formulated in terms of functional integrals, we show that the Q operator makes only a subliminal appearance and is not needed for the calculation of expectation values. Instead, the relation to the Hermitian theory is encoded via the external source j(t). These points are illustrated and amplified for two non-Hermitian quantum theories: the Swanson model, a non-Hermitianmore » transform of the simple harmonic oscillator, and the wrong-sign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator.« less

Nonreciprocal Gain in Non-Hermitian Time-Floquet Systems

NASA Astrophysics Data System (ADS)

Koutserimpas, Theodoros T.; Fleury, Romain

2018-02-01

We explore the unconventional wave scattering properties of non-Hermitian systems in which amplification or damping are induced by time-periodic modulation. These non-Hermitian time-Floquet systems are capable of nonreciprocal operations in the frequency domain, which can be exploited to induce novel physical phenomena such as unidirectional wave amplification and perfect nonreciprocal response with zero or even negative insertion losses. This unique behavior is obtained by imparting a specific low-frequency time-periodic modulation to the complex coupling between lossless resonators, promoting only upward frequency conversion, and leading to nonreciprocal parametric gain. We provide a full-wave demonstration of our findings in a one-way microwave amplifier, and establish the potential of non-Hermitian time-Floquet devices for insertion-loss free microwave isolation and unidirectional parametric amplification.

Simplification rules for birdtrack operators

NASA Astrophysics Data System (ADS)

Alcock-Zeilinger, J.; Weigert, H.

2017-05-01

This paper derives a set of easy-to-use tools designed to simplify calculations with birdtrack operators comprised of symmetrizers and antisymmetrizers. In particular, we present cancellation rules allowing one to shorten the birdtrack expressions of operators and propagation rules identifying the circumstances under which it is possible to propagate symmetrizers past antisymmetrizers and vice versa. We exhibit the power of these simplification rules by means of a short example in which we apply the tools derived in this paper on a typical operator that can be encountered in the representation theory of 𝖲𝖴 (N ) over the product space V⊗m. These rules form the basis for the construction of compact Hermitian Young projection operators and their transition operators addressed in companion papers [J. Alcock-Zeilinger and H. Weigert, "Compact Hermitian Young projection operators," e-print arXiv:1610.10088 [math-ph] and J. Alcock-Zeilinger and H. Weigert, "Transition operators," e-print arXiv:1610.08802 [math-ph

Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime

NASA Astrophysics Data System (ADS)

Fring, Andreas; Frith, Thomas

2018-06-01

We provide exact analytical solutions for a two-dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the model parameters, and has therefore a partially complex energy eigenspectrum, its time-dependent version has real energy expectation values at all times. In our solution procedure we compare the two equivalent approaches of directly solving the time-dependent Dyson equation with one employing the Lewis–Riesenfeld method of invariants. We conclude that the latter approach simplifies the solution procedure due to the fact that the invariants of the non-Hermitian and Hermitian system are related to each other in a pseudo-Hermitian fashion, which in turn does not hold for their corresponding time-dependent Hamiltonians. Thus constructing invariants and subsequently using the pseudo-Hermiticity relation between them allows to compute the Dyson map and to solve the Dyson equation indirectly. In this way one can bypass to solve nonlinear differential equations, such as the dissipative Ermakov–Pinney equation emerging in our and many other systems.

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

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

Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar

2016-06-15

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators aremore » useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.« less

Constant-intensity waves and their modulation instability in non-Hermitian potentials

NASA Astrophysics Data System (ADS)

Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2015-07-01

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

A fast, preconditioned conjugate gradient Toeplitz solver

NASA Technical Reports Server (NTRS)

Pan, Victor; Schrieber, Robert

1989-01-01

A simple factorization is given of an arbitrary hermitian, positive definite matrix in which the factors are well-conditioned, hermitian, and positive definite. In fact, given knowledge of the extreme eigenvalues of the original matrix A, an optimal improvement can be achieved, making the condition numbers of each of the two factors equal to the square root of the condition number of A. This technique is to applied to the solution of hermitian, positive definite Toeplitz systems. Large linear systems with hermitian, positive definite Toeplitz matrices arise in some signal processing applications. A stable fast algorithm is given for solving these systems that is based on the preconditioned conjugate gradient method. The algorithm exploits Toeplitz structure to reduce the cost of an iteration to O(n log n) by applying the fast Fourier Transform to compute matrix-vector products. Matrix factorization is used as a preconditioner.

Towards a double field theory on para-Hermitian manifolds

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

Vaisman, Izu

In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kähler case, this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action ofmore » the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.« less

Photonic zero mode in a non-Hermitian photonic lattice.

PubMed

Pan, Mingsen; Zhao, Han; Miao, Pei; Longhi, Stefano; Feng, Liang

2018-04-03

Zero-energy particles (such as Majorana fermions) are newly predicted quasiparticles and are expected to play an important role in fault-tolerant quantum computation. In conventional Hermitian quantum systems, however, such zero states are vulnerable and even become vanishing if couplings with surroundings are of the same topological nature. Here we demonstrate a robust photonic zero mode sustained by a spatial non-Hermitian phase transition in a parity-time (PT) symmetric lattice, despite the same topological order across the entire system. The non-Hermitian-enhanced topological protection ensures the reemergence of the zero mode at the phase transition interface when the two semi-lattices under different PT phases are decoupled effectively in their real spectra. Residing at the midgap level of the PT symmetric spectrum, the zero mode is topologically protected against topological disorder. We experimentally validated the robustness of the zero-energy mode by ultrafast heterodyne measurements of light transport dynamics in a silicon waveguide lattice.

A Generalization of the Simultaneous Diagonalization of Hermitian Matrices and its Relation to Quantum Estimation Theory

NASA Astrophysics Data System (ADS)

Nagaoka, Hiroshi

We study the problem of minimizing a quadratic quantity defined for given two Hermitian matrices X, Y and a positive-definite Hermitian matrix. This problem is reduced to the simultaneous diagonalization of X, Y when XY = YX. We derive a lower bound for the quantity, and in some special cases solve the problem by showing that the lower bound is achievable. This problem is closely related to a simultaneous measurement of quantum mechanical observables which are not commuting and has an application in the theory of quantum state estimation.

Numerical determination of partial spectrum of Hermitian matrices using a Lánczos method with selective reorthogonalization

NASA Astrophysics Data System (ADS)

Johnson, Chris; Kennedy, A. D.

2013-03-01

We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication of eigenpairs in finite-precision arithmetic, but uses a new bound to decide when such reorthogonalization is required, and only reorthogonalizes with respect to eigenpairs within the region of interest. We investigate its performance for the Hermitian Wilson-Dirac operator γ5D in lattice quantum chromodynamics, and compare it with previous methods.

Robust light transport in non-Hermitian photonic lattices

PubMed Central

Longhi, Stefano; Gatti, Davide; Valle, Giuseppe Della

2015-01-01

Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a two-dimensional structure, which break time reversal symmetry and enable one-way guiding at the edge of the medium. Here we suggest a different route toward robust transport of light in lower-dimensional (1D) photonic lattices, in which time reversal symmetry is broken because of the non-Hermitian nature of transport. While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport insensitive to disorder or imperfections in the structure. Non-Hermitian asymmetric transport can occur in tight-binding lattices with an imaginary gauge field via a non-Hermitian delocalization transition, and in periodically-driven superlattices. The possibility to observe non-Hermitian delocalization is suggested using an engineered coupled-resonator optical waveguide (CROW) structure. PMID:26314932

Robust light transport in non-Hermitian photonic lattices.

PubMed

Longhi, Stefano; Gatti, Davide; Della Valle, Giuseppe

2015-08-28

Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a two-dimensional structure, which break time reversal symmetry and enable one-way guiding at the edge of the medium. Here we suggest a different route toward robust transport of light in lower-dimensional (1D) photonic lattices, in which time reversal symmetry is broken because of the non-Hermitian nature of transport. While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport insensitive to disorder or imperfections in the structure. Non-Hermitian asymmetric transport can occur in tight-binding lattices with an imaginary gauge field via a non-Hermitian delocalization transition, and in periodically-driven superlattices. The possibility to observe non-Hermitian delocalization is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.

Nondiffracting wave beams in non-Hermitian Glauber-Fock lattice

NASA Astrophysics Data System (ADS)

Oztas, Z.

2018-05-01

We theoretically study non-Hermitian Glauber-Fock lattice with nonuniform hopping. We show how to engineer this lattice to get nondiffracting wave beams and find an exact analytical solution to nondiffracting localized waves. The exceptional points in the energy spectrum are also analyzed.

Transition operators

NASA Astrophysics Data System (ADS)

Alcock-Zeilinger, J.; Weigert, H.

2017-05-01

In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of 𝖲𝖴 (N ) , using the compact expressions of Hermitian Young projection operators derived in the work of Alcock-Zeilinger and Weigert [eprint arXiv:1610.10088 [math-ph

Parity-time symmetry meets photonics: A new twist in non-Hermitian optics

NASA Astrophysics Data System (ADS)

Longhi, Stefano

2017-12-01

In the past decade, the concept of parity-time (PT) symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile ground for studying, observing, and utilizing some of the peculiar aspects of PT symmetry in optics. Together with related concepts of non-Hermitian physics of open quantum systems, such as non-Hermitian degeneracies (exceptional points) and spectral singularities, PT symmetry represents one among the most fruitful ideas introduced in optics in the past few years. Judicious tailoring of optical gain and loss in integrated photonic structures has emerged as a new paradigm in shaping the flow of light in unprecedented ways, with major applications encompassing laser science and technology, optical sensing, and optical material engineering. In this perspective, I review some of the main achievements and emerging areas of PT -symmetric and non-Hermtian photonics, and provide an outline of challenges and directions for future research in one of the fastest growing research area of photonics.

Boson expansion based on the extended commutator method in the Tamm-Dancoff representation

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

Pedrocchi, V.G.; Tamura, T.

1983-07-01

Formal aspects of boson expansions in the Tamm-Dancoff representation are investigated in detail. This is carried out in the framework of the extended commutator method by solving in complete generality the coefficient equations, searching for Hermitian as well as non-Hermitian boson expansions. The solutions for the expansion coefficients are obtained in a new form, called the square root realization, which is then applied to carry out an analysis of the relationship between the type of expansion and the boson space in which the expansion is defined. It is shown that this new realization is reduced to various well-known boson theoriesmore » when the boson space is chosen in an appropriate manner. Further discussed, still on the basis of the square root realization, is the equivalence, on a practical level, of a few boson expansion approaches when the Tamm-Dancoff space is truncated to a single quadrupole collective component.« less

Quantization of wave equations and hermitian structures in partial differential varieties

PubMed Central

Paneitz, S. M.; Segal, I. E.

1980-01-01

Sufficiently close to 0, the solution variety of a nonlinear relativistic wave equation—e.g., of the form □ϕ + m2ϕ + gϕp = 0—admits a canonical Lorentz-invariant hermitian structure, uniquely determined by the consideration that the action of the differential scattering transformation in each tangent space be unitary. Similar results apply to linear time-dependent equations or to equations in a curved asymptotically flat space-time. A close relation of the Riemannian structure to the determination of vacuum expectation values is developed and illustrated by an explicit determination of a perturbative 2-point function for the case of interaction arising from curvature. The theory underlying these developments is in part a generalization of that of M. G. Krein and collaborators concerning stability of differential equations in Hilbert space and in part a precise relation between the unitarization of given symplectic linear actions and their full probabilistic quantization. The unique causal structure in the infinite symplectic group is instrumental in these developments. PMID:16592923

Oscillating potential well in the complex plane and the adiabatic theorem

NASA Astrophysics Data System (ADS)

Longhi, Stefano

2017-10-01

A quantum particle in a slowly changing potential well V (x ,t ) =V ( x -x0(ɛ t ) ) , periodically shaken in time at a slow frequency ɛ , provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than ˜1 /ɛ . Specifically, we consider a double-well potential V (x ) sustaining two bound states spaced in frequency by ω0 and periodically shaken in a complex plane. Two different spatial displacements x0(t ) are assumed: the real spatial displacement x0(ɛ t ) =A sin(ɛ t ) , corresponding to ordinary Hermitian shaking, and the complex one x0(ɛ t ) =A -A exp(-i ɛ t ) , corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency ɛ is close to an odd resonance of ω0. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasienergies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasienergy crossing.

Pseudospectra in non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

2015-10-01

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Equivalent Hamiltonian for the Lee model

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

Jones, H. F.

2008-03-15

Using the techniques of quasi-Hermitian quantum mechanics and quantum field theory we use a similarity transformation to construct an equivalent Hermitian Hamiltonian for the Lee model. In the field theory confined to the V/N{theta} sector it effectively decouples V, replacing the three-point interaction of the original Lee model by an additional mass term for the V particle and a four-point interaction between N and {theta}. While the construction is originally motivated by the regime where the bare coupling becomes imaginary, leading to a ghost, it applies equally to the standard Hermitian regime where the bare coupling is real. In thatmore » case the similarity transformation becomes a unitary transformation.« less

Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices

NASA Astrophysics Data System (ADS)

Chakhmakhchyan, L.; Cerf, N. J.; Garcia-Patron, R.

2017-08-01

We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithm development.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Gutknecht, Martin H.; Nachtigal, Noel M.

1991-01-01

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead.

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

A non-orthogonal decomposition of flows into discrete events

NASA Astrophysics Data System (ADS)

Boxx, Isaac; Lewalle, Jacques

1998-11-01

This work is based on the formula for the inverse Hermitian wavelet transform. A signal can be interpreted as a (non-unique) superposition of near-singular, partially overlapping events arising from Dirac functions and/or its derivatives combined with diffusion.( No dynamics implied: dimensionless diffusion is related to the definition of the analyzing wavelets.) These events correspond to local maxima of spectral energy density. We successfully fitted model events of various orders on a succession of fields, ranging from elementary signals to one-dimensional hot-wire traces. We document edge effects, event overlap and its implications on the algorithm. The interpretation of the discrete singularities as flow events (such as coherent structures) and the fundamental non-uniqueness of the decomposition are discussed. The dynamics of these events will be examined in the companion paper.

Non-hermitian quantum thermodynamics

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

Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Lastly, we propose two setups to test our predictions,more » namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.« less

Non-hermitian quantum thermodynamics

DOE PAGES

Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

2016-03-22

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Lastly, we propose two setups to test our predictions,more » namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.« less

Defect States Emerging from a Non-Hermitian Flatband of Photonic Zero Modes

NASA Astrophysics Data System (ADS)

Qi, Bingkun; Zhang, Lingxuan; Ge, Li

2018-03-01

We show the existence of a flatband consisting of photonic zero modes in a gain and loss modulated lattice system as a result of the underlying non-Hermitian particle-hole symmetry. This general finding explains the previous observation in parity-time symmetric systems where non-Hermitian particle-hole symmetry is hidden. We further discuss the defect states in these systems, whose emergence can be viewed as an unconventional alignment of a pseudospin under the influence of a complex-valued pseudomagnetic field. These defect states also behave as a chain with two types of links, one rigid in a unit cell and one soft between unit cells, as the defect states become increasingly localized with the gain and loss strength.

FAST TRACK COMMUNICATION: SUSY transformations with complex factorization constants: application to spectral singularities

NASA Astrophysics Data System (ADS)

Samsonov, Boris F.

2010-10-01

Supersymmetric (SUSY) transformation operators with complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. The obtained results are applied to Hamiltonians possessing spectral singularities which are non-Hermitian SUSY partners of self-adjoint operators. A new regularization procedure for the resolution of the identity operator in terms of a continuous biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed. It is also argued that if the binorm of continuous spectrum eigenfunctions is interpreted in the same way as the norm of similar functions in the usual Hermitian case, then one can state that the function corresponding to a spectral singularity has zero binorm.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 1

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Gutknecht, Martin H.; Nachtigal, Noel M.

1990-01-01

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. We present an implementation of a look-ahead version of the Lanczos algorithm which overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and is not restricted to steps of length 2, as earlier implementations are. Also, our implementation has the feature that it requires roughly the same number of inner products as the standard Lanczos process without look-ahead.

{\\ {PT}}-symmetric models in curved manifolds

NASA Astrophysics Data System (ADS)

Krejčiřík, David; Siegl, Petr

2010-12-01

We consider the Laplace-Beltrami operator in tubular neighborhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.

Digital super-resolution holographic data storage based on Hermitian symmetry for achieving high areal density.

PubMed

Nobukawa, Teruyoshi; Nomura, Takanori

2017-01-23

Digital super-resolution holographic data storage based on Hermitian symmetry is proposed to store digital data in a tiny area of a medium. In general, reducing a recording area with an aperture leads to the improvement in the storage capacity of holographic data storage. Conventional holographic data storage systems however have a limitation in reducing a recording area. This limitation is called a Nyquist size. Unlike the conventional systems, our proposed system can overcome the limitation with the help of a digital holographic technique and digital signal processing. Experimental result shows that the proposed system can record and retrieve a hologram in a smaller area than the Nyquist size on the basis of Hermitian symmetry.

The classical dynamic symmetry for the U(1) -Kepler problems

NASA Astrophysics Data System (ADS)

Bouarroudj, Sofiane; Meng, Guowu

2018-01-01

For the Jordan algebra of hermitian matrices of order n ≥ 2, we let X be its submanifold consisting of rank-one semi-positive definite elements. The composition of the cotangent bundle map πX: T∗ X → X with the canonical map X → CP n - 1 (i.e., the map that sends a given hermitian matrix to its column space), pulls back the Kähler form of the Fubini-Study metric on CP n - 1 to a real closed differential two-form ωK on T∗ X. Let ωX be the canonical symplectic form on T∗ X and μ a real number. A standard fact says that ωμ ≔ωX + 2 μωK turns T∗ X into a symplectic manifold, hence a Poisson manifold with Poisson bracket {,}μ. In this article we exhibit a Poisson realization of the simple real Lie algebra su(n , n) on the Poisson manifold (T∗ X ,{,}μ) , i.e., a Lie algebra homomorphism from su(n , n) to (C∞(T∗ X , R) ,{,}μ). Consequently one obtains the Laplace-Runge-Lenz vector for the classical U(1) -Kepler problem of level n and magnetic charge μ. Since the McIntosh-Cisneros-Zwanziger-Kepler problems (MICZ-Kepler Problems) are the U(1) -Kepler problems of level 2, the work presented here is a direct generalization of the work by A. Barut and G. Bornzin (1971) on the classical dynamic symmetry for the MICZ-Kepler problems.

On the extreme value statistics of normal random matrices and 2D Coulomb gases: Universality and finite N corrections

NASA Astrophysics Data System (ADS)

Ebrahimi, R.; Zohren, S.

2018-03-01

In this paper we extend the orthogonal polynomials approach for extreme value calculations of Hermitian random matrices, developed by Nadal and Majumdar (J. Stat. Mech. P04001 arXiv:1102.0738), to normal random matrices and 2D Coulomb gases in general. Firstly, we show that this approach provides an alternative derivation of results in the literature. More precisely, we show convergence of the rescaled eigenvalue with largest modulus of a normal Gaussian ensemble to a Gumbel distribution, as well as universality for an arbitrary radially symmetric potential. Secondly, it is shown that this approach can be generalised to obtain convergence of the eigenvalue with smallest modulus and its universality for ring distributions. Most interestingly, the here presented techniques are used to compute all slowly varying finite N correction of the above distributions, which is important for practical applications, given the slow convergence. Another interesting aspect of this work is the fact that we can use standard techniques from Hermitian random matrices to obtain the extreme value statistics of non-Hermitian random matrices resembling the large N expansion used in context of the double scaling limit of Hermitian matrix models in string theory.

Approximation methods in relativistic eigenvalue perturbation theory

NASA Astrophysics Data System (ADS)

Noble, Jonathan Howard

In this dissertation, three questions, concerning approximation methods for the eigenvalues of quantum mechanical systems, are investigated: (i) What is a pseudo--Hermitian Hamiltonian, and how can its eigenvalues be approximated via numerical calculations? This is a fairly broad topic, and the scope of the investigation is narrowed by focusing on a subgroup of pseudo--Hermitian operators, namely, PT--symmetric operators. Within a numerical approach, one projects a PT--symmetric Hamiltonian onto an appropriate basis, and uses a straightforward two--step algorithm to diagonalize the resulting matrix, leading to numerically approximated eigenvalues. (ii) Within an analytic ansatz, how can a relativistic Dirac Hamiltonian be decoupled into particle and antiparticle degrees of freedom, in appropriate kinematic limits? One possible answer is the Foldy--Wouthuysen transform; however, there are alter- native methods which seem to have some advantages over the time--tested approach. One such method is investigated by applying both the traditional Foldy--Wouthuysen transform and the "chiral" Foldy--Wouthuysen transform to a number of Dirac Hamiltonians, including the central-field Hamiltonian for a gravitationally bound system; namely, the Dirac-(Einstein-)Schwarzschild Hamiltonian, which requires the formal- ism of general relativity. (iii) Are there are pseudo--Hermitian variants of Dirac Hamiltonians that can be approximated using a decoupling transformation? The tachyonic Dirac Hamiltonian, which describes faster-than-light spin-1/2 particles, is gamma5--Hermitian, i.e., pseudo-Hermitian. Superluminal particles remain faster than light upon a Lorentz transformation, and hence, the Foldy--Wouthuysen program is unsuited for this case. Thus, inspired by the Foldy--Wouthuysen program, a decoupling transform in the ultrarelativistic limit is proposed, which is applicable to both sub- and superluminal particles.

A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra

NASA Astrophysics Data System (ADS)

Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia

2017-10-01

A generalized Hermitian (GH-) algebra is a generalization of the partially ordered Jordan algebra of all Hermitian operators on a Hilbert space. We introduce the notion of a gh-tribe, which is a commutative GH-algebra of functions on a nonempty set X with pointwise partial order and operations, and we prove that every commutative GH-algebra is the image of a gh-tribe under a surjective GH-morphism. Using this result, we prove that each element a of a GH-algebra A corresponds to a real observable ξa on the σ-orthomodular lattice of projections in A and that ξa determines the spectral resolution of a. Also, if f is a continuous function defined on the spectrum of a, we formulate a definition of f (a), thus obtaining a continuous functional calculus for A.

Phase operator problem and macroscopic extension of quantum mechanics

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

Ozawa, M.

1997-06-01

To find the Hermitian phase operator of a single-mode electromagnetic field in quantum mechanics, the Schr{umlt o}dinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is a Naimark extension of the optimal probability operator-valued measure for the phase parameter found by Helstrom. Eventually, the two promising approaches to themore » statistics of the phase in quantum mechanics are synthesized by means of the Hermitian phase operator in the macroscopic extension of the Schr{umlt o}dinger representation. {copyright} 1997 Academic Press, Inc.« less

Unidirectional reflectionless propagation in non-Hermitian metamaterial based on phase coupling between two resonators

NASA Astrophysics Data System (ADS)

Yin, Hongda; Bai, Ruiping; Gu, Xintong; Zhang, Cong; Gu, Guang Rui; Zhang, Ying Qiao; Jin, Xing Ri; Lee, YoungPak

2018-05-01

Unidirectional reflectionless propagation in a non-Hermitian metamaterial is obtained based on phase coupling between two resonators. The unidirectional reflectionless propagation can be obtained at exceptional point by adjusting polarization angle θ and distance d between two resonators. Moreover, coherent prefect absorptions are obtained near exceptional point with the high absorbance of ∼0.99 and high quality factor of ∼83.

Parametric instability of optical non-Hermitian systems near the exceptional point

PubMed Central

Zyablovsky, A. A.; Andrianov, E. S.; Pukhov, A. A.

2016-01-01

In contrast to Hermitian systems, the modes of non-Hermitian systems are generally nonorthogonal. As a result, the power of the system signal depends not only on the mode amplitudes but also on the phase shift between them. In this work, we show that it is possible to increase the mode amplitudes without increasing the power of the signal. Moreover, we demonstrate that when the system is at the exceptional point, any infinitesimally small change in the system parameters increases the mode amplitudes. As a result, the system becomes unstable with respect to such perturbation. We show such instability by using the example of two coupled waveguides in which loss prevails over gain and all modes are decaying. This phenomenon enables compensation for losses in dissipative systems and opens a wide range of applications in optics, plasmonics, and optoelectronics, in which loss is an inevitable problem and plays a crucial role. PMID:27405541

Observation of the exceptional point in cavity magnon-polaritons.

PubMed

Zhang, Dengke; Luo, Xiao-Qing; Wang, Yi-Pu; Li, Tie-Fu; You, J Q

2017-11-08

Magnon-polaritons are hybrid light-matter quasiparticles originating from the strong coupling between magnons and photons. They have emerged as a potential candidate for implementing quantum transducers and memories. Owing to the dampings of both photons and magnons, the polaritons have limited lifetimes. However, stationary magnon-polariton states can be reached by a dynamical balance between pumping and losses, so the intrinsically nonequilibrium system may be described by a non-Hermitian Hamiltonian. Here we design a tunable cavity quantum electrodynamics system with a small ferromagnetic sphere in a microwave cavity and engineer the dissipations of photons and magnons to create cavity magnon-polaritons which have non-Hermitian spectral degeneracies. By tuning the magnon-photon coupling strength, we observe the polaritonic coherent perfect absorption and demonstrate the phase transition at the exceptional point. Our experiment offers a novel macroscopic quantum platform to explore the non-Hermitian physics of the cavity magnon-polaritons.

Note on a Family of Monotone Quantum Relative Entropies

NASA Astrophysics Data System (ADS)

Deuchert, Andreas; Hainzl, Christian; Seiringer, Robert

2015-10-01

Given a convex function and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691-705, 2014) the relative entropy defined by . Among other things, they prove that the so-defined quantity is monotone if and only if is operator monotone. The monotonicity is then used to properly define for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections with strongly, the limit is shown to exist and to be independent of the sequence of projections . The question whether this sequence converges to its "obvious" limit, namely , has been left open. We answer this question in principle affirmatively and show that . If the operators A and B are regular enough, that is ( A - B), and are trace-class, the identity holds.

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

Forrester, Peter J., E-mail: p.forrester@ms.unimelb.edu.au; Thompson, Colin J.

The Golden-Thompson inequality, Tr (e{sup A+B}) ⩽ Tr (e{sup A}e{sup B}) for A, B Hermitian matrices, appeared in independent works by Golden and Thompson published in 1965. Both of these were motivated by considerations in statistical mechanics. In recent years the Golden-Thompson inequality has found applications to random matrix theory. In this article, we detail some historical aspects relating to Thompson's work, giving in particular a hitherto unpublished proof due to Dyson, and correspondence with Pólya. We show too how the 2 × 2 case relates to hyperbolic geometry, and how the original inequality holds true with the trace operation replaced bymore » any unitarily invariant norm. In relation to the random matrix applications, we review its use in the derivation of concentration type lemmas for sums of random matrices due to Ahlswede-Winter, and Oliveira, generalizing various classical results.« less

Acoustic metamaterials: From local resonances to broad horizons

PubMed Central

Ma, Guancong; Sheng, Ping

2016-01-01

Within a time span of 15 years, acoustic metamaterials have emerged from academic curiosity to become an active field driven by scientific discoveries and diverse application potentials. This review traces the development of acoustic metamaterials from the initial findings of mass density and bulk modulus frequency dispersions in locally resonant structures to the diverse functionalities afforded by the perspective of negative constitutive parameter values, and their implications for acoustic wave behaviors. We survey the more recent developments, which include compact phase manipulation structures, superabsorption, and actively controllable metamaterials as well as the new directions on acoustic wave transport in moving fluid, elastic, and mechanical metamaterials, graphene-inspired metamaterials, and structures whose characteristics are best delineated by non-Hermitian Hamiltonians. Many of the novel acoustic metamaterial structures have transcended the original definition of metamaterials as arising from the collective manifestations of constituent resonating units, but they continue to extend wave manipulation functionalities beyond those found in nature. PMID:26933692

Correlation Energies from the Two-Component Random Phase Approximation.

PubMed

Kühn, Michael

2014-02-11

The correlation energy within the two-component random phase approximation accounting for spin-orbit effects is derived. The resulting plasmon equation is rewritten-analogously to the scalar relativistic case-in terms of the trace of two Hermitian matrices for (Kramers-restricted) closed-shell systems and then represented as an integral over imaginary frequency using the resolution of the identity approximation. The final expression is implemented in the TURBOMOLE program suite. The code is applied to the computation of equilibrium distances and vibrational frequencies of heavy diatomic molecules. The efficiency is demonstrated by calculation of the relative energies of the Oh-, D4h-, and C5v-symmetric isomers of Pb6. Results within the random phase approximation are obtained based on two-component Kohn-Sham reference-state calculations, using effective-core potentials. These values are finally compared to other two-component and scalar relativistic methods, as well as experimental data.

Coherent scattering from semi-infinite non-Hermitian potentials

NASA Astrophysics Data System (ADS)

Ahmed, Zafar; Ghosh, Dona; Kumar, Sachin

2018-02-01

When two identical (coherent) beams are injected at a semi-infinite non-Hermitian medium from left and right, we show that both reflection (rL,rR) and transmission (tL,tR) amplitudes are nonreciprocal. In a parametric domain, there exists spectral singularity (SS) at a real energy E =E*=k*2 and the determinant of the time-reversed two port scattering matrix, i.e., |det(S (-k ) ) |=| tL(-k ) tR(-k ) -rL(-k ) rR(-k ) | , vanishes sharply at k =k* , displaying the phenomenon of coherent perfect absorption (CPA). In the complementary parametric domain, the potential becomes either left or right reflectionless at E =Ez . We rule out the existence of invisibility despite rR(Ei) =0 and tR(Ei) =1 but T (Ei)≠1 , in this avenue. We present two simple exactly solvable models where expressions for E*, Ez, Ei, and parametric conditions on the potential have been obtained in explicit and simple forms. Earlier, the phenomena of SS and CPA have been found to occur only in the scattering complex potentials which are spatially localized (vanish asymptotically) and have tL=tR .

Generalized Eigenvalues for pairs on heritian matrices

NASA Technical Reports Server (NTRS)

Rublein, George

1988-01-01

A study was made of certain special cases of a generalized eigenvalue problem. Let A and B be nxn matrics. One may construct a certain polynomial, P(A,B, lambda) which specializes to the characteristic polynomial of B when A equals I. In particular, when B is hermitian, that characteristic polynomial, P(I,B, lambda) has real roots, and one can ask: are the roots of P(A,B, lambda) real when B is hermitian. We consider the case where A is positive definite and show that when N equals 3, the roots are indeed real. The basic tools needed in the proof are Shur's theorem on majorization for eigenvalues of hermitian matrices and the interlacing theorem for the eigenvalues of a positive definite hermitian matrix and one of its principal (n-1)x(n-1) minors. The method of proof first reduces the general problem to one where the diagonal of B has a certain structure: either diag (B) = diag (1,1,1) or diag (1,1,-1), or else the 2 x 2 principal minors of B are all 1. According as B has one of these three structures, we use an appropriate method to replace A by a positive diagonal matrix. Since it can be easily verified that P(D,B, lambda) has real roots, the result follows. For other configurations of B, a scaling and a continuity argument are used to prove the result in general.

Self-hybridization within non-Hermitian localized plasmonic systems

NASA Astrophysics Data System (ADS)

Lourenço-Martins, Hugo; Das, Pabitra; Tizei, Luiz H. G.; Weil, Raphaël; Kociak, Mathieu

2018-04-01

The orthogonal eigenmodes are well-defined solutions of Hermitian equations describing many physical situations from quantum mechanics to acoustics. However, a large variety of non-Hermitian problems, including gravitational waves close to black holes or leaky electromagnetic cavities, require the use of a bi-orthogonal eigenbasis with consequences challenging our physical understanding1-4. The need to compensate for energy losses made the few successful attempts5-8 to experimentally probe non-Hermiticity extremely complicated. We overcome this problem by considering localized plasmonic systems. As the non-Hermiticity in these systems does not stem from temporal invariance breaking but from spatial symmetry breaking, its consequences can be observed more easily. We report on the theoretical and experimental evidence for non-Hermiticity-induced strong coupling between surface plasmon modes of different orders within silver nanodaggers. The symmetry conditions for triggering this counter-intuitive self-hybridization phenomenon are provided. Similar observable effects are expected to exist in any system exhibiting bi-orthogonal eigenmodes.

Investigating and improving student understanding of quantum mechanical observables and their corresponding operators in Dirac notation

NASA Astrophysics Data System (ADS)

Marshman, Emily; Singh, Chandralekha

2018-01-01

In quantum mechanics, for every physical observable, there is a corresponding Hermitian operator. According to the most common interpretation of quantum mechanics, measurement of an observable collapses the quantum state into one of the possible eigenstates of the operator and the corresponding eigenvalue is measured. Since Dirac notation is an elegant notation that is commonly used in upper-level quantum mechanics, it is important that students learn to express quantum operators corresponding to observables in Dirac notation in order to apply the quantum formalism effectively in diverse situations. Here we focus on an investigation that suggests that, even though Dirac notation is used extensively, many advanced undergraduate and PhD students in physics have difficulty expressing the identity operator and other Hermitian operators corresponding to physical observables in Dirac notation. We first describe the difficulties students have with expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We then discuss how the difficulties found via written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of these concepts. The QuILT strives to help students become proficient in expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We also discuss the effectiveness of the QuILT based on in-class evaluations.

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

Ghatak, Ananya, E-mail: gananya04@gmail.com; Mandal, Raka Dona Ray, E-mail: rakad.ray@gmail.com; Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com

We complexify a 1-d potential V(x)=V{sub 0}cosh{sup 2}μ(tanh[(x−μd)/d]+tanh(μ)){sup 2} which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ,d) becomes imaginary. For the case of μ→iμ, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from themore » left (or right) at certain discrete energies. The penetrating states in the other case (d→id) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. -- Highlights: •Existence of multiple spectral singularities (MSS) in PT-symmetric non-Hermitian system is shown. •Reciprocity is restored at discrete positive energies even for parity non-invariant complex system. •Co-existence of MSS with deep energy minima of transitivity is obtained. •Possibilities of both unidirectional and bidirectional invisibility are explored for a non-Hermitian system. •Penetrating states are shown to be reciprocal for all energies for PT-symmetric system.« less

Wavelet detection of singularities in the presence of fractal noise

NASA Astrophysics Data System (ADS)

Noel, Steven E.; Gohel, Yogesh J.; Szu, Harold H.

1997-04-01

Here we detect singularities with generalized quadrature processing using the recently developed Hermitian Hat wavelet. Our intended application is radar target detection for the optimal fuzzing of ship self-defense munitions. We first develop a wavelet-based fractal noise model to represent sea clutter. We then investigate wavelet shrinkage as a way to reduce and smooth the noise before attempting wavelet detection. Finally, we use the complex phase of the Hermitian Hat wavelet to detect a simulated target singularity in the presence of our fractal noise.

Affine group formulation of the Standard Model coupled to gravity

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

Chou, Ching-Yi, E-mail: l2897107@mail.ncku.edu.tw; Ita, Eyo, E-mail: ita@usna.edu; Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw

In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder’s affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological constant Λ, as an affine Lie algebra. We use the hermitian action of fermions coupled to gravitation and Yang–Mills theory to find the density weight one fermionic super-Hamiltonian constraint. This term, combined with the Yang–Mills and Higgs energy densities, are composed with York’s integrated time functional. The result, when combined with the imaginary part of themore » Chern–Simons functional Q, forms the affine commutation relation with the volume element V(x). Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant. -- Highlights: •Wheeler–DeWitt equation (WDW) quantized as affine algebra, realizing Klauder’s program. •WDW formulated for interaction of matter and all forces, including gravity, as affine algebra. •WDW features Hermitian generators in spite of fermionic content: Standard Model addressed. •Constructed a family of physical states for the full, coupled theory via affine coherent states. •Fundamental uncertainty relation, predicated on non-vanishing cosmological constant.« less

Non-Unitary Boson Mapping and Its Application to Nuclear Collective Motions

NASA Astrophysics Data System (ADS)

Takada, K.

First, the general theory of boson mapping for even-number many-fermion systems is surveyed. In order to overcome the confusion concerning the so-called unphysical or spurious states in the boson mapping, the correct concept of the unphysical states is precisely given in a clear-cut way. Next, a method to apply the boson mapping to a truncated many-fermion Hilbert space consisting of collective phonons is proposed, by putting special emphasis on the Dyson-type non-unitary boson mapping. On the basis of this method, it becomes possible for the first time to apply the Dyson-type boson mapping to analyses of collective motions in realistic nuclei. This method is also extended to be applicable to odd-number-fermion systems. As known well, the Dyson-type boson mapping is a non-unitary transformation and it gives a non-Hermitian boson Hamiltonian. It is not easy (but not impossible) to solve the eigenstates of the non-Hermitian Hamiltonian. A Hermitian treatment of this non-Hermitian eigenvalue problem is discussed and it is shown that this treatment is a very good approximation. Using this Hermitian treatment, we can obtain the normal-ordered Holstein-Primakoff-type boson expansion in the multi-collective-phonon subspace. Thereby the convergence of the boson expansion can be tested. Some examples of application of the Dyson-type non-unitary boson mapping to simplified models and realistic nuclei are also shown, and we can see that it is quite useful for analysis of the collective motions in realistic nuclei. In contrast to the above-mentioned ordinary type of boson mapping, which may be called a ``static'' boson mapping, the Dyson-type non-unitary selfconsistent-collective-coordinate method is discussed. The latter is, so to speak, a ``dynamical'' boson mapping, which is a dynamical extension of the ordinary boson mapping to be capable to include the coupling effects from the non-collective degrees of freedom selfconsistently. Thus all of the Dyson-type non-unitary boson mapping from A to Z is summarized in this paper.

A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix [A projected preconditioned conjugate gradient algorithm for computing a large eigenspace of a Hermitian matrix

DOE PAGES

Vecharynski, Eugene; Yang, Chao; Pask, John E.

2015-02-25

Here, we present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimalmore » block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer.« less

Boson expansions based on the random phase approximation representation

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

Pedrocchi, V.G.; Tamura, T.

1984-04-01

A new boson expansion theory based on the random phase approximation is presented. The boson expansions are derived here directly in the random phase approximation representation with the help of a technique that combines the use of the Usui operator with that of a new bosonization procedure, called the term-by-term bosonization method. The present boson expansion theory is constructed by retaining a single collective quadrupole random phase approximation component, a truncation that allows for a perturbative treatment of the whole problem. Both Hermitian, as well as non-Hermitian boson expansions, valid for even nuclei, are obtained.

Twisted supersymmetry: Twisted symmetry versus renormalizability

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

Dimitrijevic, Marija; Nikolic, Biljana; Radovanovic, Voja

We discuss a deformation of superspace based on a Hermitian twist. The twist implies a *-product that is noncommutative, Hermitian and finite when expanded in a power series of the deformation parameter. The Leibniz rule for the twisted supersymmetry transformations is deformed. A minimal deformation of the Wess-Zumino action is proposed and its renormalizability properties are discussed. There is no tadpole contribution, but the two-point function diverges. We speculate that the deformed Leibniz rule, or more generally the twisted symmetry, interferes with renormalizability properties of the model. We discuss different possibilities to render a renormalizable model.

Correlations, soliton modes, and non-Hermitian linear mode transmutation in the one-dimensional noisy Burgers equation.

PubMed

Fogedby, Hans C

2003-08-01

Using the previously developed canonical phase space approach applied to the noisy Burgers equation in one dimension, we discuss in detail the growth morphology in terms of nonlinear soliton modes and superimposed linear modes. We moreover analyze the non-Hermitian character of the linear mode spectrum and the associated dynamical pinning, and mode transmutation from diffusive to propagating behavior induced by the solitons. We discuss the anomalous diffusion of growth modes, switching and pathways, correlations in the multisoliton sector, and in detail the correlations and scaling properties in the two-soliton sector.

X-ray absorption in insulators with non-Hermitian real-time time-dependent density functional theory.

PubMed

Fernando, Ranelka G; Balhoff, Mary C; Lopata, Kenneth

2015-02-10

Non-Hermitian real-time time-dependent density functional theory was used to compute the Si L-edge X-ray absorption spectrum of α-quartz using an embedded finite cluster model and atom-centered basis sets. Using tuned range-separated functionals and molecular orbital-based imaginary absorbing potentials, the excited states spanning the pre-edge to ∼20 eV above the ionization edge were obtained in good agreement with experimental data. This approach is generalizable to TDDFT studies of core-level spectroscopy and dynamics in a wide range of materials.

A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems. Ph.D. Thesis - Massachusetts Inst. of Technology, Aug. 1991

NASA Technical Reports Server (NTRS)

Nachtigal, Noel M.

1991-01-01

The Lanczos algorithm can be used both for eigenvalue problems and to solve linear systems. However, when applied to non-Hermitian matrices, the classical Lanczos algorithm is susceptible to breakdowns and potential instabilities. In addition, the biconjugate gradient (BCG) algorithm, which is the natural generalization of the conjugate gradient algorithm to non-Hermitian linear systems, has a second source of breakdowns, independent of the Lanczos breakdowns. Here, we present two new results. We propose an implementation of a look-ahead variant of the Lanczos algorithm which overcomes the breakdowns by skipping over those steps where a breakdown or a near-breakdown would occur. The new algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products per step as the classical Lanczos algorithm without look-ahead. Based on the proposed look-ahead Lanczos algorithm, we then present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which avoids the second source of breakdowns in the BCG algorithm. We present details of the new method and discuss some of its properties. In particular, we discuss the relationship between QMR and BCG, showing how one can recover the BCG iterates, when they exist, from the QMR iterates. We also present convergence results for QMR, showing the connection between QMR and the generalized minimal residual (GMRES) algorithm, the optimal method in this class of methods. Finally, we give some numerical examples, both for eigenvalue computations and for non-Hermitian linear systems.

Ghost busting: PT-symmetric interpretation of the Lee model

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

Bender, Carl M.; Brandt, Sebastian F.; Chen, J.-H.

2005-01-15

The Lee model was introduced in the 1950s as an elementary quantum field theory in which mass, wave function, and charge renormalization could be carried out exactly. In early studies of this model it was found that there is a critical value of g{sup 2}, the square of the renormalized coupling constant, above which g{sub 0}{sup 2}, the square of the unrenormalized coupling constant, is negative. Thus, for g{sup 2} larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. It was also discovered that in this non-Hermitian regime a new state appears whose norm is negative.more » This state is called a ghost state. It has always been assumed that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess PT symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having PT symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a new time-independent operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitary. In this paper the C operator for the Lee model in the ghost regime is constructed in the V/N{theta} sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum field theory for all values of g{sup 2}.« less

Three-dimensional coil inductor

DOEpatents

Bernhardt, Anthony F.; Malba, Vincent

2002-01-01

A three-dimensional coil inductor is disclosed. The inductor includes a substrate; a set of lower electrically conductive traces positioned on the substrate; a core placed over the lower traces; a set of side electrically conductive traces laid on the core and the lower traces; and a set of upper electrically conductive traces attached to the side traces so as to form the inductor. Fabrication of the inductor includes the steps of forming a set of lower traces on a substrate; positioning a core over the lower traces; forming a set of side traces on the core; connecting the side traces to the lower traces; forming a set of upper traces on the core; and connecting the upper traces to the side traces so as to form a coil structure.

Swimming of a sphere in a viscous incompressible fluid with inertia

NASA Astrophysics Data System (ADS)

Felderhof, B. U.; Jones, R. B.

2017-08-01

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two Hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid.

Valley Physics in Non-Hermitian Artificial Acoustic Boron Nitride

NASA Astrophysics Data System (ADS)

Wang, Mudi; Ye, Liping; Christensen, J.; Liu, Zhengyou

2018-06-01

The valley can serve as a new degree of freedom in the manipulation of particles or waves in condensed matter physics, whereas systems containing combinations of gain and loss elements constitute rich building units that can mimic non-Hermitian properties. By introducing gain and loss in artificial acoustic boron nitride, we show that the acoustic valley states and the valley-projected edge states display exotic behaviors in that they sustain either attenuated or amplified wave propagation. Our findings show how non-Hermiticity introduces a mechanism in tuning topological protected valley transports, which may have significance in advanced wave control for sensing and communication applications.

Factorising the 3D topologically twisted index

NASA Astrophysics Data System (ADS)

Cabo-Bizet, Alejandro

2017-04-01

We explore the path integration — upon the contour of hermitian (non-auxliary) field configurations — of topologically twisted N=2 Chern-Simons-matter theory (TTCSM) on {S}_2 times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on {S}_2 times halves of {S}_1 , second as TTCSM on {S}_2 times {S}_1 — with a puncture, — and third as TTCSM on {S}_2× {S}_1 . In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field D is constrained to be anti-hermitian.

Flat band in disorder-driven non-Hermitian Weyl semimetals

NASA Astrophysics Data System (ADS)

Zyuzin, A. A.; Zyuzin, A. Yu.

2018-01-01

We study the interplay of disorder and band-structure topology in a Weyl semimetal with a tilted conical spectrum around the Weyl points. The spectrum of particles is given by the eigenvalues of a non-Hermitian matrix, which contains contributions from a Weyl Hamiltonian and complex self-energy due to electron elastic scattering on disorder. We find that the tilt-induced matrix structure of the self-energy gives rise to either a flat band or a nodal line segment at the interface of the electron and hole pockets in the bulk band structure of type-II Weyl semimetals depending on the Weyl cone inclination. For the tilt in a single direction in momentum space, each Weyl point expands into a flat band lying on the plane, which is transverse to the direction of the tilt. The spectrum of the flat band is fully imaginary and is separated from the in-plane dispersive part of the spectrum by the "exceptional nodal ring" where the matrix of the Green's function in momentum-frequency space is defective. The tilt in two directions might shrink a flat band into a nodal line segment with "exceptional edge points." We discuss the connection to the non-Hermitian topological theory.

Effect of the qubit relaxation on transport properties of microwave photons

NASA Astrophysics Data System (ADS)

Sultanov, A. N.; Greenberg, Ya. S.

2017-11-01

In this work, using the non-Hermitian Hamiltonian method, the transmission of a single photon in a one-dimensional waveguide interacting with the cavity containing an arbitrary number of photons and the two-level artificial atom is studied with allowance for the relaxation of the latter. For transport factors, analytical expressions which explicitly take into account the qubit relaxation parameter have been obtained. The form of the transmission (reflection) coefficient when there is more than one photon in the cavity qualitatively differs from the single-photon cavity and contains the manifestation of the photon blockade effect. The qubit lifetime depends on the number of photons in the cavity.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included.

A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

DOE PAGES

Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; ...

2016-08-16

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a thick-restart version of the Lanczos algorithm with deflation ("locking'') and a new type of polynomial filter obtained from a least-squares technique. Furthermore, the resulting algorithm can be utilized in a “spectrum-slicing” approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different subintervals independently from onemore » another.« less

Topological phases in a Kitaev chain with imbalanced pairing

NASA Astrophysics Data System (ADS)

Li, C.; Zhang, X. Z.; Zhang, G.; Song, Z.

2018-03-01

We systematically study a Kitaev chain with imbalanced pair creation and annihilation, which is introduced by non-Hermitian pairing terms. An exact phase diagram shows that the topological phase is still robust under the influence of the conditional imbalance. The gapped phases are characterized by a topological invariant, the extended Zak phase, which is defined by the biorthonormal inner product. Such phases are destroyed at the points where the coalescence of ground states occurs, associated with the time-reversal symmetry breaking. We find that the Majorana edge modes also exist in an open chain in the time-reversal symmetry-unbroken region, demonstrating the bulk-edge correspondence in such a non-Hermitian system.

Generalized continuity equations from two-field Schrödinger Lagrangians

NASA Astrophysics Data System (ADS)

Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.

2016-11-01

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.

Eigensolver for a Sparse, Large Hermitian Matrix

NASA Technical Reports Server (NTRS)

Tisdale, E. Robert; Oyafuso, Fabiano; Klimeck, Gerhard; Brown, R. Chris

2003-01-01

A parallel-processing computer program finds a few eigenvalues in a sparse Hermitian matrix that contains as many as 100 million diagonal elements. This program finds the eigenvalues faster, using less memory, than do other, comparable eigensolver programs. This program implements a Lanczos algorithm in the American National Standards Institute/ International Organization for Standardization (ANSI/ISO) C computing language, using the Message Passing Interface (MPI) standard to complement an eigensolver in PARPACK. [PARPACK (Parallel Arnoldi Package) is an extension, to parallel-processing computer architectures, of ARPACK (Arnoldi Package), which is a collection of Fortran 77 subroutines that solve large-scale eigenvalue problems.] The eigensolver runs on Beowulf clusters of computers at the Jet Propulsion Laboratory (JPL).

Non-Hermitian Operator Modelling of Basic Cancer Cell Dynamics

NASA Astrophysics Data System (ADS)

Bagarello, Fabio; Gargano, Francesco

2018-04-01

We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth.

Piecewise adiabatic following in non-Hermitian cycling

NASA Astrophysics Data System (ADS)

Gong, Jiangbin; Wang, Qing-hai

2018-05-01

The time evolution of periodically driven non-Hermitian systems is in general nonunitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics in periodically driven non-Hermitian systems. We show in this work the possibility of piecewise adiabatic following interrupted by hopping between instantaneous system eigenstates. This phenomenon is first observed in a computational model and then theoretically explained, using an exactly solvable model, in terms of the Stokes phenomenon. In the latter case, the piecewise adiabatic following is shown to be a genuine critical behavior and the precise phase boundary in the parameter space is located. Interestingly, the critical boundary for piecewise adiabatic following is found to be unrelated to the domain for exceptional points. To characterize the adiabatic following dynamics, we also advocate a simple definition of the Aharonov-Anandan (AA) phase for nonunitary cyclic dynamics, which always yields real AA phases. In the slow driving limit, the AA phase reduces to the Berry phase if adiabatic following persists throughout the driving without hopping, but oscillates violently and does not approach any limit in cases of piecewise adiabatic following. This work exposes the rich features of nonunitary dynamics in cases of slow cycling and should stimulate future applications of nonunitary dynamics.

A Schrödinger equation for solving the Bender-Brody-Müller conjecture

NASA Astrophysics Data System (ADS)

Moxley, Frederick Ira

2017-11-01

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and discuss the eigenvalues of the results. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, the Hilbert-Pólya conjecture is discussed, and it is heuristically shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

Conservation of connectivity of model-space effective interactions under a class of similarity transformation.

PubMed

Duan, Chang-Kui; Gong, Yungui; Dong, Hui-Ning; Reid, Michael F

2004-09-15

Effective interaction operators usually act on a restricted model space and give the same energies (for Hamiltonian) and matrix elements (for transition operators, etc.) as those of the original operators between the corresponding true eigenstates. Various types of effective operators are possible. Those well defined effective operators have been shown to be related to each other by similarity transformation. Some of the effective operators have been shown to have connected-diagram expansions. It is shown in this paper that under a class of very general similarity transformations, the connectivity is conserved. The similarity transformation between Hermitian and non-Hermitian Rayleigh-Schrodinger perturbative effective operators is one of such transformations and hence the connectivity can be deducted from each other.

Unidirectional reflectionless phenomenon in ultracompact non-Hermitian plasmonic waveguide system based on phase coupling

NASA Astrophysics Data System (ADS)

Zhang, Cong; Bai, Ruiping; Gu, Xintong; Jin, Yingjiu; Qiao Zhang, Ying; Jin, Xing Ri; Zhang, Shou; Lee, YoungPak

2017-12-01

Unidirectional reflectionless phenomenon is theoretically investigated based on phase coupling in an ultracompact non-Hermitian plasmonic waveguide system, which consists of two metal-insulator-metal (MIM) stub resonators side coupled to a MIM plasmonic waveguide. By appropriately tuning the phase difference between two stub resonators, the reflectivity for forward direction reaches to 0.91 and backward direction is close to 0 at the exception point (EP), while the backward absorption reaches to 0.98 and the forward absorption is close to 0.05. Hence, the unidirectional coherent perfect absorption (CPA) is realized at the vicinity of EP. This work will provide potential applications in the filter, sensor, plasmonic diode-like device, and so on.

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

Sinitsyn, N. A.

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicitmore » expressions for scattering probabilities in such systems.« less

Gegenbauer-solvable quantum chain model

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2010-11-01

An N-level quantum model is proposed in which the energies are represented by an N-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials G(n,a,x) is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians H≠H†. We managed to (i) start from elementary secular equation G(N,a,En)=0, (ii) keep our H, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric Θ≠I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as a smeared N-site lattice.

Directionality fields generated by a local Hilbert transform

NASA Astrophysics Data System (ADS)

Ahmed, W. W.; Herrero, R.; Botey, M.; Hayran, Z.; Kurt, H.; Staliunas, K.

2018-03-01

We propose an approach based on a local Hilbert transform to design non-Hermitian potentials generating arbitrary vector fields of directionality, p ⃗(r ⃗) , with desired shapes and topologies. We derive a local Hilbert transform to systematically build such potentials by modifying background potentials (being either regular or random, extended or localized). We explore particular directionality fields, for instance in the form of a focus to create sinks for probe fields (which could help to increase absorption at the sink), or to generate vortices in the probe fields. Physically, the proposed directionality fields provide a flexible mechanism for dynamical shaping and precise control over probe fields leading to novel effects in wave dynamics.

Three-dimensional polarization algebra.

PubMed

R Sheppard, Colin J; Castello, Marco; Diaspro, Alberto

2016-10-01

If light is focused or collected with a high numerical aperture lens, as may occur in imaging and optical encryption applications, polarization should be considered in three dimensions (3D). The matrix algebra of polarization behavior in 3D is discussed. It is useful to convert between the Mueller matrix and two different Hermitian matrices, representing an optical material or system, which are in the literature. Explicit transformation matrices for converting the column vector form of these different matrices are extended to the 3D case, where they are large (81×81) but can be generated using simple rules. It is found that there is some advantage in using a generalization of the Chandrasekhar phase matrix treatment, rather than that based on Gell-Mann matrices, as the resultant matrices are of simpler form and reduce to the two-dimensional case more easily. Explicit expressions are given for 3D complex field components in terms of Chandrasekhar-Stokes parameters.

BFV quantization on hermitian symmetric spaces

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1995-02-01

Gauge-invariant BFV approach to geometric quantization is applied to the case of hermitian symmetric spaces G/ H. In particular, gauge invariant quantization on the Lobachevski plane and sphere is carried out. Due to the presence of symmetry, master equations for the first-class constraints, quantum observables and physical quantum states are exactly solvable. BFV-BRST operator defines a flat G-connection in the Fock bundle over G/ H. Physical quantum states are covariantly constant sections with respect to this connection and are shown to coincide with the generalized coherent states for the group G. Vacuum expectation values of the quantum observables commuting with the quantum first-class constraints reduce to the covariant symbols of Berezin. The gauge-invariant approach to quantization on symplectic manifolds synthesizes geometric, deformation and Berezin quantization approaches.

Quantum jumps on Anderson attractors

NASA Astrophysics Data System (ADS)

Yusipov, I. I.; Laptyeva, T. V.; Ivanchenko, M. V.

2018-01-01

In a closed single-particle quantum system, spatial disorder induces Anderson localization of eigenstates and halts wave propagation. The phenomenon is vulnerable to interaction with environment and decoherence that is believed to restore normal diffusion. We demonstrate that for a class of experimentally feasible non-Hermitian dissipators, which admit signatures of localization in asymptotic states, quantum particle opts between diffusive and ballistic regimes, depending on the phase parameter of dissipators, with sticking about localization centers. In a diffusive regime, statistics of quantum jumps is non-Poissonian and has a power-law interval, a footprint of intermittent locking in Anderson modes. Ballistic propagation reflects dispersion of an ordered lattice and introduces the second timescale for jumps, resulting in non-nonmonotonous probability distribution. Hermitian dephasing dissipation makes localization features vanish, and Poissonian jump statistics along with normal diffusion are recovered.

State-independent uncertainty relations and entanglement detection

NASA Astrophysics Data System (ADS)

Qian, Chen; Li, Jun-Li; Qiao, Cong-Feng

2018-04-01

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of zero lower bounds. Here we develop a method to get uncertainty relations with state-independent lower bounds. The method works by exploring the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible observables and is applicable for both pure and mixed states and for arbitrary number of N-dimensional observables. The uncertainty relation for the incompatible observables can be explained by geometric relations related to the parallel postulate and the inequalities in Horn's conjecture on Hermitian matrix sum. Practical entanglement criteria are also presented based on the derived uncertainty relations.

Pure connection formulation, twistors, and the chase for a twistor action for general relativity

NASA Astrophysics Data System (ADS)

Herfray, Yannick

2017-11-01

This paper establishes the relation between traditional results from the (Euclidean) twistor theory and chiral formulations of general relativity (GR), especially the pure connection formulation. Starting from an SU(2)-connection only, we show how to construct natural complex data on twistor space, mainly an almost Hermitian structure and a connection on some complex line bundle. Only when this almost Hermitian structure is integrable is the connection related to an anti-self-dual-Einstein metric and makes contact with the usual results. This leads to a new proof of the non-linear graviton theorem. Finally, we discuss what new strategies this "connection approach" to twistors suggests for constructing a twistor action for gravity. In Appendix A, we also review all known chiral Lagrangians for GR.

Constacyclic codes over the ring F_q+v{F}_q+v2F_q and their applications of constructing new non-binary quantum codes

NASA Astrophysics Data System (ADS)

Ma, Fanghui; Gao, Jian; Fu, Fang-Wei

2018-06-01

Let R={F}_q+v{F}_q+v2{F}_q be a finite non-chain ring, where q is an odd prime power and v^3=v. In this paper, we propose two methods of constructing quantum codes from (α +β v+γ v2)-constacyclic codes over R. The first one is obtained via the Gray map and the Calderbank-Shor-Steane construction from Euclidean dual-containing (α +β v+γ v2)-constacyclic codes over R. The second one is obtained via the Gray map and the Hermitian construction from Hermitian dual-containing (α +β v+γ v2)-constacyclic codes over R. As an application, some new non-binary quantum codes are obtained.

A uniform object-oriented solution to the eigenvalue problem for real symmetric and Hermitian matrices

NASA Astrophysics Data System (ADS)

Castro, María Eugenia; Díaz, Javier; Muñoz-Caro, Camelia; Niño, Alfonso

2011-09-01

We present a system of classes, SHMatrix, to deal in a unified way with the computation of eigenvalues and eigenvectors in real symmetric and Hermitian matrices. Thus, two descendant classes, one for the real symmetric and other for the Hermitian cases, override the abstract methods defined in a base class. The use of the inheritance relationship and polymorphism allows handling objects of any descendant class using a single reference of the base class. The system of classes is intended to be the core element of more sophisticated methods to deal with large eigenvalue problems, as those arising in the variational treatment of realistic quantum mechanical problems. The present system of classes allows computing a subset of all the possible eigenvalues and, optionally, the corresponding eigenvectors. Comparison with well established solutions for analogous eigenvalue problems, as those included in LAPACK, shows that the present solution is competitive against them. Program summaryProgram title: SHMatrix Catalogue identifier: AEHZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHZ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2616 No. of bytes in distributed program, including test data, etc.: 127 312 Distribution format: tar.gz Programming language: Standard ANSI C++. Computer: PCs and workstations. Operating system: Linux, Windows. Classification: 4.8. Nature of problem: The treatment of problems involving eigensystems is a central topic in the quantum mechanical field. Here, the use of the variational approach leads to the computation of eigenvalues and eigenvectors of real symmetric and Hermitian Hamiltonian matrices. Realistic models with several degrees of freedom leads to large (sometimes very large) matrices. Different techniques, such as divide and conquer, can be used to factorize the matrices in order to apply a parallel computing approach. However, it is still interesting to have a core procedure able to tackle the computation of eigenvalues and eigenvectors once the matrix has been factorized to pieces of enough small size. Several available software packages, such as LAPACK, tackled this problem under the traditional imperative programming paradigm. In order to ease the modelling of complex quantum mechanical models it could be interesting to apply an object-oriented approach to the treatment of the eigenproblem. This approach offers the advantage of a single, uniform treatment for the real symmetric and Hermitian cases. Solution method: To reach the above goals, we have developed a system of classes: SHMatrix. SHMatrix is composed by an abstract base class and two descendant classes, one for real symmetric matrices and the other for the Hermitian case. The object-oriented characteristics of inheritance and polymorphism allows handling both cases using a single reference of the base class. The basic computing strategy applied in SHMatrix allows computing subsets of eigenvalues and (optionally) eigenvectors. The tests performed show that SHMatrix is competitive, and more efficient for large matrices, than the equivalent routines of the LAPACK package. Running time: The examples included in the distribution take only a couple of seconds to run.

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

Znojil, Miloslav

An N-level quantum model is proposed in which the energies are represented by an N-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials G(n,a,x) is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians H{ne}H{sup {dagger}.} We managed to (i) start from elementary secular equation G(N,a,E{sub n})=0, (ii) keep our H, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric {Theta}{ne}I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as amore » smeared N-site lattice.« less

Traces of Drosophila Memory

PubMed Central

Davis, Ronald L.

2012-01-01

Summary Studies using functional cellullar imaging of living flies have identified six memory traces that form in the olfactory nervous system after conditioning with odors. These traces occur in distinct nodes of the olfactory nervous system, form and disappear across different windows of time, and are detected in the imaged neurons as increased calcium influx or synaptic release in response to the conditioned odor. Three traces form at, or near acquisition and co-exist with short-term behavioral memory. One trace forms with a delay after learning and co-exists with intermediate-term behavioral memory. Two traces form many hours after acquisition and co-exist with long-term behavioral memory. The transient memory traces may support behavior across the time-windows of their existence. The experimental approaches for dissecting memory formation in the fly, ranging from the molecular to the systems, make it an ideal system for dissecting the logic by which the nervous system organizes and stores different temporal forms of memory. PMID:21482352

Coherent perfect absorption and laser modes in a cylindrical structure of conjugate metamaterials

NASA Astrophysics Data System (ADS)

Fu, Yangyang; Xu, Yadong; Chen, Huanyang; Cummer, Steven A.

2018-01-01

In this work, we theoretically find that coherent perfect absorption (CPA) and laser modes can be realized in a two-dimensional cylindrical structure composed of conjugate metamaterials (CMs). The required phase factors of CMs for achieving CPA and laser modes are determined by the geometric size of the CM cylinder, which is a unique feature compared with other non-Hermitian optical systems. Based on this property, we also demonstrate that CPA and laser modes can exist simultaneously in a CM cylinder with an extremely large size, where the excitations of CPA and laser modes depend on the angular momentum of coherent incident light. Therefore, compared with the well known parity time symmetry, our work opens up a brand-new path to obtaining CPA and laser modes, and is a significant advance in non-Hermitian optical systems.

On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland W.

1992-01-01

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.

Lie algebraic similarity transformed Hamiltonians for lattice model systems

NASA Astrophysics Data System (ADS)

Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.

2015-01-01

We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.

Algorithm 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems.

PubMed

Choi, Sou-Cheng T; Saunders, Michael A

2014-02-01

We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP.

Asymptotics for the Fredholm determinant of the sine kernel on a union of intervals

NASA Astrophysics Data System (ADS)

Widom, Harold

1995-07-01

In the bulk scaling limit of the Gaussian Unitary Ensemble of hermitian matrices the probability that an interval of length s contains no eigenvalues is the Fredholm determinant of the sine kernel{sin (x - y)}/{π (x - y)} over this interval. A formal asymptotic expansion for the determinant as s tends to infinity was obtained by Dyson. In this paper we replace a single interval of length s by sJ, where J is a union of m intervals and present a proof of the asymptotics up to second order. The logarithmic derivative with respect to s of the determinant equals a constant (expressible in terms of hyperelliptic integrals) times s, plus a bounded oscillatory function of s (zero if m=1, periodic if m=2, and in general expressible in terms of the solution of a Jacobi inversion problem), plus o(1). Also determined are the asymptotics of the trace of the resolvent operator, which is the ratio in the same model of the probability that the set contains exactly one eigenvalue to the probability that it contains none. The proofs use ideas from orthogonal polynomial theory.

FormTracer. A mathematica tracing package using FORM

NASA Astrophysics Data System (ADS)

Cyrol, Anton K.; Mitter, Mario; Strodthoff, Nils

2017-10-01

We present FormTracer, a high-performance, general purpose, easy-to-use Mathematica tracing package which uses FORM. It supports arbitrary space and spinor dimensions as well as an arbitrary number of simple compact Lie groups. While keeping the usability of the Mathematica interface, it relies on the efficiency of FORM. An additional performance gain is achieved by a decomposition algorithm that avoids redundant traces in the product tensors spaces. FormTracer supports a wide range of syntaxes which endows it with a high flexibility. Mathematica notebooks that automatically install the package and guide the user through performing standard traces in space-time, spinor and gauge-group spaces are provided. Program Files doi:http://dx.doi.org/10.17632/7rd29h4p3m.1 Licensing provisions: GPLv3 Programming language: Mathematica and FORM Nature of problem: Efficiently compute traces of large expressions Solution method: The expression to be traced is decomposed into its subspaces by a recursive Mathematica expansion algorithm. The result is subsequently translated to a FORM script that takes the traces. After FORM is executed, the final result is either imported into Mathematica or exported as optimized C/C++/Fortran code. Unusual features: The outstanding features of FormTracer are the simple interface, the capability to efficiently handle an arbitrary number of Lie groups in addition to Dirac and Lorentz tensors, and a customizable input-syntax.

Virial expansion for almost diagonal random matrices

NASA Astrophysics Data System (ADS)

Yevtushenko, Oleg; Kravtsov, Vladimir E.

2003-08-01

Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\

Anti-Hermitian photodetector facilitating efficient subwavelength photon sorting.

PubMed

Kim, Soo Jin; Kang, Ju-Hyung; Mutlu, Mehmet; Park, Joonsuk; Park, Woosung; Goodson, Kenneth E; Sinclair, Robert; Fan, Shanhui; Kik, Pieter G; Brongersma, Mark L

2018-01-22

The ability to split an incident light beam into separate wavelength bands is central to a diverse set of optical applications, including imaging, biosensing, communication, photocatalysis, and photovoltaics. Entirely new opportunities are currently emerging with the recently demonstrated possibility to spectrally split light at a subwavelength scale with optical antennas. Unfortunately, such small structures offer limited spectral control and are hard to exploit in optoelectronic devices. Here, we overcome both challenges and demonstrate how within a single-layer metafilm one can laterally sort photons of different wavelengths below the free-space diffraction limit and extract a useful photocurrent. This chipscale demonstration of anti-Hermitian coupling between resonant photodetector elements also facilitates near-unity photon-sorting efficiencies, near-unity absorption, and a narrow spectral response (∼ 30 nm) for the different wavelength channels. This work opens up entirely new design paradigms for image sensors and energy harvesting systems in which the active elements both sort and detect photons.

Unidirectional reflectionless light propagation at exceptional points

NASA Astrophysics Data System (ADS)

Huang, Yin; Shen, Yuecheng; Min, Changjun; Fan, Shanhui; Veronis, Georgios

2017-05-01

In this paper, we provide a comprehensive review of unidirectional reflectionless light propagation in photonic devices at exceptional points (EPs). EPs, which are branch point singularities of the spectrum, associated with the coalescence of both eigenvalues and corresponding eigenstates, lead to interesting phenomena, such as level repulsion and crossing, bifurcation, chaos, and phase transitions in open quantum systems described by non-Hermitian Hamiltonians. Recently, it was shown that judiciously designed photonic synthetic matters could mimic the complex non-Hermitian Hamiltonians in quantum mechanics and realize unidirectional reflection at optical EPs. Unidirectional reflectionlessness is of great interest for optical invisibility. Achieving unidirectional reflectionless light propagation could also be potentially important for developing optical devices, such as optical network analyzers. Here, we discuss unidirectional reflectionlessness at EPs in both parity-time (PT)-symmetric and non-PT-symmetric optical systems. We also provide an outlook on possible future directions in this field.

Probing non-Hermitian physics with flying atoms

NASA Astrophysics Data System (ADS)

Wen, Jianming; Xiao, Yanhong; Peng, Peng; Cao, Wanxia; Shen, Ce; Qu, Weizhi; Jiang, Liang

2016-05-01

Non-Hermtian optical systems with parity-time (PT) symmetry provide new means for light manipulation and control. To date, most of experimental demonstrations on PT symmetry rely on advanced nanotechnologies and sophisticated fabrication techniques to manmade solid-state materials. Here, we report the first experimental realization of optical anti-PT symmetry, a counterpart of conventional PT symmetry, in a warm atomic-vapor cell. By exploiting rapid coherence transport via flying atoms, we observe essential features of anti-PT symmetry with an unprecedented precision on phase-transition threshold. Moreover, our system allows nonlocal interference of two spatially-separated fields as well as anti-PT assisted four-wave mixing. Besides, another intriguing feature offered by the system is refractionless (or unit-refraction) light propagation. Our results thus represent a significant advance in non-Hermitian physics by bridging a firm connection with the AMO field, where novel phenomena and applications in quantum and nonlinear optics aided by (anti-)PT symmetry can be anticipated.

Computing resonance energies, widths, and wave functions using a Lanczos method in real arithmetic.

PubMed

Tremblay, Jean Christophe; Carrington, Tucker

2005-06-22

We introduce new ideas for calculating resonance energies and widths. It is shown that a non-Hermitian-Lanczos approach can be used to compute eigenvalues of H+W, where H is the Hamiltonian and W is a complex absorbing potential (CAP), without evaluating complex matrix-vector products. This is done by exploiting the link between a CAP-modified Hamiltonian matrix and a real but nonsymmetric matrix U suggested by Mandelshtam and Neumaier [J. Theor. Comput. Chem. 1, 1 (2002)] and using a coupled-two-term Lanczos procedure. We use approximate resonance eigenvectors obtained from the non-Hermitian-Lanczos algorithm and a very good CAP to obtain very accurate energies and widths without solving eigenvalue problems for many values of the CAP strength parameter and searching for cusps. The method is applied to the resonances of HCO. We compare properties of the method with those of established approaches.

A biconjugate gradient type algorithm on massively parallel architectures

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Hochbruck, Marlis

1991-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. Recently, Freund and Nachtigal have proposed a novel BCG type approach, the quasi-minimal residual method (QMR), which overcomes the problems of BCG. Here, an implementation is presented of QMR based on an s-step version of the nonsymmetric look-ahead Lanczos algorithm. The main feature of the s-step Lanczos algorithm is that, in general, all inner products, except for one, can be computed in parallel at the end of each block; this is unlike the other standard Lanczos process where inner products are generated sequentially. The resulting implementation of QMR is particularly attractive on massively parallel SIMD architectures, such as the Connection Machine.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

New quantum codes derived from a family of antiprimitive BCH codes

NASA Astrophysics Data System (ADS)

Liu, Yang; Li, Ruihu; Lü, Liangdong; Guo, Luobin

The Bose-Chaudhuri-Hocquenghem (BCH) codes have been studied for more than 57 years and have found wide application in classical communication system and quantum information theory. In this paper, we study the construction of quantum codes from a family of q2-ary BCH codes with length n=q2m+1 (also called antiprimitive BCH codes in the literature), where q≥4 is a power of 2 and m≥2. By a detailed analysis of some useful properties about q2-ary cyclotomic cosets modulo n, Hermitian dual-containing conditions for a family of non-narrow-sense antiprimitive BCH codes are presented, which are similar to those of q2-ary primitive BCH codes. Consequently, via Hermitian Construction, a family of new quantum codes can be derived from these dual-containing BCH codes. Some of these new antiprimitive quantum BCH codes are comparable with those derived from primitive BCH codes.

Algorithm 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems

PubMed Central

Choi, Sou-Cheng T.; Saunders, Michael A.

2014-01-01

We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP. PMID:25328255

Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices

NASA Astrophysics Data System (ADS)

Passemier, Damien; McKay, Matthew R.; Chen, Yang

2015-07-01

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked correlation), non-central Wishart with rank-one non-centrality, and a related class of non-central matrices. For a generic linear statistic, we derive simple and explicit CLT expressions as the matrix dimensions grow large. For all three ensembles under consideration, we find that the primary effect of the spike is to introduce an correction term to the asymptotic mean of the linear spectral statistic, which we characterize with simple formulas. The utility of our proposed framework is demonstrated through application to three different linear statistics problems: the classical likelihood ratio test for a population covariance, the capacity analysis of multi-antenna wireless communication systems with a line-of-sight transmission path, and a classical multiple sample significance testing problem.

Exact results for models of multichannel quantum nonadiabatic transitions

DOE PAGES

Sinitsyn, N. A.

2014-12-11

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicitmore » expressions for scattering probabilities in such systems.« less

Particle in a box in PT-symmetric quantum mechanics and an electromagnetic analog

NASA Astrophysics Data System (ADS)

Dasarathy, Anirudh; Isaacson, Joshua P.; Jones-Smith, Katherine; Tabachnik, Jason; Mathur, Harsh

2013-06-01

In PT-symmetric quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be Hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time reversal. Here we study the role of boundary conditions in PT-symmetric quantum mechanics by constructing a simple model that is the PT-symmetric analog of a particle in a box. The model has the usual particle-in-a-box Hamiltonian but boundary conditions that respect PT symmetry rather than Hermiticity. We find that for a broad class of PT-symmetric boundary conditions the model respects the condition of unbroken PT symmetry, namely, that the Hamiltonian and the symmetry operator PT have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is self-adjoint under the PT-symmetric inner product. Thus we obtain a simple soluble model that fulfills all the requirements of PT-symmetric quantum mechanics. In the second part of this paper we formulate a variational principle for PT-symmetric quantum mechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the PT-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a Breit-Wigner line shape in transmission and a Fano line shape in reflection; by contrast, in the corresponding Hermitian case the line shapes always have a Breit-Wigner form in both transmission and reflection.

Enhanced sensitivity at higher-order exceptional points

NASA Astrophysics Data System (ADS)

Hodaei, Hossein; Hassan, Absar U.; Wittek, Steffen; Garcia-Gracia, Hipolito; El-Ganainy, Ramy; Christodoulides, Demetrios N.; Khajavikhan, Mercedeh

2017-08-01

Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the environment. They correspond to points in parameter space at which the eigenvalues of the underlying system and the corresponding eigenvectors simultaneously coalesce. In optics, the abrupt nature of the phase transitions that are encountered around exceptional points has been shown to lead to many intriguing phenomena, such as loss-induced transparency, unidirectional invisibility, band merging, topological chirality and laser mode selectivity. Recently, it has been shown that the bifurcation properties of second-order non-Hermitian degeneracies can provide a means of enhancing the sensitivity (frequency shifts) of resonant optical structures to external perturbations. Of particular interest is the use of even higher-order exceptional points (greater than second order), which in principle could further amplify the effect of perturbations, leading to even greater sensitivity. Although a growing number of theoretical studies have been devoted to such higher-order degeneracies, their experimental demonstration in the optical domain has so far remained elusive. Here we report the observation of higher-order exceptional points in a coupled cavity arrangement—specifically, a ternary, parity-time-symmetric photonic laser molecule—with a carefully tailored gain-loss distribution. We study the system in the spectral domain and find that the frequency response associated with this system follows a cube-root dependence on induced perturbations in the refractive index. Our work paves the way for utilizing non-Hermitian degeneracies in fields including photonics, optomechanics, microwaves and atomic physics.

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.

Unimodular lattices in dimensions 14 and 15 over the Eisenstein integers

NASA Astrophysics Data System (ADS)

Abdukhalikov, Kanat; Scharlau, Rudolf

2009-03-01

All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in mathbb{Q}(sqrt{-3}) are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3.

On Polynomial Solutions of Linear Differential Equations with Polynomial Coefficients

ERIC Educational Resources Information Center

Si, Do Tan

1977-01-01

Demonstrates a method for solving linear differential equations with polynomial coefficients based on the fact that the operators z and D + d/dz are known to be Hermitian conjugates with respect to the Bargman and Louck-Galbraith scalar products. (MLH)

Wave-function functionals

NASA Astrophysics Data System (ADS)

Pan, Xiao-Yin; Slamet, Marlina; Sahni, Viraht

2010-04-01

We extend our prior work on the construction of variational wave functions ψ that are functionals of functions χ:ψ=ψ[χ] rather than simply being functions. In this manner, the space of variations is expanded over those of traditional variational wave functions. In this article we perform the constrained search over the functions χ chosen such that the functional ψ[χ] satisfies simultaneously the constraints of normalization and the exact expectation value of an arbitrary single- or two-particle Hermitian operator, while also leading to a rigorous upper bound to the energy. As such the wave function functional is accurate not only in the region of space in which the principal contributions to the energy arise but also in the other region of the space represented by the Hermitian operator. To demonstrate the efficacy of these ideas, we apply such a constrained search to the ground state of the negative ion of atomic hydrogen H-, the helium atom He, and its positive ions Li+ and Be2+. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W=∑irin,n=-2,-1,1,2, W=∑iδ(ri), W=-(1)/(2)∑i∇i2, and the two-particle operators W=∑nun,n=-2,-1,1,2, where u=|ri-rj|. Comparisons with the method of Lagrangian multipliers and of other constructions of wave-function functionals are made. Finally, we present further insights into the construction of wave-function functionals by studying a previously proposed construction of functionals ψ[χ] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schrödinger equation, there exist ψ[χ] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.

Work distributions for random sudden quantum quenches

NASA Astrophysics Data System (ADS)

Łobejko, Marcin; Łuczka, Jerzy; Talkner, Peter

2017-05-01

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.

An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach

DOE PAGES

Yu, Hua-Gen

2002-01-01

We present a full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. Moreover, the vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem ismore » solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. Ultimately, we made a comparison with previous results.« less

Matrix superpotentials

NASA Astrophysics Data System (ADS)

Nikitin, Anatoly G.; Karadzhov, Yuri

2011-07-01

We present a collection of matrix-valued shape invariant potentials which give rise to new exactly solvable problems of SUSY quantum mechanics. It includes all irreducible matrix superpotentials of the generic form W=kQ+\\frac{1}{k} R+P, where k is a variable parameter, Q is the unit matrix multiplied by a real-valued function of independent variable x, and P and R are the Hermitian matrices depending on x. In particular, we recover the Pron'ko-Stroganov 'matrix Coulomb potential' and all known scalar shape invariant potentials of SUSY quantum mechanics. In addition, five new shape invariant potentials are presented. Three of them admit a dual shape invariance, i.e. the related Hamiltonians can be factorized using two non-equivalent superpotentials. We find discrete spectrum and eigenvectors for the corresponding Schrödinger equations and prove that these eigenvectors are normalizable.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

An efficient solver for large structured eigenvalue problems in relativistic quantum chemistry

NASA Astrophysics Data System (ADS)

Shiozaki, Toru

2017-01-01

We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalisation of matrices of dimension N > 10, 000 is now routine on a single computer node. Such matrices appear frequently in relativistic quantum chemistry owing to the time-reversal symmetry. The implementation is based on a blocked version of the Paige-Van Loan algorithm, which allows us to use the Level 3 BLAS subroutines for most of the computations. Taking advantage of the symmetry, the program is faster by up to a factor of 2 than state-of-the-art implementations of complex Hermitian diagonalisation; diagonalising a 12, 800 × 12, 800 matrix took 42.8 (9.5) and 85.6 (12.6) minutes with 1 CPU core (16 CPU cores) using our symmetry-adapted solver and Intel Math Kernel Library's ZHEEV that is not structure-preserving, respectively. The source code is publicly available under the FreeBSD licence.

Low-energy effective field theory below the electroweak scale: operators and matching

NASA Astrophysics Data System (ADS)

Jenkins, Elizabeth E.; Manohar, Aneesh V.; Stoffer, Peter

2018-03-01

The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as Δ B = ±Δ L = ±1, Δ L = ±2, and Δ L = ±4 operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order 1 /Λ2 is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.

Enhanced response of non-Hermitian photonic systems near exceptional points

NASA Astrophysics Data System (ADS)

Sunada, Satoshi

2018-04-01

This paper theoretically and numerically studies the response characteristics of non-Hermitian resonant photonic systems operating near an exceptional point (EP), where two resonant eigenmodes coalesce. It is shown that a system near an EP can exhibit a non-Lorentzian frequency response, whose line shape and intensity strongly depend on the modal decay rate and coupling parameters for the input waves, unlike a normal Lorentzian response around a single resonance. In particular, it is shown that the peak intensity of the frequency response is inversely proportional to the fourth power of the modal decay rate and can be significantly enhanced with the aid of optical gain. The theoretical results are numerically verified by a full wave simulation of a microring cavity with gain. In addition, the effects of the nonlinear gain saturation and spontaneous emission are discussed. The response enhancement and its parametric dependence may be useful for designing and controlling the excitation of eigenmodes by external fields.

Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials.

PubMed

Ginzburg, Pavel; Rodríguez-Fortuño, Francisco J; Martínez, Alejandro; Zayats, Anatoly V

2012-12-12

The Hanle effect, one of the first manifestations of quantum theory introducing the concept of coherent superposition between pure states, plays a key role in numerous aspects of science varying from applicative spectroscopy to fundamental astrophysical investigations. Optical analogues of quantum effects help to achieve deeper understanding of quantum phenomena and, in turn, to develop cross-disciplinary approaches to realizations of new applications in photonics. Here we show that metallic nanostructures can be designed to exhibit a plasmonic analogue of the quantum Hanle effect and the associated polarization rotation. In the original Hanle effect, time-reversal symmetry is broken by a static magnetic field. We achieve this by introducing dissipative level crossing of localized surface plasmons due to nonuniform losses, designed using a non-Hermitian formulation of quantum mechanics. Such artificial plasmonic "atoms" have been shown to exhibit strong circular birefringence and circular dichroism which depends on the value of loss or gain in the metal-dielectric nanostructure.

Probing quantum correlation functions through energy-absorption interferometry

NASA Astrophysics Data System (ADS)

Withington, S.; Thomas, C. N.; Goldie, D. J.

2017-08-01

An interferometric technique is described for determining the spatial forms of the individual degrees of freedom through which a many-body system can absorb energy from its environment. The method separates out the spatial forms of the coherent excitations present at any single frequency; it is not necessary to sweep the frequency and then infer the spatial forms of possible excitations from resonant absorption features. The system under test is excited with two external sources, which create generalized forces, and the fringe in the total power dissipated is measured as the relative phase between the sources is varied. If the complex fringe visibility is measured for different pairs of source locations, the anti-Hermitian part of the complex-valued nonlocal correlation tensor can be determined, which can then be decomposed to give the natural dynamical modes of the system and their relative responsivities. If each source in the interferometer creates a different kind of force, the spatial forms of the individual excitations that are responsible for cross-correlated response can be found. The technique is related to holography, but measures the state of coherence to which the system is maximally sensitive. It can be applied across a wide range of wavelengths, in a variety of ways, to homogeneous media, thin films, patterned structures, and components such as sensors, detectors, and energy-harvesting absorbers.

Electrode configuration and signal subtraction technique for single polarity charge carrier sensing in ionization detectors

DOEpatents

Luke, Paul

1996-01-01

An ionization detector electrode and signal subtraction apparatus and method provides at least one first conductive trace formed onto the first surface of an ionization detector. The first surface opposes a second surface of the ionization detector. At least one second conductive trace is also formed on the first surface of the ionization detector in a substantially interlaced and symmetrical pattern with the at least one first conductive trace. Both of the traces are held at a voltage potential of a first polarity type. By forming the traces in a substantially interlaced and symmetric pattern, signals generated by a charge carrier are substantially of equal strength with respect to both of the traces. The only significant difference in measured signal strength occurs when the charge carrier moves to within close proximity of the traces and is received at the collecting trace. The measured signals are then subtracted and compared to quantitatively measure the magnitude of the charge and to determine the position at which the charge carrier originated within the ionization detector.

Electrode configuration and signal subtraction technique for single polarity charge carrier sensing in ionization detectors

DOEpatents

Luke, P.

1996-06-25

An ionization detector electrode and signal subtraction apparatus and method provide at least one first conductive trace formed onto the first surface of an ionization detector. The first surface opposes a second surface of the ionization detector. At least one second conductive trace is also formed on the first surface of the ionization detector in a substantially interlaced and symmetrical pattern with the at least one first conductive trace. Both of the traces are held at a voltage potential of a first polarity type. By forming the traces in a substantially interlaced and symmetric pattern, signals generated by a charge carrier are substantially of equal strength with respect to both of the traces. The only significant difference in measured signal strength occurs when the charge carrier moves to within close proximity of the traces and is received at the collecting trace. The measured signals are then subtracted and compared to quantitatively measure the magnitude of the charge and to determine the position at which the charge carrier originated within the ionization detector. 9 figs.

Conformally encapsulated multi-electrode arrays with seamless insulation

DOEpatents

Tabada, Phillipe J.; Shah, Kedar G.; Tolosa, Vanessa; Pannu, Satinderall S.; Tooker, Angela; Delima, Terri; Sheth, Heeral; Felix, Sarah

2016-11-22

Thin-film multi-electrode arrays (MEA) having one or more electrically conductive beams conformally encapsulated in a seamless block of electrically insulating material, and methods of fabricating such MEAs using reproducible, microfabrication processes. One or more electrically conductive traces are formed on scaffold material that is subsequently removed to suspend the traces over a substrate by support portions of the trace beam in contact with the substrate. By encapsulating the suspended traces, either individually or together, with a single continuous layer of an electrically insulating material, a seamless block of electrically insulating material is formed that conforms to the shape of the trace beam structure, including any trace backings which provide suspension support. Electrical contacts, electrodes, or leads of the traces are exposed from the encapsulated trace beam structure by removing the substrate.

Polar decomposition for attitude determination from vector observations

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.

1993-01-01

This work treats the problem of weighted least squares fitting of a 3D Euclidean-coordinate transformation matrix to a set of unit vectors measured in the reference and transformed coordinates. A closed-form analytic solution to the problem is re-derived. The fact that the solution is the closest orthogonal matrix to some matrix defined on the measured vectors and their weights is clearly demonstrated. Several known algorithms for computing the analytic closed form solution are considered. An algorithm is discussed which is based on the polar decomposition of matrices into the closest unitary matrix to the decomposed matrix and a Hermitian matrix. A somewhat longer improved algorithm is suggested too. A comparison of several algorithms is carried out using simulated data as well as real data from the Upper Atmosphere Research Satellite. The comparison is based on accuracy and time consumption. It is concluded that the algorithms based on polar decomposition yield a simple although somewhat less accurate solution. The precision of the latter algorithms increase with the number of the measured vectors and with the accuracy of their measurement.

Properties of the Bayesian Knowledge Tracing Model

ERIC Educational Resources Information Center

van de Sande, Brett

2013-01-01

Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model…

Trace conditioning in insects—keep the trace!

PubMed Central

Dylla, Kristina V.; Galili, Dana S.; Szyszka, Paul; Lüdke, Alja

2013-01-01

Trace conditioning is a form of associative learning that can be induced by presenting a conditioned stimulus (CS) and an unconditioned stimulus (US) following each other, but separated by a temporal gap. This gap distinguishes trace conditioning from classical delay conditioning, where the CS and US overlap. To bridge the temporal gap between both stimuli and to form an association between CS and US in trace conditioning, the brain must keep a neural representation of the CS after its termination—a stimulus trace. Behavioral and physiological studies on trace and delay conditioning revealed similarities between the two forms of learning, like similar memory decay and similar odor identity perception in invertebrates. On the other hand differences were reported also, like the requirement of distinct brain structures in vertebrates or disparities in molecular mechanisms in both vertebrates and invertebrates. For example, in commonly used vertebrate conditioning paradigms the hippocampus is necessary for trace but not for delay conditioning, and Drosophila delay conditioning requires the Rutabaga adenylyl cyclase (Rut-AC), which is dispensable in trace conditioning. It is still unknown how the brain encodes CS traces and how they are associated with a US in trace conditioning. Insects serve as powerful models to address the mechanisms underlying trace conditioning, due to their simple brain anatomy, behavioral accessibility and established methods of genetic interference. In this review we summarize the recent progress in insect trace conditioning on the behavioral and physiological level and emphasize similarities and differences compared to delay conditioning. Moreover, we examine proposed molecular and computational models and reassess different experimental approaches used for trace conditioning. PMID:23986710

Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems

NASA Astrophysics Data System (ADS)

Link, Valentin; Strunz, Walter T.

2017-11-01

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments. The Schrödinger equation in the coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operators. In this picture the reduced state of the system can be obtained as a stochastic average over pure state trajectories, for any temperature of the bath. The corresponding non-Markovian stochastic Schrödinger equations include a memory integral over the past states. In the case of harmonic environments and linear coupling the approach gives a new form of the established non-Markovian quantum state diffusion stochastic Schrödinger equation without functional derivatives. Utilizing spin coherent states, the evolution equation for spin environments resembles the bosonic case with, however, a non-Gaussian average for the reduced density operator.

Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain.

PubMed

Hickey, James M; Flindt, Christian; Garrahan, Juan P

2013-07-01

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

Generalized conformal realizations of Kac-Moody algebras

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

Palmkvist, Jakob

2009-01-15

We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our generalization utilizes a new relation between different generalized Jordan triple systems, together with their known connections to Jordan and Lie algebras. Applied to the Jordan algebra of Hermitian 3x3 matrices over the division algebras R, C, H, O, the construction gives the exceptional Lie algebras f{sub 4}, e{sub 6}, e{sub 7}, e{sub 8} for n=2. Moreover, we obtain their infinite-dimensional extensions for n{>=}3. In the casemore » of 2x2 matrices, the resulting Lie algebras are of the form so(p+n,q+n) and the concomitant nonlinear realization generalizes the conformal transformations in a spacetime of signature (p,q)« less

Generalized Ince Gaussian beams

NASA Astrophysics Data System (ADS)

Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

2006-08-01

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

PubMed

Chou, Chia-Chun; Kouri, Donald J

2013-04-25

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

DTIC Science & Technology

2012-03-22

with performance profiles, Math. Program., 91 (2002), pp. 201–213. [6] P. DRINEAS, R. KANNAN, AND M. W. MAHONEY , Fast Monte Carlo algorithms for matrices...computing invariant subspaces of non-Hermitian matri- ces, Numer. Math., 25 ( 1975 /76), pp. 123–136. [25] , Matrix algorithms Vol. II: Eigensystems

Efficient Numerical Diagonalization of Hermitian 3 × 3 Matrices

NASA Astrophysics Data System (ADS)

Kopp, Joachim

A very common problem in science is the numerical diagonalization of symmetric or hermitian 3 × 3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with an alytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. The analytical algorithm outperforms the others by more than a factor of 2, but becomes inaccurate or may even fail completely if the matrix entries differ greatly in magnitude. This can mostly be circumvented by using a hybrid method, which falls back to QL if conditions are such that the analytical calculation might become too inaccurate. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from .

Linear response theory for a pseudo-Hermitian system-reservoir interaction

NASA Astrophysics Data System (ADS)

Duarte, O. S.; Luiz, F. S.; Moussa, M. H. Y.

2018-03-01

We present here an extension of the Caldeira-Leggett linear response model considering a pseudo-Hermitian PT} -symmetric system-reservoir interaction. Our generalized Feynman-Vernon functional, derived from the PT} -symmetric coupling, accounts for two influence channels: a velocity-dependent one, which can act in reverse, providing energy to the system instead of draining it as usual, and an acceleration-dependent drain, analogue to the radiation-emission process. Therefore, an adequate choice of the Hamiltonian's parameters may allow the system to extract energy from the reservoir even at absolute zero for a period that may be much longer than the characteristic relaxation time. After this energy supply, the system is driven to a steady state whose energy is necessarily higher than the thermodynamic equilibrium energy due to the velocity-dependent pump. This heating mechanism of the system is more pronounced the more distant from the hermiticity is its coupling with the reservoir. An analytical derivation of the high-temperature master equation is provided helping us to better understand the whole scenario and to compute the associated relaxation and decoherence rates.

Making almost commuting matrices commute

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

Hastings, Matthew B

Suppose two Hermitian matrices A, B almost commute ({parallel}[A,B]{parallel} {<=} {delta}). Are they close to a commuting pair of Hermitian matrices, A', B', with {parallel}A-A'{parallel},{parallel}B-B'{parallel} {<=} {epsilon}? A theorem of H. Lin shows that this is uniformly true, in that for every {epsilon} > 0 there exists a {delta} > 0, independent of the size N of the matrices, for which almost commuting implies being close to a commuting pair. However, this theorem does not specifiy how {delta} depends on {epsilon}. We give uniform bounds relating {delta} and {epsilon}. The proof is constructive, giving an explicit algorithm to construct A'more » and B'. We provide tighter bounds in the case of block tridiagonal and tridiagnonal matrices. Within the context of quantum measurement, this implies an algorithm to construct a basis in which we can make a projective measurement that approximately measures two approximately commuting operators simultaneously. Finally, we comment briefly on the case of approximately measuring three or more approximately commuting operators using POVMs (positive operator-valued measures) instead of projective measurements.« less

Quantum control and the challenge of non-Hermitian model-building

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2015-06-01

In a way inspired by the brief 2002 note “The challenge of nonhermitian structures in physics” by Ramirez and Mielnik (with the text most easily available via arXiv:quant- ph/0211048) the situation in the theory is briefly summarized here as it looks twelve years later. Our text has three parts. In the first one we briefly mention the pre-history (dating back to the Freeman Dyson's proposal of the non-Hermitian-Hamiltonian method in 1956 and to its subsequent successful “interacting boson model” applications in nuclear physics) and, first of all, the amazing recent progress reached, in the stationary case, using, in essence, an inversion of the Dyson's approach. The impact on the latter idea upon abstract quantum physics is sampled, first of all, by the reference to papers by Bender et al. (who made the non-Hermitian model-building popular under the nickname of parity-times-time-reflection- symmetric alias PT-symmetric quantum mechanics) and by Mostafazadeh (who reinterpreted PT-symmetry as P-pseudo-Hermiticity). In the second part of our review the emphasis is shifted to the newest, non-stationary upgrade of the formalism which we proposed in the year 2009 and which is characterized by the simultaneous participation of a triplet of Hilbert spaces H in the representation of a single quantum system. In the third part of the review we finally emphasize that the majority of applications of our three-Hilbert-space (THS) recipe is still ahead of us because the enhancement of the flexibility is necessarily accompanied by an enhancement of the technical difficulties. An escape out of the technical trap is proposed to be sought in a restriction of attention to quantum models living in finite-dimensional Hilbert spaces H. As long as the use of such spaces is so typical for the quantum-control considerations, we conclude with conjecture that the THS formalism should start searching for implementations in the field of quantum control.

Optical reflection from planetary surfaces as an operator-eigenvalue problem

USGS Publications Warehouse

Wildey, R.L.

1986-01-01

The understanding of quantum mechanical phenomena has come to rely heavily on theory framed in terms of operators and their eigenvalue equations. This paper investigates the utility of that technique as related to the reciprocity principle in diffuse reflection. The reciprocity operator is shown to be unitary and Hermitian; hence, its eigenvectors form a complete orthonormal basis. The relevant eigenvalue is found to be infinitely degenerate. A superposition of the eigenfunctions found from solution by separation of variables is inadequate to form a general solution that can be fitted to a one-dimensional boundary condition, because the difficulty of resolving the reciprocity operator into a superposition of independent one-dimensional operators has yet to be overcome. A particular lunar application in the form of a failed prediction of limb-darkening of the full Moon from brightness versus phase illustrates this problem. A general solution is derived which fully exploits the determinative powers of the reciprocity operator as an unresolved two-dimensional operator. However, a solution based on a sum of one-dimensional operators, if possible, would be much more powerful. A close association is found between the reciprocity operator and the particle-exchange operator of quantum mechanics, which may indicate the direction for further successful exploitation of the approach based on the operational calculus. ?? 1986 D. Reidel Publishing Company.

Concentrations and chemical forms of trace metals in coastal seawater on coral reef and their seasonal variation

NASA Astrophysics Data System (ADS)

Ganaha, S.; ITOH, A.

2011-12-01

Coastal seawater on coral reef near Okinawa island in Japan, which is in oligotrophic condition, has a diverse and unique ecosystem. It is possible that nutritive sals and trace metals, classified into nutrient type, are effectively supplied to marine phytoplankton and zooxanthellae from seawater. However, the concentrations and chemical forms of trace metals in coastal seawater on coral reef have been scarcely reported so far. In the present study, the characteristics of the concentrations and chemical forms of trace metals in such a seawater were investigated with seasonal variation by analyzing the coastal seawater at every month, after an analytical method for a simple chemical speciation including on-site treatment was established. The analytical method using a chelating resin and a disposable syringe was employed for de-salt and preconcentration of trace metals in costal seawater. After that, trace metals in the concentrated solution were measured by ICP-MS. Three types of chemical forms of an ionic, a dissolved, and an acid-soluble were separated without any treatment, by filtering with membrane filter of 0.45 μm, and by filtering after adding nitric acid, respectively. Then, a monitoring investigation of the coastal seawater on coral reef, located at Sesoko island near the northern part of Okinawa island, was carried out once at every month from Sep. 2010 to Aug. 2011. As a result, 10 elements in the dissolved form in each sample could be determined. The average concentrations for all samples from Sep. 2010 to Apr. 2011 were as follows: Mo:10.7 ppb, U:3.2 ppb, V:1.5 ppb, Mn:0.17 ppb, Ni:0.16 ppb, Zn:0.13 ppb, Cu:0.070 ppb, Pb:0.024 ppb, Co:0.0022 ppb, Cd:0.0016ppb. The concentrations for most trace metals were almost close to ones in open surface seawater of the Pacific ocean. For the acid-soluble form, the concentrations of V, Mo, and U were almost same with those of the dissolved form, and ones of Mn, Co, Ni, Cu, and Cd were slightly larger than ones in the dissolved form, while ones in Zn and Pb were 3.1- and 2.5-fold larger. These results suggest that a part of trace metals in the nutrient type exists as biogenic particulate matters. For the ionic form, the concentration of Cu was 3-fold smaller than one in the dissolved form. It is considered from the result that a part of Cu in the dissolved form exists not only as the ionic form but also as the colloids and organic complexes. The seasonal variation for each chemical form is now being investigated.

Spectral singularities and Bragg scattering in complex crystals

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

Longhi, S.

2010-02-15

Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a PT-symmetric complex crystal.

Solving the Integral of Quadratic Forms of Covariance Matrices for Applications in Polarimetric Radar Imagery

NASA Astrophysics Data System (ADS)

Marino, Armando; Hajnsek, Irena

2015-04-01

In this work, the solution of quadratic forms with special application to polarimetric and interferometric covariance matrices is investigated. An analytical solution for the integral of a single quadratic form is derived. Additionally, the integral of the Pol-InSAR coherence (expressed as combination of quadratic forms) is investigated. An approximation for such integral is proposed and defined as Trace coherence. Such approximation is tested on real data to verify that the error is acceptable. The trace coherence can be used for tackle problems related to change detection. Moreover, the use of the Trace coherence in model inversion (as for the RVoG three stage inversion) will be investigated in the future.

Kirchhoff's rule for quantum wires

NASA Astrophysics Data System (ADS)

Kostrykin, V.; Schrader, R.

1999-01-01

We formulate and discuss one-particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with n channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy E>0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low-energy behaviour of one theory gives the high-energy behaviour of the transformed theory. Finally, we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs use only known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitian symplectic forms.

TraceContract: A Scala DSL for Trace Analysis

NASA Technical Reports Server (NTRS)

Barringer, Howard; Havelund, Klaus

2011-01-01

In this paper we describe TRACECONTRACT, an API for trace analysis, implemented in the SCALA programming language. We argue that for certain forms of trace analysis the best weapon is a high level programming language augmented with constructs for temporal reasoning. A trace is a sequence of events, which may for example be generated by a running program, instrumented appropriately to generate events. The API supports writing properties in a notation that combines an advanced form of data parameterized state machines with temporal logic. The implementation utilizes SCALA's support for defining internal Domain Specific Languages (DSLs). Furthermore SCALA's combination of object oriented and functional programming features, including partial functions and pattern matching, makes it an ideal host language for such an API.

The Antarctic cold desert and the search for traces of life on Mars.

PubMed

Friedmann, E I

1986-01-01

The cryptoendolithic microorganisms that live inside rocks in the frigid Ross Desert of Antarctica can serve as a terrestrial model for what may have happened to life forms on Mars when the planet became dry and cold. Trace fossils of microbial rock colonization exist in Antarctica, and similar structures could have formed on Mars. In some respects, such trace fossils could be an easier target for life-detection systems than fossils of cellular structures.

The Antarctic cold desert and the search for traces of life on Mars

NASA Technical Reports Server (NTRS)

Friedmann, E. I.

1986-01-01

The cryptoendolithic microoganisms that live inside rocks in the frigid Ross Desert of Antarctica can serve as a terrestrial model for what may have happened to life forms on Mars when the planet became dry and cold. Trace fossils of microbial rock colonization exist in Antarctica, and similar structures could have formed on Mars. In some respects, such trace fossils could be an easier target for life-detection systems than fossils of cellular structures.

Effect of supplemental trace mineral level and form on peripubertal bulls

USDA-ARS?s Scientific Manuscript database

The objectives were to determine if different supplemental trace mineral levels and /or forms (sulfate and metal amino acid complexes) influence age at puberty, semen quality, endocrine status and scrotal circumference in peripubertal bulls. Fifty crossbred, peripubertal bulls were blocked by age (...

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Brody, Dorje C.

2018-04-01

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

Harwell Subroutine Library. A Catalogue of Subroutines (1973),

DTIC Science & Technology

1973-07-01

up the equations AT Ax = ATb. There may be more than one right-hand size. Remark: If the solution is required see MAO9A. Versions: MAOA ; MAOBAD. Calls...Hermitian MEO8A source decks-modification of OEOIA real gene .’al to Hessenberg sparsity pattern TDO2A MC08A, MCI4A spherical co-ordinates GAOIA real

Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator

NASA Astrophysics Data System (ADS)

Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.

2017-10-01

In position dependent mass (PDM) problems, the quantum dynamics of the associated systems have been understood well in the literature for particular orderings. However, no efforts seem to have been made to solve such PDM problems for general orderings to obtain a global picture. In this connection, we here consider the general ordered quantum Hamiltonian of an interesting position dependent mass problem, namely, the Mathews-Lakshmanan oscillator, and try to solve the quantum problem for all possible orderings including Hermitian and non-Hermitian ones. The other interesting point in our study is that for all possible orderings, although the Schrödinger equation of this Mathews-Lakshmanan oscillator is uniquely reduced to the associated Legendre differential equation, their eigenfunctions cannot be represented in terms of the associated Legendre polynomials with integral degree and order. Rather the eigenfunctions are represented in terms of associated Legendre polynomials with non-integral degree and order. We here explore such polynomials and represent the discrete and continuum states of the system. We also exploit the connection between associated Legendre polynomials with non-integral degree with other orthogonal polynomials such as Jacobi and Gegenbauer polynomials.

Hermitian symmetry free optical-single-carrier frequency division multiple access for visible light communication

NASA Astrophysics Data System (ADS)

Azim, Ali W.; Le Guennec, Yannis; Maury, Ghislaine

2018-05-01

Optical-orthogonal frequency division multiplexing (O-OFDM) is an effective scheme for visible light communications (VLC), offering a candid extension to multiple access (MA) scenarios, i.e., O-OFDMA. However, O-OFDMA exhibits high peak-to-average power ratio (PAPR), which exacerbates the non-linear distortions from the light emitting diode (LED). To overcome high PAPR while sustaining MA, optical-single-carrier frequency-division multiple access (O-SCFDMA) is used. For both O-OFDMA and O-SCFDMA, Hermitian symmetry (HS) constraint is imposed in frequency-domain (FD) to obtain a real-valued time-domain (TD) signal for intensity modulation-direct detection (IM-DD) implementation of VLC. Howbeit, HS results in an increase of PAPR for O-SCFDMA. In this regard, we propose HS free (HSF) O-SCFDMA (HSFO-SCFDMA). We compare HSFO-SCFDMA with several approaches in key parameters, such as, bit error rate (BER), optical power penalty, PAPR, quantization, electrical power efficiency and system complexity. BER performance and optical power penalty is evaluated considering multipath VLC channel and taking into account the bandwidth limitation of LED in combination with its optimized driver. It is illustrated that HSFO-SCFDMA outperforms other alternatives.

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.

PubMed

Chen, Yong; Yan, Zhenya

2016-03-22

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

PubMed Central

Chen, Yong; Yan, Zhenya

2016-01-01

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543

Supersymmetrical bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states

PubMed Central

Afzal, Muhammad Imran; Lee, Yong Tak

2016-01-01

Von Neumann and Wigner theorized the bounding and anti-crossing of eigenstates. Experiments have demonstrated that owing to anti-crossing and similar radiation rates, the graphene-like resonance of inhomogeneously strained photonic eigenstates can generate a pseudomagnetic field, bandgaps and Landau levels, whereas exponential or dissimilar rates induce non-Hermicity. Here, we experimentally demonstrate higher-order supersymmetry and quantum phase transitions by resonance between similar one-dimensional lattices. The lattices consisted of inhomogeneous strain-like phases of triangular solitons. The resonance created two-dimensional, inhomogeneously deformed photonic graphene. All parent eigenstates were annihilated. Eigenstates of mildly strained solitons were annihilated at similar rates through one tail and generated Hermitian bounded eigenstates. The strongly strained solitons with positive phase defects were annihilated at exponential rates through one tail, which bounded eigenstates through non-Hermitianally generated exceptional points. Supersymmetry was evident, with preservation of the shapes and relative phase differences of the parent solitons. Localizations of energies generated from annihilations of mildly and strongly strained soliton eigenstates were responsible for geometrical (Berry) and topological phase transitions, respectively. Both contributed to generating a quantum Zeno phase, whereas only strong twists generated topological (Anderson) localization. Anti-bunching-like condensation was also observed. PMID:27966596

Computing eigenfunctions and eigenvalues of boundary-value problems with the orthogonal spectral renormalization method

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Musslimani, Ziad H.; Schwarz, Lukas; Wunner, Günter

2018-03-01

The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian PT -symmetric models.

Operators up to dimension seven in standard model effective field theory extended with sterile neutrinos

NASA Astrophysics Data System (ADS)

Liao, Yi; Ma, Xiao-Dong

2017-07-01

We revisit the effective field theory of the standard model that is extended with sterile neutrinos, N . We examine the basis of complete and independent effective operators involving N up to mass dimension seven (dim-7). By employing equations of motion, integration by parts, and Fierz and group identities, we construct relations among operators that were considered independent in the previous literature, and we find 7 redundant operators at dim-6, as well as 16 redundant operators and two new operators at dim-7. The correct numbers of operators involving N are, without counting Hermitian conjugates, 16 (L ∩B )+1 (L ∩B )+2 (L ∩ B) at dim-6 and 47 (L ∩B )+5 (L ∩ B) at dim-7. Here L /B (L/B) stands for lepton/baryon number conservation (violation). We verify our counting by the Hilbert series approach for nf generations of the standard model fermions and sterile neutrinos. When operators involving different flavors of fermions are counted separately and their Hermitian conjugates are included, we find there are 29 (1614) and 80 (4206) operators involving sterile neutrinos at dim-6 and dim-7, respectively, for nf=1 (3).

The boomerang effect in electron-hydrogen molecule scattering as determined by time-dependent calculations

NASA Astrophysics Data System (ADS)

Ben-Asher, Anael; Moiseyev, Nimrod

2017-05-01

The appearance of oscillations in the energy-dependent cross sections of the vibrational excitation ν =0 →ν ≥3 of the hydrogen molecule in its electronic ground state as predicted by Mündel, Berman, and Domcke [Phys. Rev. A 32, 181 (1985)] was confirmed in the electron scattering experiments by Allan [J. Phys. B: At. Mol. Phys. 18, L451 (1985)]. These unusual structures were obtained in spite of the extremely short lifetime of H2- in its ro-vibrational states. Based on the standard (Hermitian) time-independent scattering calculations, Horáček et al. [Phys. Rev. A 73, 022701 (2006)] associated these oscillations with the boomerang effect. Here, we show the boomerang effect as developed in time, based on our time-dependent nuclear wavepacket (WP) calculations. The nuclear WP dynamics of H2- is determined using the non-Hermitian quantum mechanics (NH-QM) which enables the use of the Born-Oppenheimer approximation with complex potential energy surfaces. This NH-QM approach, which enables us the association of the nuclear WP dynamics as obtained from the complex potential energy curve of H2- with the evolution of cross section in time, can enlighten the dynamics in other scattering experiments.

The boomerang effect in electron-hydrogen molecule scattering as determined by time-dependent calculations.

PubMed

Ben-Asher, Anael; Moiseyev, Nimrod

2017-05-28

The appearance of oscillations in the energy-dependent cross sections of the vibrational excitation ν=0→ν≥3 of the hydrogen molecule in its electronic ground state as predicted by Mündel, Berman, and Domcke [Phys. Rev. A 32, 181 (1985)] was confirmed in the electron scattering experiments by Allan [J. Phys. B: At. Mol. Phys. 18, L451 (1985)]. These unusual structures were obtained in spite of the extremely short lifetime of H 2 - in its ro-vibrational states. Based on the standard (Hermitian) time-independent scattering calculations, Horáček et al. [Phys. Rev. A 73, 022701 (2006)] associated these oscillations with the boomerang effect. Here, we show the boomerang effect as developed in time, based on our time-dependent nuclear wavepacket (WP) calculations. The nuclear WP dynamics of H 2 - is determined using the non-Hermitian quantum mechanics (NH-QM) which enables the use of the Born-Oppenheimer approximation with complex potential energy surfaces. This NH-QM approach, which enables us the association of the nuclear WP dynamics as obtained from the complex potential energy curve of H 2 - with the evolution of cross section in time, can enlighten the dynamics in other scattering experiments.

Quadratic squeezing: An overview

NASA Technical Reports Server (NTRS)

Hillery, M.; Yu, D.; Bergou, J.

1992-01-01

The amplitude of the electric field of a mode of the electromagnetic field is not a fixed quantity: there are always quantum mechanical fluctuations. The amplitude, having both a magnitude and a phase, is a complex number and is described by the mode annihilation operator a. It is also possible to characterize the amplitude by its real and imaginary parts which correspond to the Hermitian and anti-Hermitian parts of a, X sub 1 = 1/2(a(sup +) + a) and X sub 2 = i/2(a(sup +) - a), respectively. These operators do not commute and, as a result, obey the uncertainty relation (h = 1) delta X sub 1(delta X sub 2) greater than or = 1/4. From this relation we see that the amplitude fluctuates within an 'error box' in the complex plane whose area is at least 1/4. Coherent states, among them the vacuum state, are minimum uncertainty states with delta X sub 1 = delta X sub 2 = 1/2. A squeezed state, squeezed in the X sub 1 direction, has the property that delta X sub 1 is less than 1/2. A squeezed state need not be a minimum uncertainty state, but those that are can be obtained by applying the squeeze operator.

Semiblind channel estimation for MIMO-OFDM systems

NASA Astrophysics Data System (ADS)

Chen, Yi-Sheng; Song, Jyu-Han

2012-12-01

This article proposes a semiblind channel estimation method for multiple-input multiple-output orthogonal frequency-division multiplexing systems based on circular precoding. Relying on the precoding scheme at the transmitters, the autocorrelation matrix of the received data induces a structure relating the outer product of the channel frequency response matrix and precoding coefficients. This structure makes it possible to extract information about channel product matrices, which can be used to form a Hermitian matrix whose positive eigenvalues and corresponding eigenvectors yield the channel impulse response matrix. This article also tests the resistance of the precoding design to finite-sample estimation errors, and explores the effects of the precoding scheme on channel equalization by performing pairwise error probability analysis. The proposed method is immune to channel zero locations, and is reasonably robust to channel order overestimation. The proposed method is applicable to the scenarios in which the number of transmitters exceeds that of the receivers. Simulation results demonstrate the performance of the proposed method and compare it with some existing methods.

Spectra, current flow, and wave-function morphology in a model PT -symmetric quantum dot with external interactions

NASA Astrophysics Data System (ADS)

Tellander, Felix; Berggren, Karl-Fredrik

2017-04-01

In this paper we use numerical simulations to study a two-dimensional (2D) quantum dot (cavity) with two leads for passing currents (electrons, photons, etc.) through the system. By introducing an imaginary potential in each lead the system is made symmetric under parity-time inversion (PT symmetric). This system is experimentally realizable in the form of, e.g., quantum dots in low-dimensional semiconductors, optical and electromagnetic cavities, and other classical wave analogs. The computational model introduced here for studying spectra, exceptional points (EPs), wave-function symmetries and morphology, and current flow includes thousands of interacting states. This supplements previous analytic studies of few interacting states by providing more detail and higher resolution. The Hamiltonian describing the system is non-Hermitian; thus, the eigenvalues are, in general, complex. The structure of the wave functions and probability current densities are studied in detail at and in between EPs. The statistics for EPs is evaluated, and reasons for a gradual dynamical crossover are identified.

The product form for path integrals on curved manifolds

NASA Astrophysics Data System (ADS)

Grosche, C.

1988-03-01

A general and simple framework for treating path integrals on curved manifolds is presented. The crucial point will be a product ansatz for the metric tensor and the quantum hamiltonian, i.e. we shall write g αβ = h αγh βγ and H = (1/2m)h αγp αp βh βγ + V + ΔV , respectively, a prescription which we shall call “product form” definition. The p α are hermitian momenta and Δ V is a well-defined quantum correction. We shall show that this ansatz, which looks quite special, is in fact - under reasonable assumptions in quantum mechanics - a very general one. We shall derive the lagrangian path integral in the “product form” definition and shall also prove that the Schro¨dinger equation can be derived from the corresponding short-time kernel. We shall discuss briefly an application of this prescription to the problem of free quantum motion on the Poincare´upper half-plane.

Three dimensional ray tracing of the Jovian magnetosphere in the low frequency range

NASA Technical Reports Server (NTRS)

Menietti, J. D.

1984-01-01

Ray tracing studies of Jovian low frequency emissions were studied. A comprehensive three-dimensional ray tracing computer code for examination of model Jovian decametric (DAM) emission was developed. The improvements to the computer code are outlined and described. The results of the ray tracings of Jovian emissions will be presented in summary form.

Hawking radiation and classical tunneling: A ray phase space approach

NASA Astrophysics Data System (ADS)

Tracy, E. R.; Zhigunov, D.

2016-01-01

Acoustic waves in fluids undergoing the transition from sub- to supersonic flow satisfy governing equations similar to those for light waves in the immediate vicinity of a black hole event horizon. This acoustic analogy has been used by Unruh and others as a conceptual model for "Hawking radiation." Here, we use variational methods, originally introduced by Brizard for the study of linearized MHD, and ray phase space methods, to analyze linearized acoustics in the presence of background flows. The variational formulation endows the evolution equations with natural Hermitian and symplectic structures that prove useful for later analysis. We derive a 2 × 2 normal form governing the wave evolution in the vicinity of the "event horizon." This shows that the acoustic model can be reduced locally (in ray phase space) to a standard (scalar) tunneling process weakly coupled to a unidirectional non-dispersive wave (the "incoming wave"). Given the normal form, the Hawking "thermal spectrum" can be derived by invoking standard tunneling theory, but only by ignoring the coupling to the incoming wave. Deriving the normal form requires a novel extension of the modular ray-based theory used previously to study tunneling and mode conversion in plasmas. We also discuss how ray phase space methods can be used to change representation, which brings the problem into a form where the wave functions are less singular than in the usual formulation, a fact that might prove useful in numerical studies.

Thin Lens Ray Tracing.

ERIC Educational Resources Information Center

Gatland, Ian R.

2002-01-01

Proposes a ray tracing approach to thin lens analysis based on a vector form of Snell's law for paraxial rays as an alternative to the usual approach in introductory physics courses. The ray tracing approach accommodates skew rays and thus provides a complete analysis. (Author/KHR)

Can We Trace "Arbitrary" Rays to Locate an Image Formed by a Thin Lens?

ERIC Educational Resources Information Center

Suppapittayaporn, Decha; Panijpan, Bhinyo; Emarat, Narumon

2010-01-01

After learning how to trace the principal rays [Fig. 1(i)] through a thin lens in order to form the image in the conventional way, students sometimes ask whether it is possible to use other rays emanating from the object to form exactly the same image--for example, the two arbitrary rays shown in Fig. 1(ii). The answer is a definite yes, and this…

Deformation quantization with separation of variables of an endomorphism bundle

NASA Astrophysics Data System (ADS)

Karabegov, Alexander

2014-01-01

Given a holomorphic Hermitian vector bundle E and a star-product with separation of variables on a pseudo-Kähler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle E∗ which also has the appropriately generalized property of separation of variables. For this star product we prove a generalization of Gammelgaard's graph-theoretic formula.

Two Classes of New Optimal Asymmetric Quantum Codes

NASA Astrophysics Data System (ADS)

Chen, Xiaojing; Zhu, Shixin; Kai, Xiaoshan

2018-03-01

Let q be an even prime power and ω be a primitive element of F_{q2}. By analyzing the structure of cyclotomic cosets, we determine a sufficient condition for ω q- 1-constacyclic codes over F_{q2} to be Hermitian dual-containing codes. By the CSS construction, two classes of new optimal AQECCs are obtained according to the Singleton bound for AQECCs.

Linearizable quantum supersymmetric σ models

NASA Astrophysics Data System (ADS)

Haba, Z.

1988-07-01

Euclidean quantization of superfields with values in a Hermitian manifold and defined on a super-Riemann surface is discussed. It is shown that stochastic differential equations relating an interacting σ superfield to the free one become linear if the field takes values in a generalized Poincaré upper half-plane. A renormalized perturbative solution is obtained. Fields with values in a Riemann surface are discussed in brief.

Uniqueness and characterization theorems for generalized entropies

NASA Astrophysics Data System (ADS)

Enciso, Alberto; Tempesta, Piergiulio

2017-12-01

The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the only composable generalized entropy in trace form is the Tsallis one-parameter family (which contains Boltzmann-Gibbs as a particular case). This result leads to the use of generalized entropies that are not of trace form, such as Rényi’s entropy, in the study of complex systems. In this direction, we also present a characterization theorem for a large class of composable non-trace-form entropy functions with features akin to those of Rényi’s entropy.

Seismic transmission operator reciprocity - II: impedance-operator symmetry via elastic lateral modes

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2015-08-01

The properties of the overburden transmission response are of particular interest for the analysis of reflectivity illumination or blurring in seismic depth imaging. The first step to showing a transmission-operator reciprocity property is to identify the symmetry of the so-called displacement-to-traction operators. The latter are analogous to Dirichlet-to-Neumann operators and they may also be called impedance operators. Their symmetry is deduced here after development of a formal spectral or modal theory of lateral wavefunctions in a laterally heterogeneous generally anisotropic elastic medium. The elastic lateral modes are displacement-traction 6-vectors and they are built from two auxiliary 3-vector lateral-mode bases. These auxiliary modes arise from Hermitian and anti-Hermitian operators, so they have familiar properties such as orthogonality. There is no assumption of down/up symmetry of the elasticity tensor, but basic assumptions are made about the existence and completeness of the elastic modes. A point-symmetry property appears and plays a central role. The 6-vector elastic modes have a symplectic orthogonality property, which facilitates the development of modal expansions for 6-vector functions of the lateral coordinates when completeness is assumed. While the elastic modal theory is consistent with the laterally homogeneous case, numerical work would provide confidence that it is correct in general. An appendix contains an introductory overview of acoustic lateral modes that were studied by other authors, given from the perspective of this new work. A distinction is drawn between unit normalization of scalar auxiliary modes and a separate energy-flux normalization of 2-vector acoustic modes. Neither is crucial to the form of acoustic pressure-to-velocity or impedance operators. This statement carries over to the elastic case for the 3-vector auxiliary- and 6-vector elastic-mode normalizations. The modal theory is used to construct the kernel of the elastic displacement-to-traction or impedance operator. Symmetry properties of this operator are then deduced, which is the main goal of this paper. The implications of elastic impedance-operator symmetry and the symplectic property for the transmission and reflection responses of finite regions are described in a companion paper.

TRACES: An Economic Model That Works.

ERIC Educational Resources Information Center

Libby, Richard M.

The Training, Research, and Assistance Cooperative Extension Service (TRACES) was formed to provide a central source of technical and training resources, knowledge, and avenues of government funding for the benefit of businesses and small to mid-sized industries in southeastern Ohio. The 16 organizations involved in TRACES are educational…

Distributed trace using central performance counter memory

DOEpatents

Satterfield, David L; Sexton, James C

2013-10-22

A plurality of processing cores, are central storage unit having at least memory connected in a daisy chain manner, forming a daisy chain ring layout on an integrated chip. At least one of the plurality of processing cores places trace data on the daisy chain connection for transmitting the trace data to the central storage unit, and the central storage unit detects the trace data and stores the trace data in the memory co-located in with the central storage unit.

Distributed trace using central performance counter memory

DOEpatents

Satterfield, David L.; Sexton, James C.

2013-01-22

A plurality of processing cores, are central storage unit having at least memory connected in a daisy chain manner, forming a daisy chain ring layout on an integrated chip. At least one of the plurality of processing cores places trace data on the daisy chain connection for transmitting the trace data to the central storage unit, and the central storage unit detects the trace data and stores the trace data in the memory co-located in with the central storage unit.

Research on Pin Tumbler Locks and the Characteristics of Surface Traces Formed by Unlocking Guns

NASA Astrophysics Data System (ADS)

Yi, Gao; Yifeng, Jin; Yanping, Bai; Hongcheng, Mei; Zhen, Xu

2018-02-01

In this paper, taking the structure of the pin tumbler locks and the principle of opening and closing locks as breakthrough point, we have studied the machining traces of pin tumbler components and trace characters of pin surface during normal operating. At the same time, taking the unlocking gun as an example, the paper analyzes the unlocking technology and the formation of traces, and summarizes the changing rules of the surface traces of elastic bead locks by comparing the positions and the characteristics of the traces, which provides technical support for the future study of traces of pin tumbler locks.

A Rotor Tip Vortex Tracing Algorithm for Image Post-Processing

NASA Technical Reports Server (NTRS)

Overmeyer, Austin D.

2015-01-01

A neurite tracing algorithm, originally developed for medical image processing, was used to trace the location of the rotor tip vortex in density gradient flow visualization images. The tracing algorithm was applied to several representative test images to form case studies. The accuracy of the tracing algorithm was compared to two current methods including a manual point and click method and a cross-correlation template method. It is shown that the neurite tracing algorithm can reduce the post-processing time to trace the vortex by a factor of 10 to 15 without compromising the accuracy of the tip vortex location compared to other methods presented in literature.

Minimal Krylov Subspaces for Dimension Reduction

DTIC Science & Technology

2013-01-01

these applications realized a maximal compute time improvement with minimal Krylov subspaces. More recently, Halko et . al . [36] have investigated... Halko et . al . proposed a variety of them in [36], but we focus on the “direct eigenvalue approximation for Hermitian matri- ces with random...result due to Halko et . al . Theorem 5 ( Halko , Martinsson and Tropp [36]). Let A ∈ Rn×m be the input matrix with partitioned singular value

Majorana-Hubbard model on the square lattice

NASA Astrophysics Data System (ADS)

Affleck, Ian; Rahmani, Armin; Pikulin, Dmitry

2017-09-01

We study a tight-binding model of interacting Majorana (Hermitian) modes on a square lattice. The model may have an experimental realization in a superconducting-film-topological-insulator heterostructure in a magnetic field. We find a rich phase diagram, as a function of interaction strength, including an emergent superfluid phase with spontaneous breaking of an emergent U (1 ) symmetry, separated by a supersymmetric transition from a gapless normal phase.

A new precoding scheme for spectral efficient optical OFDM systems

NASA Astrophysics Data System (ADS)

Hardan, Saad Mshhain; Bayat, Oguz; Abdulkafi, Ayad Atiyah

2018-07-01

Achieving high spectral efficiency is the key requirement of 5G and optical wireless communication systems and has recently attracted much attention, aiming to satisfy the ever increasing demand for high data rates in communications systems. In this paper, we propose a new precoding/decoding algorithm for spectral efficient optical orthogonal frequency division multiplexing (OFDM) scheme based visible light communication (VLC) systems. The proposed coded modulated optical (CMO) based OFDM system can be applied for both single input single output (SISO) and multiple input multiple-output (MIMO) architectures. Firstly, the real OFDM time domain signal is obtained through invoking the precoding/decoding algorithm without the Hermitian symmetry. After that, the positive signal is achieved either by adding a DC-bias or by using the spatial multiplexing technique. The proposed CMO-OFDM scheme efficiently improves the spectral efficiency of the VLC system as it does not require the Hermitian symmetry constraint to yield real signals. A comparison of the performance improvement of the proposed scheme with other OFDM approaches is also presented in this work. Simulation results show that the proposed CMO-OFDM scheme can not only enhance the spectral efficiency of OFDM-based VLC systems but also improve bit error rate (BER) performance compared with other optical OFDM schemes.

Realization of the three-qubit quantum controlled gate based on matching Hermitian generators

NASA Astrophysics Data System (ADS)

Gautam, Kumar; Rawat, Tarun Kumar; Parthasarathy, Harish; Sharma, Navneet; Upadhyaya, Varun

2017-05-01

This paper deals with the design of quantum unitary gate by matching the Hermitian generators. A given complicated quantum controlled gate is approximated by perturbing a simple quantum system with a small time-varying potential. The basic idea is to evaluate the generator H_φ of the perturbed system approximately using first-order perturbation theory in the interaction picture. H_φ depends on a modulating signal φ(t){:} 0≤t≤T which modulates a known potential V. The generator H_φ of the given gate U_g is evaluated using H_g=ι log U_g. The optimal modulating signal φ(t) is chosen so that \\Vert H_g - H_φ \\Vert is a minimum. The simple quantum system chosen for our simulation is harmonic oscillator with charge perturbed by an electric field that is a constant in space but time varying and is controlled externally. This is used to approximate the controlled unitary gate obtained by perturbing the oscillator with an anharmonic term proportional to q^3. Simulations results show significantly small noise-to-signal ratio. Finally, we discuss how the proposed method is particularly suitable for designing some commonly used unitary gates. Another example was chosen to illustrate this method of gate design is the ion-trap model.

Evaluation of Partial k-space strategies to speed up Time-domain EPR Imaging

PubMed Central

Subramanian, Sankaran; Chandramouli, Gadisetti VR; McMillan, Alan; Gullapalli, Rao P; Devasahayam, Nallathamby; Mitchell, James B.; Matsumoto, Shingo; Krishna, Murali C

2012-01-01

Narrow-line spin probes derived from the trityl radical have led to the development of fast in vivo time-domain EPR imaging. Pure phase-encoding imaging modalities based on the Single Point Imaging scheme (SPI) have demonstrated the feasibility of 3D oximetric images with functional information in minutes. In this paper, we explore techniques to improve the temporal resolution and circumvent the relatively short biological half-lives of trityl probes using partial k-space strategies. There are two main approaches: one involves the use of the Hermitian character of the k-space by which only part of the k-space is measured and the unmeasured part is generated using the Hermitian symmetry. This approach is limited in success by the accuracy of numerical estimate of the phase roll in the k-space that corrupts the Hermiticy. The other approach is to measure only a judicially chosen reduced region of k-space (a centrosymmetric ellipsoid region) that more or less accounts for >70% of the k-space energy. Both of these aspects were explored in FT-EPR imaging with a doubling of scan speed demonstrated by considering ellipsoid geometry of the k-space. Partial k-space strategies help improve the temporal resolution in studying fast dynamics of functional aspects in vivo with infused spin probes. PMID:23045171

Arthrophycus in the Silurian of Alabama (USA) and the problem of compound trace fossils

USGS Publications Warehouse

Rindsberg, Andrew K.; Martin, A.J.

2003-01-01

Arthrophycus brongniartii (Harlan, 1832) is common in marginal-marine deposits in the Silurian Red Mountain Formation of Alabama. The ichnospecies, the second to be named in North America, is revived and emended after long disuse. Transitional forms to Rusophycus isp. and other morphologic evidence indicate that the maker of Arthrophycus was an arthropod, perhaps a trinucleine (raphiophorid?) trilobite. Interconnection of Arthrophycus and Nereites biserialis, as well as intergradation of Arthrophycus with Cruziana aff. quadrata, Phycodes flabellum, and Asterosoma ludwigae, indicate that these Red Mountain trace fossils were made by the same species of arthropod. Possible relationships with Arthrophycus alleghaniensis (Harlan, 1831) in the Silurian belt from Ontario to Tennessee are also explored. Ichnofamily Arthrophycidae Schimper, 1879 is emended. The ichnofamily is interpreted as chiefly the work of arthropods. Arthrophycus and other trace fossils from the Silurian of Alabama constitute a test case to build criteria for recognizing the members of complexes of trace fossils. In general, criteria such as interconnection of different forms, intergradation among unconnected forms, similarity of size, similarity of morphologic elements, and co-occurrence should be examined in order to determine the biologic and ethologic interrelationships of trace fossils. ?? 2003 Elsevier Science B.V. All rights reserved.

[Analysis of primary elemental speciation distribution in mungbean during enzymatic hydrolization].

PubMed

Li, Ji-Hua; Huang, Mao-Fang; Zhu, De-Ming; Zheng, Wei-Wan; Zhong, Ye-Jun

2009-03-01

In the present paper, trace elements contents of cuprum, zincum, manganese and ferrum in mungbean and their primary speciation distribution during enzymatic hydrolization were investigated with ICP-AES OPTIMA 5300DV plasma emission spectroscopy. The trace elements were separated into two forms, i.e. dissolvable form and particulate form, by cellulose membrane with 0.45 microm of pore diameter. All the samples were digested by strong acid (perchloric acid and nitric acid with 1 : 4 ratio ). The parameters of primary speciations of the four elements were calculated and discussed. The results showed: (1) Contents of cuprum, zincum, manganese and ferrum in mungbean were 12.77, 31.26, 18.14 and 69.38 microg x g(-1) (of dry matter), respectively. Different treatment resulted in different elemental formulation in product, indicating that more attention should be paid to the trace elements pattern when producing mungbean beverage with different processes. (2) Extraction rates of cuprum, zincum, manganese and ferrum in extract were 68.84%, 51.84%, 63.97% and 30.40% with enzymatic treatments and 36.22%, 17.58%, 7.85% and 22.99% with boil treatment, respectively. Both boil and enzymatic treatments led to poor elemental extraction rates, which proved that it was necessary to take deep enzymatic hydrolysis treatment in mungbean beverage process as the trace element utilization rate was concerned. (3) Amylase, protease and cellulose showed different extraction effectiveness of the four trace elements. Generally, protease exhibited highest efficiency for the four elements extraction. All of the four trace elements were mostly in dissolvable form in all hydrolysates and soup. (4) Relative standard deviations and recovery yields are within 0.12%-0.90% (n = 11) and 98.6%-101.4%, respectively. The analysis method in this paper proved to be accurate.

On Distributed Strategies in Defense of a High Value Unit (HVU) Against a Swarm Attack

DTIC Science & Technology

2012-09-01

function [ lam ,U] = tqr(a,b,U) % [ lam u] = tqr(a,b) or [ lam U] = tqr(a,b,U... lam u] = tqr(a,b): % % The column lam contains the eigenvalues of the Hermitian tridiagonal % matrix T = mxt(a,b) computed by one version of the...computed. The computed eigenvalues are real and are sorted to be % nonincreasing. % % [ lam U] = tqr(a,b,U): % % This replaces the input U

Creating 3, 4, 6 and 10-dimensional spacetime from W3 symmetry

NASA Astrophysics Data System (ADS)

Ambjørn, J.; Watabiki, Y.

2017-07-01

We describe a model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four ;magical; Jordan algebras of 3 × 3 Hermitian matrices with real, complex, quaternion and octonion entries, respectively. The simplest symmetry breaking leads to universes with spacetime dimensions 3, 4, 6, and 10.

Optical inspection system for cylindrical objects

DOEpatents

Brenden, Byron B.; Peters, Timothy J.

1989-01-01

In the inspection of cylindrical objects, particularly O-rings, the object is translated through a field of view and a linear light trace is projected on its surface. An image of the light trace is projected on a mask, which has a size and shape corresponding to the size and shape which the image would have if the surface of the object were perfect. If there is a defect, light will pass the mask and be sensed by a detector positioned behind the mask. Preferably, two masks and associated detectors are used, one mask being convex to pass light when the light trace falls on a projection from the surface and the other concave, to pass light when the light trace falls on a depression in the surface. The light trace may be either dynamic, formed by a scanned laser beam, or static, formed by such a beam focussed by a cylindrical lens. Means are provided to automatically keep the illuminating receiving systems properly aligned.

Ichnology of an upper carboniferous fluvio-estuarine paleovalley: The tonganoxie sandstone, buildex quarry, eastern Kansas, USA

USGS Publications Warehouse

Buatois, L.A.; Mangano, M.G.; Maples, C.G.; Lanier, Wendy E.

1998-01-01

Tidal rhythmites of the Tonganoxie Sandstone Member (Stranger Formation, Douglas Group) at Buildex Quarry, eastern Kansas, contain a relatively diverse ichnofauna. The assemblage includes arthropod locomotion (Dendroidichnites irregulare, Diplichnites gouldi type A and B, Diplopodichnus biformis, Kouphichnium isp., Mirandaichnium famatinense, and Stiaria intermedia), resting (Tonganoxichnus buildexensis) and feeding traces (Stiallia pilosa, Tonganoxichnus ottawensis); grazing traces (Gordia indianaensis, Helminthoidichnites tenuis, Helminthopsis hieroglyphica); feeding structures (Circulichnis montanus, Treptichnus bifurcus, Treptichnus pollardi, irregular networks), fish traces (Undichna britannica, Undichna simplicitas), tetrapod trackways, and root traces. The taxonomy of some of these ichnotaxa is briefly reviewed and emended diagnoses for Gordia indianaensis and Helminthoidichnites tenuis are proposed. Additionally, the combined name Dendroidichnites irregulare is proposed for nested chevron trackways. Traces previously regarded as produced by isopods are reinterpreted as myriapod trackways (D. gouldi type B). Trackways formerly interpreted as limulid crawling and swimming traces are assigned herein to Kouphichnium isp and Dendroidichnites irregulare, respectively. Taphonomic analysis suggests that most grazing and feeding traces were formed before the arthropod trackways and resting traces. Grazing/feeding traces were formed in a soft, probably submerged substrate. Conversely, the majority of trackways and resting traces probably were produced subaerially in a firmer, dewatered and desiccated sediment. The Buildex Quarry ichnofauna records the activity of a terrestrial and freshwater biota. The presence of this assemblage in tidal rhythmites is consistent with deposition on tidal flats in the most proximal zone of the inner estuary, between the maximum landward limit of tidal currents and the salinity limit further towards the sea.

Pattern Formation and Strong Nonlinear Interactions in Exciton-Polariton Condensates

NASA Astrophysics Data System (ADS)

Ge, Li; Nersisyan, Ani; Oztop, Baris; Tureci, Hakan

2014-03-01

Exciton-polaritons generated by light-induced potentials can spontaneously condense into macroscopic quantum states that display nontrivial spatial and temporal density modulation. While these patterns and their dynamics can be reproduced through the solution of the generalized Gross-Pitaevskii equation, a predictive theory of their thresholds, oscillation frequencies, and multi-pattern interactions has so far been lacking. Here we represent such an approach based on current-carrying quasi-modes of the non-Hermitian potential induced by the pump. The presented theory allows us to capture the patterns formed in the steady-state directly and account for nonlinearities exactly. We find a simple but powerful expression for thresholds of condensation and the associated frequencies of oscillations, quantifying the contribution of particle formation, leakage, and interactions. We also show that the evolution of the condensate with increasing pump strength is strongly geometry dependent and can display contrasting features such as enhancement or reduction of the spatial localization of the condensate. We acknowledge support by DARPA under Grant No. N66001-11-1-4162 and NSF under CAREER Grant No. DMR-1151810.

Scalar curvature of Lagrangian Riemannian submersions and their harmonicity

NASA Astrophysics Data System (ADS)

Eken Meri˙ç, Şemsi; Kiliç, Erol; Sağiroğlu, Yasemi˙n

In this paper, we consider a Lagrangian Riemannian submersion from a Hermitian manifold to a Riemannian manifold and establish some basic inequalities to obtain relationships between the intrinsic and extrinsic invariants for such a submersion. Indeed, using these inequalities, we provide necessary and sufficient conditions for which a Lagrangian Riemannian submersion π has totally geodesic or totally umbilical fibers. Moreover, we study the harmonicity of Lagrangian Riemannian submersions and obtain a characterization for such submersions to be harmonic.

Tensionless Strings and Supersymmetric Sigma Models: Aspects of the Target Space Geometry

NASA Astrophysics Data System (ADS)

Bredthauer, Andreas

2007-01-01

In this thesis, two aspects of string theory are discussed, tensionless strings and supersymmetric sigma models. The equivalent to a massless particle in string theory is a tensionless string. Even almost 30 years after it was first mentioned, it is still quite poorly understood. We discuss how tensionless strings give rise to exact solutions to supergravity and solve closed tensionless string theory in the ten dimensional maximally supersymmetric plane wave background, a contraction of AdS(5)xS(5) where tensionless strings are of great interest due to their proposed relation to higher spin gauge theory via the AdS/CFT correspondence. For a sigma model, the amount of supersymmetry on its worldsheet restricts the geometry of the target space. For N=(2,2) supersymmetry, for example, the target space has to be bi-hermitian. Recently, with generalized complex geometry, a new mathematical framework was developed that is especially suited to discuss the target space geometry of sigma models in a Hamiltonian formulation. Bi-hermitian geometry is so-called generalized Kaehler geometry but the relation is involved. We discuss various amounts of supersymmetry in phase space and show that this relation can be established by considering the equivalence between the Hamilton and Lagrange formulation of the sigma model. In the study of generalized supersymmetric sigma models, we find objects that favor a geometrical interpretation beyond generalized complex geometry.

Decoherence of odd compass states in the phase-sensitive amplifying/dissipating environment

NASA Astrophysics Data System (ADS)

Dodonov, V. V.; Valverde, C.; Souza, L. S.; Baseia, B.

2016-08-01

We study the evolution of odd compass states (specific superpositions of four coherent states), governed by the standard master equation with phase-sensitive amplifying/attenuating terms, in the presence of a Hamiltonian describing a parametric degenerate linear amplifier. Explicit expressions for the time-dependent Wigner function are obtained. The time of disappearance of the so called ;sub-Planck structures; is calculated using the negative value of the Wigner function at the origin of phase space. It is shown that this value rapidly decreases during a short ;conventional interference degradation time; (CIDT), which is inversely proportional to the size of quantum superposition, provided the anti-Hermitian terms in the master equation are of the same order (or stronger) as the Hermitian ones (governing the parametric amplification). The CIDT is compared with the final positivization time (FPT), when the Wigner function becomes positive. It appears that the FPT does not depend on the size of superpositions, moreover, it can be much bigger in the amplifying media than in the attenuating ones. Paradoxically, strengthening the Hamiltonian part results in decreasing the CIDT, so that the CIDT almost does not depend on the size of superpositions in the asymptotical case of very weak reservoir coupling. We also analyze the evolution of the Mandel factor, showing that for some sets of parameters this factor remains significantly negative, even when the Wigner function becomes positive.

Evaluation of partial k-space strategies to speed up time-domain EPR imaging.

PubMed

Subramanian, Sankaran; Chandramouli, Gadisetti V R; McMillan, Alan; Gullapalli, Rao P; Devasahayam, Nallathamby; Mitchell, James B; Matsumoto, Shingo; Krishna, Murali C

2013-09-01

Narrow-line spin probes derived from the trityl radical have led to the development of fast in vivo time-domain EPR imaging. Pure phase-encoding imaging modalities based on the single-point imaging scheme have demonstrated the feasibility of three-dimensional oximetric images with functional information in minutes. In this article, we explore techniques to improve the temporal resolution and circumvent the relatively short biological half-lives of trityl probes using partial k-space strategies. There are two main approaches: one involves the use of the Hermitian character of the k-space by which only part of the k-space is measured and the unmeasured part is generated using the Hermitian symmetry. This approach is limited in success by the accuracy of numerical estimate of the phase roll in the k-space that corrupts the Hermiticy. The other approach is to measure only a judicially chosen reduced region of k-space (a centrosymmetric ellipsoid region) that more or less accounts for >70% of the k-space energy. Both of these aspects were explored in Fourier transform-EPR imaging with a doubling of scan speed demonstrated by considering ellipsoid geometry of the k-space. Partial k-space strategies help improve the temporal resolution in studying fast dynamics of functional aspects in vivo with infused spin probes. Copyright © 2012 Wiley Periodicals, Inc.

Response of infaunal organisms represented by trace fossils to sea-level changes in the Ordovician Black River and Trenton Group limestones, upstate New York

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

Tegan, J.R.; Curran, H.A.

Small-scale fluctuations in sea level were revealed by detailed analysis of trace fossil assemblages formed by infaunal organisms within the Lowville (Black River Grp.), Napanee, and Kings Falls limestones (Trenton Grp.) at Ingham Mills. The paleodepositional environment of the Lowville Limestone (LL) is interpreted as peritidal, representing the high intertidal to shallow subtidal zones. The trace fossil assemblages define clearly several fluctuations within this environment. Large, well-formed specimens of the trace fossil Beaconites barretti occur within tidal channel and levee beds of the LL. In other regions this trace fossil has consistently been associated with channel and levee beds, mostmore » commonly in fluvial settings. The occurrence of Beaconites in the LL extends the age range of this ichnogenus to Ordovician time (oldest previous record is Silurian) and broadens its paleoenvironment range. The Napanee (Np) and lower Kings Falls (KF), limestones have most commonly been described as being deposited in a lagoonal setting. Both formations contain well-preserved trace fossils; the primary difference being that the Np exhibits much lower trace and body fossil diversities than the KF. The low diversity of trace fossils in the Np was most likely the result of limiting environmental conditions such as low oxygen and/or hypersalinity. The higher diversity of trace fossils in the KF indicates that the ancient lagoon became increasingly controlled by normal marine conditions, and, therefore, hospitable to a more diverse group of organisms. The trace fossil assemblages of the Black River and Trenton Group limestones indicate that the infaunal organisms of these Ordovician communities were highly sensitive to small-scale sea-level fluctuations.« less

Trace elements in magnetite as petrogenetic indicators

NASA Astrophysics Data System (ADS)

Dare, Sarah A. S.; Barnes, Sarah-Jane; Beaudoin, Georges; Méric, Julien; Boutroy, Emilie; Potvin-Doucet, Christophe

2014-10-01

We have characterized the distribution of 25 trace elements in magnetite (Mg, Al, Si, P, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Zn, Ga, Ge, Y, Zr, Nb, Mo, Sn, Hf, Ta, W, and Pb), using laser ablation ICP-MS and electron microprobe, from a variety of magmatic and hydrothermal ore-forming environments and compared them with data from the literature. We propose a new multielement diagram, normalized to bulk continental crust, designed to emphasize the partitioning behavior of trace elements between magnetite, the melt/fluid, and co-crystallizing phases. The normalized pattern of magnetite reflects the composition of the melt/fluid, which in both magmatic and hydrothermal systems varies with temperature. Thus, it is possible to distinguish magnetite formed at different degrees of crystal fractionation in both silicate and sulfide melts. The crystallization of ilmenite or sulfide before magnetite is recorded as a marked depletion in Ti or Cu, respectively. The chemical signature of hydrothermal magnetite is distinct being depleted in elements that are relatively immobile during alteration and commonly enriched in elements that are highly incompatible into magnetite (e.g., Si and Ca). Magnetite formed from low-temperature fluids has the lowest overall abundance of trace elements due to their lower solubility. Chemical zonation of magnetite is rare but occurs in some hydrothermal deposits where laser mapping reveals oscillatory zoning, which records the changing conditions and composition of the fluid during magnetite growth. This new way of plotting all 25 trace elements on 1 diagram, normalized to bulk continental crust and elements in order of compatibility into magnetite, provides a tool to help understand the processes that control partitioning of a full suit of trace elements in magnetite and aid discrimination of magnetite formed in different environments. It has applications in both petrogenetic and provenance studies, such as in the exploration of ore deposits and in sedimentology.

Functional form for the leading correction to the distribution of the largest eigenvalue in the GUE and LUE

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Trinh, Allan K.

2018-05-01

The neighbourhood of the largest eigenvalue λmax in the Gaussian unitary ensemble (GUE) and Laguerre unitary ensemble (LUE) is referred to as the soft edge. It is known that there exists a particular centring and scaling such that the distribution of λmax tends to a universal form, with an error term bounded by 1/N2/3. We take up the problem of computing the exact functional form of the leading error term in a large N asymptotic expansion for both the GUE and LUE—two versions of the LUE are considered, one with the parameter a fixed and the other with a proportional to N. Both settings in the LUE case allow for an interpretation in terms of the distribution of a particular weighted path length in a model involving exponential variables on a rectangular grid, as the grid size gets large. We give operator theoretic forms of the corrections, which are corollaries of knowledge of the first two terms in the large N expansion of the scaled kernel and are readily computed using a method due to Bornemann. We also give expressions in terms of the solutions of particular systems of coupled differential equations, which provide an alternative method of computation. Both characterisations are well suited to a thinned generalisation of the original ensemble, whereby each eigenvalue is deleted independently with probability (1 - ξ). In Sec. V, we investigate using simulation the question of whether upon an appropriate centring and scaling a wider class of complex Hermitian random matrix ensembles have their leading correction to the distribution of λmax proportional to 1/N2/3.

Fossilized bioelectric wire - the trace fossil Trichichnus

NASA Astrophysics Data System (ADS)

Kędzierski, M.; Uchman, A.; Sawlowicz, Z.; Briguglio, A.

2014-12-01

The trace fossil Trichichnus is proposed as an indicator of fossil bioelectric bacterial activity at the interface oxic - anoxic zone of marine sediments. This fulfils the idea that such processes, commonly found in the modern realm, should be also present in the geological past. Trichichnus is an exceptional trace fossil due to its very thin diameter (mostly less than 1 mm) and common pyritic filling. It is ubiquitous in some fine-grained sediments, where it has been interpreted as a burrow formed deeper than any other trace fossils, below the redox boundary. Trichichnus formerly referred to as deeply burrowed invertebrates, has been found as remnant of a fossilized intrasediment bacterial mat that is pyritized. As visualized in 3-D by means of X-ray computed microtomography scanner, Trichichnus forms dense filamentous fabric, which reflects that produced by modern large, mat-forming, sulphide-oxidizing bacteria, belonging mostly to Trichichnus-related taxa, which are able to house a complex bacterial consortium. Several stages of Trichichnus formation, including filamentous, bacterial mat and its pyritization, are proposed to explain an electron exchange between oxic and suboxic/anoxic layers in the sediment. Therefore, Trichichnus can be considered a fossilized "electric wire".

Fossilized bioelectric wire - the trace fossil Trichichnus

NASA Astrophysics Data System (ADS)

Kędzierski, M.; Uchman, A.; Sawlowicz, Z.; Briguglio, A.

2015-04-01

The trace fossil Trichichnus is proposed as an indicator of fossil bioelectric bacterial activity at the oxic-anoxic interface zone of marine sediments. This fulfils the idea that such processes, commonly found in the modern realm, should be also present in the geological past. Trichichnus is an exceptional trace fossil due to its very thin diameter (mostly less than 1 mm) and common pyritic filling. It is ubiquitous in some fine-grained sediments, where it has been interpreted as a burrow formed deeper than any other trace fossils, below the redox boundary. Trichichnus, formerly referred to as deeply burrowed invertebrates, has been found as remnant of a fossilized intrasediment bacterial mat that is pyritized. As visualized in 3-D by means of X-ray computed microtomography scanner, Trichichnus forms dense filamentous fabric, which reflects that it is produced by modern large, mat-forming, sulfide-oxidizing bacteria, belonging mostly to Thioploca-related taxa, which are able to house a complex bacterial consortium. Several stages of Trichichnus formation, including filamentous, bacterial mat and its pyritization, are proposed to explain an electron exchange between oxic and suboxic/anoxic layers in the sediment. Therefore, Trichichnus can be considered a fossilized "electric wire".

Intracranial distribution of the sympathetic system in mice: DiI tracing and immunocytochemical labeling

NASA Technical Reports Server (NTRS)

Maklad, A.; Quinn, T.; Fritzsch, B.

2001-01-01

The intracranial distribution of the cephalic branches of the superior cervical ganglion (scg) was studied in mice using indocarbocyanine dye (DiI) anterograde tracing. Two main branches were traced from the scg. The first branch joined the nerve of the pterygoid canal (the vidian nerve), npc, from which several intracranial sympathetic branches passed to the branches of the trigeminal nerve (tgn), abducent nerve (abn), trochlear nerve (trn), and oculomotor nerve (ocn). Most of the second branch joined the abn, from which sympathetic fibers dispersed in the distal region of the trigeminal ganglion (tgg) to form a plexus close to the ganglion's branches. Branches from this plexus joined the branches of the tgn, trn, and ocn. Several minor branches arising from the second branch of the scg were also observed. One formed a sympathetic plexus around the internal carotid artery (ica); a second formed a sympathetic plexus in the proximal region of tgg, close to its root; and a third branch coursed laterally to reach the ear by passing along the greater petrosal nerve (gpn). All of the intracranial trajectories traced from scg were found to be catecholaminergic, and likely sympathetic, using tyrosine hydroxylase (TH) immunocytochemistry.

Fabp4-CreER lineage tracing reveals two distinctive coronary vascular populations.

PubMed

He, Lingjuan; Tian, Xueying; Zhang, Hui; Wythe, Joshua D; Zhou, Bin

2014-11-01

Over the last two decades, genetic lineage tracing has allowed for the elucidation of the cellular origins and fates during both embryogenesis and in pathological settings in adults. Recent lineage tracing studies using Apln-CreER tool indicated that a large number of post-natal coronary vessels do not form from pre-existing vessels. Instead, they form de novo after birth, which represents a coronary vascular population (CVP) distinct from the pre-existing one. Herein, we present new coronary vasculature lineage tracing results using a novel tool, Fabp4-CreER. Our results confirm the distinct existence of two unique CVPs. The 1(st) CVP, which is labelled by Fabp4-CreER, arises through angiogenic sprouting of pre-existing vessels established during early embryogenesis. The 2(nd) CVP is not labelled by Fabp4, suggesting that these vessels form de novo, rather than through expansion of the 1(st) CVP. These results support the de novo formation of vessels in the post-natal heart, which has implications for studies in cardiovascular disease and heart regeneration. © 2014 The Authors. Journal of Cellular and Molecular Medicine published by John Wiley & Sons Ltd and Foundation for Cellular and Molecular Medicine.

Fossilized bioelectric wire – the trace fossil Trichichnus

PubMed Central

Kędzierski, M.; Uchman, A.; Sawlowicz, Z.; Briguglio, A.

2015-01-01

The trace fossil Trichichnus is proposed as an indicator of fossil bioelectric bacterial activity at the oxic–anoxic interface zone of marine sediments. This fulfils the idea that such processes, commonly found in the modern realm, should be also present in the geological past. Trichichnus is an exceptional trace fossil due to its very thin diameter (mostly less than 1 mm) and common pyritic filling. It is ubiquitous in some fine-grained sediments, where it has been interpreted as a burrow formed deeper than any other trace fossils, below the redox boundary. Trichichnus, formerly referred to as deeply burrowed invertebrates, has been found as remnant of a fossilized intrasediment bacterial mat that is pyritized. As visualized in 3-D by means of X-ray computed microtomography scanner, Trichichnus forms dense filamentous fabric, which reflects that it is produced by modern large, mat-forming, sulfide-oxidizing bacteria, belonging mostly to Thioploca-related taxa, which are able to house a complex bacterial consortium. Several stages of Trichichnus formation, including filamentous, bacterial mat and its pyritization, are proposed to explain an electron exchange between oxic and suboxic/anoxic layers in the sediment. Therefore, Trichichnus can be considered a fossilized “electric wire”. PMID:26290671

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

Smilga, A. V.

We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by nonanticommutative deformations belong in many cases to this class. (ii) When the deformation parameter is small, the deformed theory enjoys the same supersymmetry algebra as the undeformed one. Half of the supersymmetries are manifest and the existence of another half can be deduced from the structure of the spectrum. (iii) Generically, the conventionally defined S-matrix is not unitary for such theories.

Parametric amplification in quasi-PT symmetric coupled waveguide structures

NASA Astrophysics Data System (ADS)

Zhong, Q.; Ahmed, A.; Dadap, J. I.; Osgood, R. M., Jr.; El-Ganainy, R.

2016-12-01

The concept of non-Hermitian parametric amplification was recently proposed as a means to achieve an efficient energy conversion throughout the process of nonlinear three wave mixing in the absence of phase matching. Here we investigate this effect in a waveguide coupler arrangement whose characteristics are tailored to introduce passive PT symmetry only for the idler component. By means of analytical solutions and numerical analysis, we demonstrate the utility of these novel schemes and obtain the optimal design conditions for these devices.

Optical force rectifiers based on PT-symmetric metasurfaces

NASA Astrophysics Data System (ADS)

Alaee, Rasoul; Gurlek, Burak; Christensen, Johan; Kadic, Muamer

2018-05-01

We introduce here the concept of optical force rectifier based on parity-time symmetric metasurfaces. Directly linked to the properties of non-Hermitian systems engineered by balanced loss and gain constituents, we show that light can exert asymmetric pulling or pushing forces on metasurfaces depending on the direction of the impinging light. This generates a complete force rectification in the vicinity of the exceptional point. Our findings have the potential to spark the design of applications in optical manipulation where the forces, strictly speaking, act unidirectionally.

Percolation, sliding, localization and relaxation in topologically closed circuits

NASA Astrophysics Data System (ADS)

Hurowitz, Daniel; Cohen, Doron

2016-03-01

Considering a random walk in a random environment in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the “delocalization” of eigenstates of non-hermitian Hamiltonians has been addressed by Hatano, Nelson, and followers. But we show that for a conservative stochastic process the implied spectral properties are dramatically different. In particular we determine the threshold for under-damped relaxation, and observe “complexity saturation” as the bias is increased.

Wigner surmises and the two-dimensional homogeneous Poisson point process.

PubMed

Sakhr, Jamal; Nieminen, John M

2006-04-01

We derive a set of identities that relate the higher-order interpoint spacing statistics of the two-dimensional homogeneous Poisson point process to the Wigner surmises for the higher-order spacing distributions of eigenvalues from the three classical random matrix ensembles. We also report a remarkable identity that equates the second-nearest-neighbor spacing statistics of the points of the Poisson process and the nearest-neighbor spacing statistics of complex eigenvalues from Ginibre's ensemble of 2 x 2 complex non-Hermitian random matrices.

Reflective limiters based on self-induced violation of C T symmetry

NASA Astrophysics Data System (ADS)

Makri, Eleana; Thomas, Roney; Kottos, Tsampikos

2018-04-01

Non-Hermitian bipartite photonic lattices with charge-conjugation (C T ) symmetry can support resonant defect modes which are resilient to bipartite losses and structural imperfections. When, however, a (self-)induced violation of the C T symmetry occurs via tiny permittivity variations, the resonant mode is exposed to the bipartite losses and it is destroyed. Consequently, the transmission peak is suppressed while the reflectance becomes (almost) unity. We propose the use of such photonic systems as power switches, limiters, and sensors.

Parallel algorithm for computation of second-order sequential best rotations

NASA Astrophysics Data System (ADS)

Redif, Soydan; Kasap, Server

2013-12-01

Algorithms for computing an approximate polynomial matrix eigenvalue decomposition of para-Hermitian systems have emerged as a powerful, generic signal processing tool. A technique that has shown much success in this regard is the sequential best rotation (SBR2) algorithm. Proposed is a scheme for parallelising SBR2 with a view to exploiting the modern architectural features and inherent parallelism of field-programmable gate array (FPGA) technology. Experiments show that the proposed scheme can achieve low execution times while requiring minimal FPGA resources.

Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

NASA Astrophysics Data System (ADS)

Bagarello, F.

2011-12-01

We have recently proposed a strategy to produce, starting from a given Hamiltonian h and a certain operator x for which [h,xx]=0 and xx is invertible, a second Hamiltonian h with the same eigenvalues as h and whose eigenvectors are related to those of h by x. Here we extend this procedure to build up a second Hamiltonian, whose eigenvalues are different from those of h, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian Hamiltonians.

Generic Friedberg-Lee symmetry of Dirac neutrinos

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

Luo Shu; Xing Zhizhong; Li Xin

2008-12-01

We write out the generic Dirac neutrino mass operator which possesses the Friedberg-Lee symmetry and find that its corresponding neutrino mass matrix is asymmetric. Following a simple way to break the Friedberg-Lee symmetry, we calculate the neutrino mass eigenvalues and show that the resultant neutrino mixing pattern is nearly tri-bimaximal. Imposing the Hermitian condition on the neutrino mass matrix, we also show that the simplified ansatz is consistent with current experimental data and favors the normal neutrino mass hierarchy.

Generalized Preconditioned Locally Harmonic Residual Eigensolver (GPLHR) v0.1

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

VECHARYNSKI, EUGENE; YANG, CHAO

The software contains a MATLAB implementation of the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly useful for computing a subset of eigenvalues, and their eigen- or Schur vectors, closest to a given shift. The proposed method is based on block iterations and can take advantage of a preconditioner if it is available. It does not need to perform exact shift-and-invert transformation. Standard and generalized eigenproblems are handled in a unified framework.

Bethe-Salpeter Eigenvalue Solver Package (BSEPACK) v0.1

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

SHAO, MEIYEU; YANG, CHAO

2017-04-25

The BSEPACK contains a set of subroutines for solving the Bethe-Salpeter Eigenvalue (BSE) problem. This type of problem arises in this study of optical excitation of nanoscale materials. The BSE problem is a structured non-Hermitian eigenvalue problem. The BSEPACK software can be used to compute all or subset of eigenpairs of a BSE Hamiltonian. It can also be used to compute the optical absorption spectrum without computing BSE eigenvalues and eigenvectors explicitly. The package makes use of the ScaLAPACK, LAPACK and BLAS.

Banach Synaptic Algebras

NASA Astrophysics Data System (ADS)

Foulis, David J.; Pulmannov, Sylvia

2018-04-01

Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

A training rule which guarantees finite-region stability for a class of closed-loop neural-network control systems.

PubMed

Kuntanapreeda, S; Fullmer, R R

1996-01-01

A training method for a class of neural network controllers is presented which guarantees closed-loop system stability. The controllers are assumed to be nonlinear, feedforward, sampled-data, full-state regulators implemented as single hidden-layer neural networks. The controlled systems must be locally hermitian and observable. Stability of the closed-loop system is demonstrated by determining a Lyapunov function, which can be used to identify a finite stability region about the regulator point.

Practical applications of trace minerals for dairy cattle.

PubMed

Overton, T R; Yasui, T

2014-02-01

Trace minerals have critical roles in the key interrelated systems of immune function, oxidative metabolism, and energy metabolism in ruminants. To date, the primary trace elements of interest in diets for dairy cattle have included Zn, Cu, Mn, and Se although data also support potentially important roles of Cr, Co, and Fe in diets. Trace minerals such as Zn, Cu, Mn, and Se are essential with classically defined roles as components of key antioxidant enzymes and proteins. Available evidence indicates that these trace minerals can modulate aspects of oxidative metabolism and immune function in dairy cattle, particularly during the transition period and early lactation. Chromium has been shown to influence both immune function and energy metabolism of cattle; dairy cows fed Cr during the transition period and early lactation have evidence of improved immune function, increased milk production, and decreased cytological endometritis. Factors that complicate trace mineral nutrition at the farm level include the existence of a large number of antagonisms affecting bioavailability of individual trace minerals and uncertainty in terms of requirements under all physiological and management conditions; therefore, determining the optimum level and source of trace minerals under each specific situation continues to be a challenge. Typical factorial approaches to determine requirements for dairy cattle do not account for nuances in biological function observed with supplementation with various forms and amounts of trace minerals. Trace mineral nutrition modulates production, health, and reproduction in cattle although both formal meta-analysis and informal survey of the literature reveal substantial heterogeneity of response in these outcome variables. The industry has largely moved away from oxide-based programs toward sulfate-based programs; however, some evidence favors shifting supplementation strategies further toward more bioavailable forms of inorganic and organic trace minerals. Furthermore, opportunities for specific modulation of aspects of health, milk production, and reproduction through supplementation strategies for diets of transition dairy cows are attractive because of the known dynamics of energy metabolism, immune function, and oxidative metabolism during this timeframe.

Extraction of trace metals from fly ash

DOEpatents

Blander, M.; Wai, C.M.; Nagy, Z.

1983-08-15

A process is described for recovering silver, gallium and/or other trace metals from a fine grained industrial fly ash associated with a process for producing phosphorous. The fly ash has a silicate base and contains surface deposits of the trace metals as oxides, chlorides or the like. The process is carried out by contacting the fly ash with AlCl/sub 3/ in an alkali halide melt to react the trace metals with the AlCl/sub 3/ to form compositions soluble in the melt and a residue containing the silicate and aluminum oxide or other aluminum precipitate, and separating the desired trace metal or metals from the melt by electrolysis or other separation techniques.

Extraction of trace metals from fly ash

DOEpatents

Blander, Milton; Wai, Chien M.; Nagy, Zoltan

1984-01-01

A process for recovering silver, gallium and/or other trace metals from a fine grained industrial fly ash associated with a process for producing phosphorous, the fly ash having a silicate base and containing surface deposits of the trace metals as oxides, chlorides or the like, with the process being carried out by contacting the fly ash with AlCl.sub.3 in an alkali halide melt to react the trace metals with the AlCl.sub.3 to form compositions soluble in the melt and a residue containing the silicate and aluminum oxide or other aluminum precipitate, and separating the desired trace metal or metals from the melt by electrolysis or other separation techniques.

Recycling of trace elements required for humans in CELSS.

PubMed

Ashida, A

1994-11-01

Recycle of complete nourishment necessary for human should be constructed in CELSS (Controlled Ecological Life Support Systems). Essential elements necessary for human support are categorized as major elements, semi-major elements and trace elements. Recently, trace elements have been identified from considerations of local diseases, food additive problems, pollution problems and adult diseases, consisting of Fe, Zn, Cu, Se, Co, F, Si, Mn, Cr, I, As, Mo, Ni, V, Sn, Li, Br, Cd, Pb, B. A review of the biogeochemical history of the earth's biosphere and the physiological nature of humans and plants explains some of the requirements. A possible route for intake of trace elements is considered that trace elements are dissolved in some chemical form in water, absorbed by plants through their roots and then transfered to human as foods. There may be a possibility that living things absorb some trace elements from atmosphere. Management and recycling of trace elements in CELSS is discussed.

Recycling of trace elements required for humans in CELSS

NASA Astrophysics Data System (ADS)

Ashida, A.

1994-11-01

Recycle of complete nourishment necessary for human should be constructed in CELSS (Controlled Ecological Life Support Systems). Essential elements necessary for human support are categorized as major elements, semi-major elements and trace elements. Recently, trace elements have been identified from considerations of local diseases, food additive problems, pollution problems and adult diseases, consisting of Fe, Zn, Cu, Se, Co, F, Si, Mn, Cr, I, As, Mo, Ni, V, Sn, Li, Br, Cd, Pb, B. A review of the biogeochemical history of the earth's biosphere and the physiological nature of humans and plants explains some of the requirements. A possible route for intake of trace elements is considered that trace elements are dissolved in some chemical form in water, absorbed by plants through their roots and then transfered to human as foods. There may be a posibility that living things absorb some trace elements from atmosphere. Management and recycling of trace elements in CELSS is discussed.

Orientation estimation of anatomical structures in medical images for object recognition

NASA Astrophysics Data System (ADS)

Bağci, Ulaş; Udupa, Jayaram K.; Chen, Xinjian

2011-03-01

Recognition of anatomical structures is an important step in model based medical image segmentation. It provides pose estimation of objects and information about "where" roughly the objects are in the image and distinguishing them from other object-like entities. In,1 we presented a general method of model-based multi-object recognition to assist in segmentation (delineation) tasks. It exploits the pose relationship that can be encoded, via the concept of ball scale (b-scale), between the binary training objects and their associated grey images. The goal was to place the model, in a single shot, close to the right pose (position, orientation, and scale) in a given image so that the model boundaries fall in the close vicinity of object boundaries in the image. Unlike position and scale parameters, we observe that orientation parameters require more attention when estimating the pose of the model as even small differences in orientation parameters can lead to inappropriate recognition. Motivated from the non-Euclidean nature of the pose information, we propose in this paper the use of non-Euclidean metrics to estimate orientation of the anatomical structures for more accurate recognition and segmentation. We statistically analyze and evaluate the following metrics for orientation estimation: Euclidean, Log-Euclidean, Root-Euclidean, Procrustes Size-and-Shape, and mean Hermitian metrics. The results show that mean Hermitian and Cholesky decomposition metrics provide more accurate orientation estimates than other Euclidean and non-Euclidean metrics.

Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

NASA Astrophysics Data System (ADS)

Lempert, László; Szőke, Róbert

2014-04-01

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H s of Hilbert spaces, and the question arises if the spaces H s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787-902, 1991) and Hitchin (Commun. Math. Phys. 131:347-380, 1990) suggest viewing H s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle along a non-proper map . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Szőke (Bull. Lond. Math. Soc. 44:367-374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.

Efficient geometry optimization by Hellmann-Feynman forces with the anti-Hermitian contracted Schrödinger equation

NASA Astrophysics Data System (ADS)

Foley, Jonathan J.; Mazziotti, David A.

2010-10-01

An efficient method for geometry optimization based on solving the anti-Hermitian contracted Schrödinger equation (ACSE) is presented. We formulate a reduced version of the Hellmann-Feynman theorem (HFT) in terms of the two-electron reduced Hamiltonian operator and the two-electron reduced density matrix (2-RDM). The HFT offers a considerable reduction in computational cost over methods which rely on numerical derivatives. While previous geometry optimizations with numerical gradients required 2M evaluations of the ACSE where M is the number of nuclear degrees of freedom, the HFT requires only a single ACSE calculation of the 2-RDM per gradient. Synthesizing geometry optimization techniques with recent extensions of the ACSE theory to arbitrary electronic and spin states provides an important suite of tools for accurately determining equilibrium and transition-state structures of ground- and excited-state molecules in closed- and open-shell configurations. The ability of the ACSE to balance single- and multi-reference correlation is particularly advantageous in the determination of excited-state geometries where the electronic configurations differ greatly from the ground-state reference. Applications are made to closed-shell molecules N2, CO, H2O, the open-shell molecules B2 and CH, and the excited state molecules N2, B2, and BH. We also study the HCN ↔ HNC isomerization and the geometry optimization of hydroxyurea, a molecule which has a significant role in the treatment of sickle-cell anaemia.

Trace-element record in zircons during exhumation from UHP conditions, North-East Greenland Caledonides

USGS Publications Warehouse

McClelland, W.C.; Gilotti, J.A.; Mazdab, F.K.; Wooden, J.L.

2009-01-01

Coesite-bearing zircon formed at ultrahigh-pressure (UHP) conditions share general characteristics of eclogite-facies zircon with trace-element signatures characterized by depleted heavy rare earth elements (HREE), lack of an Eu anomaly, and low Th/ U ratios. Trace-element signatures of zircons from the Caledonian UHP terrane in North-East Greenland were used to examine the possible changes in signature with age during exhumation. Collection and interpretation of age and trace-element analyses of zircon from three samples of quartzofeldspathic gneiss and two leucocratic intrusions were guided by core vs. rim zoning patterns as imaged by cathodoluminesence. Change from igneous to eclogite-facies metamorphic trace-element signature in protolith zircon is characterized by gradual depletion of HREE, whereas newly formed metamorphic rims have flat HREE patterns and REE concentrations that are distinct from the recrystallized inherited cores. The signature associated with eclogite-facies metamorphic zircon is observed in coesite-bearing zircon formed at 358 ?? 4 Ma, metamorphic rims formed at 348 ?? 5 Ma during the initial stages of exhumation, and metamorphic rims formed at 337 ?? 5 Ma. Zircons from a garnet-bearing granite emplaced in the neck of an eclogite boudin and a leucocratic dike that cross-cuts amphibolite-facies structural fabrics have steeply sloping HREE patterns, variably developed negative Eu anomalies, and low Th/U ratios. The granite records initial decompression melting and exhumation at 347 ?? 2 Ma and later zircon rim growth at 329 ?? 5. The leucocratic dike was likely emplaced at amphibolite-facies conditions at 330 ?? 2 Ma, but records additional growth of compositionally similar zircon at 321 ??2 Ma. The difference between the trace-element signature of metamorphic zircon in the gneisses and in part coeval leucocratic intrusions indicates that the zircon signature varies as a function of lithology and context, thus enhancing its ability to aid in the interpretation of U-Pb data and track the exhumation history of UHP terranes. The differences may reflect variation in elemental availability through breakdown reactions in quartzofeldpathic gneiss vs. availability during melt production and/or crystallization. UHP rocks in North-East Greenland began exhumation by 347 ?? 2 Ma, were still at HP eclogite-facies conditions at 337 ?? 5 Ma and were at amphibolite-facies conditions by 330 ?? 2 Ma. ?? 2009 E. Schweizerbart'sche Verlagsbuchhandlung.

Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2016-12-01

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

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

Brabec, Jiri; Lin, Lin; Shao, Meiyue

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires halfmore » of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.« less

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

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

Degroote, M.; Henderson, T. M.; Zhao, J.

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero.more » Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.« less

Numerical Aspects of Atomic Physics: Helium Basis Sets and Matrix Diagonalization

NASA Astrophysics Data System (ADS)

Jentschura, Ulrich; Noble, Jonathan

2014-03-01

We present a matrix diagonalization algorithm for complex symmetric matrices, which can be used in order to determine the resonance energies of auto-ionizing states of comparatively simple quantum many-body systems such as helium. The algorithm is based in multi-precision arithmetic and proceeds via a tridiagonalization of the complex symmetric (not necessarily Hermitian) input matrix using generalized Householder transformations. Example calculations involving so-called PT-symmetric quantum systems lead to reference values which pertain to the imaginary cubic perturbation (the imaginary cubic anharmonic oscillator). We then proceed to novel basis sets for the helium atom and present results for Bethe logarithms in hydrogen and helium, obtained using the enhanced numerical techniques. Some intricacies of ``canned'' algorithms such as those used in LAPACK will be discussed. Our algorithm, for complex symmetric matrices such as those describing cubic resonances after complex scaling, is faster than LAPACK's built-in routines, for specific classes of input matrices. It also offer flexibility in terms of the calculation of the so-called implicit shift, which is used in order to ``pivot'' the system toward the convergence to diagonal form. We conclude with a wider overview.

Rigorous modal analysis of plasmonic nanoresonators

NASA Astrophysics Data System (ADS)

Yan, Wei; Faggiani, Rémi; Lalanne, Philippe

2018-05-01

The specificity of modal-expansion formalisms is their capabilities to model the physical properties in the natural resonance-state basis of the system in question, leading to a transparent interpretation of the numerical results. In electromagnetism, modal-expansion formalisms are routinely used for optical waveguides. In contrast, they are much less mature for analyzing open non-Hermitian systems, such as micro- and nanoresonators. Here, by accounting for material dispersion with auxiliary fields, we considerably extend the capabilities of these formalisms, in terms of computational effectiveness, number of states handled, and range of validity. We implement an efficient finite-element solver to compute the resonance states, and derive closed-form expressions of the modal excitation coefficients for reconstructing the scattered fields. Together, these two achievements allow us to perform rigorous modal analysis of complicated plasmonic resonators, being not limited to a few resonance states, with straightforward physical interpretations and remarkable computation speeds. We particularly show that, when the number of states retained in the expansion increases, convergence toward accurate predictions is achieved, offering a solid theoretical foundation for analyzing important issues, e.g., Fano interference, quenching, and coupling with the continuum, which are critical in nanophotonic research.

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

DOE PAGES

Brabec, Jiri; Lin, Lin; Shao, Meiyue; ...

2015-10-06

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires halfmore » of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.« less

A Unitary ESPRIT Scheme of Joint Angle Estimation for MOTS MIMO Radar

PubMed Central

Wen, Chao; Shi, Guangming

2014-01-01

The transmit array of multi-overlapped-transmit-subarray configured bistatic multiple-input multiple-output (MOTS MIMO) radar is partitioned into a number of overlapped subarrays, which is different from the traditional bistatic MIMO radar. In this paper, a new unitary ESPRIT scheme for joint estimation of the direction of departure (DOD) and the direction of arrival (DOA) for MOTS MIMO radar is proposed. In our method, each overlapped-transmit-subarray (OTS) with the identical effective aperture is regarded as a transmit element and the characteristics that the phase delays between the two OTSs is utilized. First, the measurements corresponding to all the OTSs are partitioned into two groups which have a rotational invariance relationship with each other. Then, the properties of centro-Hermitian matrices and real-valued rotational invariance factors are exploited to double the measurement samples and reduce computational complexity. Finally, the close-formed solution of automatically paired DOAs and DODs of targets is derived in a new manner. The proposed scheme provides increased estimation accuracy with the combination of inherent advantages of MOTS MIMO radar with unitary ESPRIT. Simulation results are presented to demonstrate the effectiveness and advantage of the proposed scheme. PMID:25106023

A unitary ESPRIT scheme of joint angle estimation for MOTS MIMO radar.

PubMed

Wen, Chao; Shi, Guangming

2014-08-07

The transmit array of multi-overlapped-transmit-subarray configured bistatic multiple-input multiple-output (MOTS MIMO) radar is partitioned into a number of overlapped subarrays, which is different from the traditional bistatic MIMO radar. In this paper, a new unitary ESPRIT scheme for joint estimation of the direction of departure (DOD) and the direction of arrival (DOA) for MOTS MIMO radar is proposed. In our method, each overlapped-transmit-subarray (OTS) with the identical effective aperture is regarded as a transmit element and the characteristics that the phase delays between the two OTSs is utilized. First, the measurements corresponding to all the OTSs are partitioned into two groups which have a rotational invariance relationship with each other. Then, the properties of centro-Hermitian matrices and real-valued rotational invariance factors are exploited to double the measurement samples and reduce computational complexity. Finally, the close-formed solution of automatically paired DOAs and DODs of targets is derived in a new manner. The proposed scheme provides increased estimation accuracy with the combination of inherent advantages of MOTS MIMO radar with unitary ESPRIT. Simulation results are presented to demonstrate the effectiveness and advantage of the proposed scheme.

77 FR 22067 - Proposed Collection of Information: Trace Request for Electronic Funds Transfer (EFT) Payment...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-04-12

... Electronic Funds Transfer (EFT) Payment; and Trace Request Direct Deposit AGENCY: Financial Management... collection. By this notice, the Financial Management Service solicits comments concerning forms FMS-150.1... comments to Financial Management Service, 3700 East West Highway, Records and Information Management Branch...

Miniature modified Faraday cup for micro electron beams

DOEpatents

Teruya, Alan T.; Elmer, John W.; Palmer, Todd A.; Walton, Chris C.

2008-05-27

A micro beam Faraday cup assembly includes a refractory metal layer with an odd number of thin, radially positioned traces in this refractory metal layer. Some of the radially positioned traces are located at the edge of the micro modified Faraday cup body and some of the radially positioned traces are located in the central portion of the micro modified Faraday cup body. Each set of traces is connected to a separate data acquisition channel to form multiple independent diagnostic networks. The data obtained from the two diagnostic networks are combined and inputted into a computed tomography algorithm to reconstruct the beam shape, size, and power density distribution.

Magnonic analog of relativistic Zitterbewegung in an antiferromagnetic spin chain

NASA Astrophysics Data System (ADS)

Wang, Weiwei; Gu, Chenjie; Zhou, Yan; Fangohr, Hans

2017-07-01

We theoretically investigate the spin-wave (magnon) excitations in a classical antiferromagnetic spin chain with easy-axis anisotropy. We obtain a Dirac-like equation by linearizing the Landau-Lifshitz-Gilbert equation in this antiferromagnetic system, in contrast to the ferromagnetic system in which a Schrödinger-type equation is derived. The Hamiltonian operator in the Dirac-like equation is a pseudo-Hermitian. We compute and demonstrate relativistic Zitterbewegung (trembling motion) in the antiferromagnetic spin chain by measuring the expectation values of the wave-packet position.

Geometrical Method for the Calculation of Spherical Harmonics up to an Arbitrary Degree and Order

NASA Astrophysics Data System (ADS)

Svehla, D.

2009-12-01

We introduce a novel method for the computation and rotation of spherical harmonics, Legendre polynomials and associated Legendre functions without making use of recursive relations. This novel geometrical approach allows calculation of spherical harmonics without any numerical instability up to an arbitrary degree and order, i.e. up to a degree and order 1e6 and beyond. It is shown, that spherical harmonics can be treated as vectors in Hilbert hyperspace leading to the unitary hermitian rotation matrices with geometric properties.

Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials

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

Aptekarev, Alexander I; Lysov, Vladimir G; Tulyakov, Dmitrii N

2011-02-28

Ensembles of random Hermitian matrices with a distribution measure defined by an anharmonic potential perturbed by an external source are considered. The limiting characteristics of the eigenvalue distribution of the matrices in these ensembles are related to the asymptotic behaviour of a certain system of multiple orthogonal polynomials. Strong asymptotic formulae are derived for this system. As a consequence, for matrices in this ensemble the limit mean eigenvalue density is found, and a variational principle is proposed to characterize this density. Bibliography: 35 titles.

Noisy Spins and the Richardson-Gaudin Model

NASA Astrophysics Data System (ADS)

Rowlands, Daniel A.; Lamacraft, Austen

2018-03-01

We study a system of spins (qubits) coupled to a common noisy environment, each precessing at its own frequency. The correlated noise experienced by the spins implies long-lived correlations that relax only due to the differing frequencies. We use a mapping to a non-Hermitian integrable Richardson-Gaudin model to find the exact spectrum of the quantum master equation in the high-temperature limit and, hence, determine the decay rate. Our solution can be used to evaluate the effect of inhomogeneous splittings on a system of qubits coupled to a common bath.

Tunable χ /PT Symmetry in Noisy Graphene

NASA Astrophysics Data System (ADS)

Silva, E. Frade; Barbosa, A. L. R.; Hussein, M. S.; Ramos, J. G. G. S.

2018-05-01

We investigate the resonant regime of a mesoscopic cavity made of graphene or a doped beam splitter. Using Non-Hermitian Quantum Mechanics, we consider the Bender-Boettcher assumption that a system must obey parity and time reversal symmetry. Therefore, we describe such system by coupling chirality, parity, and time reversal symmetries through the scattering matrix formalism and apply it in the shot noise functions, also derived here. Finally, we show how to achieve the resonant regime only by setting properly the parameters concerning the chirality and the PT symmetry.

Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model

NASA Astrophysics Data System (ADS)

Margarint, Vlad

2018-06-01

We consider Hermitian random band matrices H in d ≥slant 1 dimensions. The matrix elements H_{xy}, indexed by x, y \\in Λ \\subset Z^d, are independent, uniformly distributed random variable if |x-y| is less than the band width W, and zero otherwise. We update the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The result is uniformly in the size |Λ| of the matrix.

Spectral statistics of the uni-modular ensemble

NASA Astrophysics Data System (ADS)

Joyner, Christopher H.; Smilansky, Uzy; Weidenmüller, Hans A.

2017-09-01

We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U(1) , called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a supersymmetric integration method, a combinatorial graph-theoretical analysis and a Brownian motion approach, we are able to derive expressions for 1 / N corrections to the mean spectral moments and also analyse the fluctuations about this mean. By addressing the same ensemble from three different point of view, we can critically compare their relative advantages and derive some new results.

Generalized Choi states and 2-distillability of quantum states

NASA Astrophysics Data System (ADS)

Chen, Lin; Tang, Wai-Shing; Yang, Yu

2018-05-01

We investigate the distillability of bipartite quantum states in terms of positive and completely positive maps. We construct the so-called generalized Choi states and show that it is distillable when it has negative partial transpose. We convert the distillability problem of 2-copy n× n Werner states into the determination of the positivity of an Hermitian matrix. We obtain several sufficient conditions by which the positivity holds. Further, we investigate the case n=3 by the classification of 2× 3× 3 pure states.

Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

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

Jiang, Tongsong, E-mail: jiangtongsong@sina.com; Department of Mathematics, Heze University, Heze, Shandong 274015; Jiang, Ziwu

In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.

Optical Pulling and Pushing Forces in Bilayer P T -Symmetric Structures

NASA Astrophysics Data System (ADS)

Alaee, Rasoul; Christensen, Johan; Kadic, Muamer

2018-01-01

We investigate the optical force exerted on a parity-time-symmetric bilayer made of balanced gain and loss. We show that an asymmetric optical pulling or pushing force can be exerted on this system depending on the direction of impinging light. The optical pulling or pushing force has a direct physical link to the optical characteristics embedded in the non-Hermitian bilayer. Furthermore, we suggest taking advantage of the optically generated asymmetric force to launch vibrations of an arbitrary shape, which is useful for the contactless probing of mechanical deformations.

Synthetic magnetism for photon fluids

NASA Astrophysics Data System (ADS)

Westerberg, N.; Maitland, C.; Faccio, D.; Wilson, K.; Öhberg, P.; Wright, E. M.

2016-08-01

We develop a theory of artificial gauge fields in photon fluids for the cases of both second-order and third-order optical nonlinearities. This applies to weak excitations in the presence of pump fields carrying orbital angular momentum and is thus a type of Bogoliubov theory. The resulting artificial gauge fields experienced by the weak excitations are an interesting generalization of previous cases and reflect the PT-symmetry properties of the underlying non-Hermitian Hamiltonian. We illustrate the observable consequences of the resulting synthetic magnetic fields for examples involving both second-order and third-order nonlinearities.

Quantum simulation of dissipative processes without reservoir engineering

DOE PAGES

Di Candia, R.; Pedernales, J. S.; del Campo, A.; ...

2015-05-29

We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify its accuracy.

Specialised emission pattern of leaf trace in a late Permian (253 million-years old) conifer

PubMed Central

Wei, Hai-Bo; Feng, Zhuo; Yang, Ji-Yuan; Chen, Yu-Xuan; Shen, Jia-Jia; He, Xiao-Yuan

2015-01-01

Leaf traces are important structures in higher plants that connect leaves and the stem vascular system. The anatomy and emission pattern of leaf traces are well studied in extant vascular plants, but remain poorly understood in fossil lineages. We quantitatively analysed the leaf traces in the late Permian conifer Ningxiaites specialis from Northwest China based on serial sections through pith, primary and secondary xylems. A complete leaf traces emission pattern of a conifer is presented for the first time from the late Palaeozoic. Three to five monarch leaf traces are grouped in clusters, arranged in a helical phyllotaxis. The leaf traces in each cluster can be divided into upper, middle and lower portions, and initiate at the pith periphery and cross the wood horizontally. The upper leaf trace increases its diameter during the first growth increment and then diminishes completely, which indicates leaf abscission at the end of the first year. The middle trace immediately bifurcates once or twice to form two or three vascular bundles. The lower trace persists as a single bundle during its entire length. The intricate leaf trace dynamics indicates this fossil plant had a novel evolutionary habit by promoting photosynthetic capability for the matured plant. PMID:26198410

Mise en Scene: Conversion of Scenarios to CSP Traces for the Requirements-to-Design-to-Code Project

NASA Technical Reports Server (NTRS)

Carter. John D.; Gardner, William B.; Rash, James L.; Hinchey, Michael G.

2007-01-01

The "Requirements-to-Design-to-Code" (R2D2C) project at NASA's Goddard Space Flight Center is based on deriving a formal specification expressed in Communicating Sequential Processes (CSP) notation from system requirements supplied in the form of CSP traces. The traces, in turn, are to be extracted from scenarios, a user-friendly medium often used to describe the required behavior of computer systems under development. This work, called Mise en Scene, defines a new scenario medium (Scenario Notation Language, SNL) suitable for control-dominated systems, coupled with a two-stage process for automatic translation of scenarios to a new trace medium (Trace Notation Language, TNL) that encompasses CSP traces. Mise en Scene is offered as an initial solution to the problem of the scenarios-to-traces "D2" phase of R2D2C. A survey of the "scenario" concept and some case studies are also provided.

Meteoritic material on the moon

NASA Technical Reports Server (NTRS)

Morgan, J. W.; Ganapathy, R.; Higuchi, H.; Anders, E.

1974-01-01

Micrometeorites, ancient planetesimal debris from the early intense bombardment, and debris of recent, crater-forming projectiles are discussed and their amounts and compositions have been determined from trace element studies. The micrometeorite component is uniformly distrubuted over the entire lunar surface, but is seen most clearly in mare soils whereas, the ancient component is seen in highland breccias and soils. A few properties of the basin-forming objects are inferred from the trace element data. An attempt is made to reconstruct the bombardment history of the moon from the observation that only basin-forming objects fell on the moon after crustal differentiation. The apparent half-life of basin-forming bodies is close to the calculated value for earth-crossing planetesimals. It is shown that a gap in radiometric ages is expected between the Imbrium and Nectaris impacts, because all 7 basins formed in this interval lie on the farside or east limb.

Highly accurate surface maps from profilometer measurements

NASA Astrophysics Data System (ADS)

Medicus, Kate M.; Nelson, Jessica D.; Mandina, Mike P.

2013-04-01

Many aspheres and free-form optical surfaces are measured using a single line trace profilometer which is limiting because accurate 3D corrections are not possible with the single trace. We show a method to produce an accurate fully 2.5D surface height map when measuring a surface with a profilometer using only 6 traces and without expensive hardware. The 6 traces are taken at varying angular positions of the lens, rotating the part between each trace. The output height map contains low form error only, the first 36 Zernikes. The accuracy of the height map is ±10% of the actual Zernike values and within ±3% of the actual peak to valley number. The calculated Zernike values are affected by errors in the angular positioning, by the centering of the lens, and to a small effect, choices made in the processing algorithm. We have found that the angular positioning of the part should be better than 1?, which is achievable with typical hardware. The centering of the lens is essential to achieving accurate measurements. The part must be centered to within 0.5% of the diameter to achieve accurate results. This value is achievable with care, with an indicator, but the part must be edged to a clean diameter.

Spinel from Apollo 12 Olivine Mare Basalts: Chemical Systematics of Selected Major, Minor, and Trace Elements

NASA Technical Reports Server (NTRS)

Papike, J. J.; Karner, J. M.; Shearer, C. K.; Spilde, M. N.

2002-01-01

Spinels from Apollo 12 Olivine basalts have been studied by Electron and Ion microprobe techniques. The zoning trends of major, minor and trace elements provide new insights into the conditions under which planetary basalts form. Additional information is contained in the original extended abstract.

Using Logistic Approximations of Marginal Trace Lines to Develop Short Assessments

ERIC Educational Resources Information Center

Stucky, Brian D.; Thissen, David; Edelen, Maria Orlando

2013-01-01

Test developers often need to create unidimensional scales from multidimensional data. For item analysis, "marginal trace lines" capture the relation with the general dimension while accounting for nuisance dimensions and may prove to be a useful technique for creating short-form tests. This article describes the computations needed to obtain…

The role of working memory and declarative memory in trace conditioning

PubMed Central

Connor, David A.; Gould, Thomas J.

2017-01-01

Translational assays of cognition that are similarly implemented in both lower and higher-order species, such as rodents and primates, provide a means to reconcile preclinical modeling of psychiatric neuropathology and clinical research. To this end, Pavlovian conditioning has provided a useful tool for investigating cognitive processes in both lab animal models and humans. This review focuses on trace conditioning, a form of Pavlovian conditioning typified by the insertion of a temporal gap (i.e., trace interval) between presentations of a conditioned stimulus (CS) and an unconditioned stimulus (US). This review aims to discuss pre-clinical and clinical work investigating the mnemonic processes recruited for trace conditioning. Much work suggests that trace conditioning involves unique neurocognitive mechanisms to facilitate formation of trace memories in contrast to standard Pavlovian conditioning. For example, the hippocampus and prefrontal cortex (PFC) appear to play critical roles in trace conditioning. Moreover, cognitive mechanistic accounts in human studies suggest that working memory and declarative memory processes are engaged to facilitate formation of trace memories. The aim of this review is to integrate cognitive and neurobiological accounts of trace conditioning from preclinical and clinical studies to examine involvement of working and declarative memory. PMID:27422017

Super-resolution Doppler beam sharpening method using fast iterative adaptive approach-based spectral estimation

NASA Astrophysics Data System (ADS)

Mao, Deqing; Zhang, Yin; Zhang, Yongchao; Huang, Yulin; Yang, Jianyu

2018-01-01

Doppler beam sharpening (DBS) is a critical technology for airborne radar ground mapping in forward-squint region. In conventional DBS technology, the narrow-band Doppler filter groups formed by fast Fourier transform (FFT) method suffer from low spectral resolution and high side lobe levels. The iterative adaptive approach (IAA), based on the weighted least squares (WLS), is applied to the DBS imaging applications, forming narrower Doppler filter groups than the FFT with lower side lobe levels. Regrettably, the IAA is iterative, and requires matrix multiplication and inverse operation when forming the covariance matrix, its inverse and traversing the WLS estimate for each sampling point, resulting in a notably high computational complexity for cubic time. We propose a fast IAA (FIAA)-based super-resolution DBS imaging method, taking advantage of the rich matrix structures of the classical narrow-band filtering. First, we formulate the covariance matrix via the FFT instead of the conventional matrix multiplication operation, based on the typical Fourier structure of the steering matrix. Then, by exploiting the Gohberg-Semencul representation, the inverse of the Toeplitz covariance matrix is computed by the celebrated Levinson-Durbin (LD) and Toeplitz-vector algorithm. Finally, the FFT and fast Toeplitz-vector algorithm are further used to traverse the WLS estimates based on the data-dependent trigonometric polynomials. The method uses the Hermitian feature of the echo autocorrelation matrix R to achieve its fast solution and uses the Toeplitz structure of R to realize its fast inversion. The proposed method enjoys a lower computational complexity without performance loss compared with the conventional IAA-based super-resolution DBS imaging method. The results based on simulations and measured data verify the imaging performance and the operational efficiency.

Asymptotic analysis of the local potential approximation to the Wetterich equation

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Sarkar, Sarben

2018-06-01

This paper reports a study of the nonlinear partial differential equation that arises in the local potential approximation to the Wetterich formulation of the functional renormalization group equation. A cut-off-dependent shift of the potential in this partial differential equation is performed. This shift allows a perturbative asymptotic treatment of the differential equation for large values of the infrared cut-off. To leading order in perturbation theory the differential equation becomes a heat equation, where the sign of the diffusion constant changes as the space-time dimension D passes through 2. When D  <  2, one obtains a forward heat equation whose initial-value problem is well-posed. However, for D  >  2 one obtains a backward heat equation whose initial-value problem is ill-posed. For the special case D  =  1 the asymptotic series for cubic and quartic models is extrapolated to the small infrared-cut-off limit by using Padé techniques. The effective potential thus obtained from the partial differential equation is then used in a Schrödinger-equation setting to study the stability of the ground state. For cubic potentials it is found that this Padé procedure distinguishes between a -symmetric theory and a conventional Hermitian theory (g real). For an theory the effective potential is nonsingular and has a stable ground state but for a conventional theory the effective potential is singular. For a conventional Hermitian theory and a -symmetric theory (g  >  0) the results are similar; the effective potentials in both cases are nonsingular and possess stable ground states.

A Historical Review of Diachrony and Semantic Dimensions of Trace in Neurosciences and Lacanian Psychoanalysis

PubMed Central

Escobar, Carolina; Ansermet, François; Magistretti, Pierre J.

2017-01-01

Experience leaves a trace in the nervous system through plasticity. However, the exact meaning of the mnesic trace is poorly defined in current literature. This article provides a historical review of the term trace in neuroscience and psychoanalysis literature, to highlight two relevant aspects: the diachronic and the semantic dimensions. There has been a general interest in diachrony, or a form of evolution of the trace, but its indissociable semantic dimension remains partially disregarded. Although frequently implied, the diachronic and semantic dimensions of the trace are rarely clearly articulated. We situate this discussion into the classical opposition of syntax, or rules of inscription of the trace in the nervous system, and semantics, or the content of the trace, which takes into consideration the attempt of the human being to build coherence. A general observation is that the study of the term trace follows trends of the thought of the given epoch. This historical analysis also reveals the decay of the idea that the trace is reliable to the experience. From the articulation between neurosciences and psychoanalysis in a historical perspective, this review shows that the trend is to consider trace as a production of the subject, resulting in a permanent rewriting in an attempt to give meaning to the experience. This trend is becoming increasingly evident in light of recent research in neurosciences and psychoanalysis. PMID:28690553

Abundance, distribution and bioavailability of major and trace elements in surface sediments from the Cai River estuary and Nha Trang Bay (South China Sea, Vietnam)

NASA Astrophysics Data System (ADS)

Koukina, S. E.; Lobus, N. V.; Peresypkin, V. I.; Dara, O. M.; Smurov, A. V.

2017-11-01

Major (Si, Al, Fe, Ti, Mg, Ca, Na, K, S, P), minor (Mn) and trace (Li, V, Cr, Co, Ni, Cu, Zn, As, Sr, Zr, Mo, Cd, Ag, Sn, Sb, Cs, Ba, Hg, Pb, Bi and U) elements, their chemical forms and the mineral composition, organic matter (TOC) and carbonates (TIC) in surface sediments from the Cai River estuary and Nha Trang Bay were first determined along the salinity gradient. The abundance and ratio of major and trace elements in surface sediments are discussed in relation to the mineralogy, grain size, depositional conditions, reference background and SQG values. Most trace-element contents are at natural levels and are derived from the composition of rocks and soils in the watershed. A severe enrichment of Ag is most likely derived from metal-rich detrital heavy minerals such as Ag-sulfosalts. Along the salinity gradient, several zones of metal enrichment occur in surface sediments because of the geochemical fractionation of the riverine material. The parts of actually and potentially bioavailable forms (isolated by four single chemical reagent extractions) are most elevated for Mn and Pb (up to 36% and 32% of total content, respectively). The possible anthropogenic input of Pb in the region requires further study. Overall, the most bioavailable parts of trace elements are associated with easily soluble amorphous Fe and Mn oxyhydroxides. The sediments are primarily enriched with bioavailable metal forms in the riverine part of the estuary. Natural (such as turbidities) and human-generated (such as urban and industrial activities) pressures are shown to influence the abundance and speciation of potential contaminants and therefore change their bioavailability in this estuarine system.

Method and apparatus for detecting and measuring trace impurities in flowing gases

DOEpatents

Taylor, Gene W.; Dowdy, Edward J.

1979-01-01

Trace impurities in flowing gases may be detected and measured by a dynamic atomic molecular emission spectrograph utilizing as its energy source the energy transfer reactions of metastable species, atomic or molecular, with the impurities in the flowing gas. An electronically metastable species which maintains a stable afterglow is formed and mixed with the flowing gas in a region downstream from and separate from the region in which the metastable species is formed. Impurity levels are determined quantitatively by the measurement of line and/or band intensity as a function of concentration employing emission spectroscopic techniques.

UAV Communication Management and Coordination for Multitarget Tracking

DTIC Science & Technology

2009-02-26

6.3 Weighted Trace Penalty 16 6.4 Results with WTP for ECTG 17 7 Multiple UAV Case 20 7.1 Extension of WTP 20 7.2 Coordinated sensor motion...growth by a weighted trace penalty ( WTP ) term, which is a product of the current covariancc trace and the minimum distance to observability (MDO) for a...Specifically, the terminal cost or ECTG term using the WTP has the form J(b) = JWTP(b) := iD(s, e) Tfc P\\ (6.1) where 7 is a positive constant, i is the

Method for removing trace pollutants from aqueous solutions

DOEpatents

Silver, Gary L.

1986-01-01

A method of substantially removing a trace metallic contaminant from a liquid containing the same comprises, adding an oxidizing agent to a liquid containing a trace amount of a metallic contaminant of a concentration of up to about 10.sup.-1 ppm, the oxidizing agent being one which oxidizes the contaminant to form an oxidized product which is insoluble in the liquid and precipitates therefrom, and the conditions of the addition being selected to ensure that the precipitation of the oxidized product is homogeneous, and separating the homogeneously precipitated product from the liquid.

Trace element geochemistry of Archean volcanic rocks

NASA Technical Reports Server (NTRS)

Jahn, B.-M.; Shih, C.-Y.; Murthy, V. R.

1974-01-01

The K, Rb, Sr, Ba and rare-earth-element contents of some Archean volcanic rocks from the Vermilion greenstone belt, northeast Minnesota, were determined by the isotopic dilution method. The characteristics of trace element abundances, supported by the field occurrences and major element chemistry, suggest that these volcanic rocks were formed in an ancient island arc system.

Performance Factors Analysis -- A New Alternative to Knowledge Tracing

ERIC Educational Resources Information Center

Pavlik, Philip I., Jr.; Cen, Hao; Koedinger, Kenneth R.

2009-01-01

Knowledge tracing (KT)[1] has been used in various forms for adaptive computerized instruction for more than 40 years. However, despite its long history of application, it is difficult to use in domain model search procedures, has not been used to capture learning where multiple skills are needed to perform a single action, and has not been used…

WET EFFLUENT PARALLEL PLATE DIFFUSION DENUDER COUPLED CAPILLARY ION CHROMATOGRAPH FOR THE DETERMINATION OF ATMOSPHERIC TRACE GASES. (R825344)

EPA Science Inventory

We describe an inexpensive, compact parallel plate diffusion denuder coupled capillary IC system for the determination of soluble ionogenic atmospheric trace gases. The active sampling area (0.6×10 cm) of the denuder is formed in a novel manner by thermally bonding silica ge...

Forms of trace arsenic, cesium, cadmium, and lead transported into river water for the irrigation of Japanese paddy rice fields

NASA Astrophysics Data System (ADS)

Nakaya, Shinji; Chi, Hai; Muroda, Kengo; Masuda, Harue

2018-06-01

In this study, we focus on the behavior of geogenic, toxic trace elements, particularly As, Cs, Cd, and Pb, during their transportation in two rivers for irrigation commonly used in monsoon Asia; one river originates from an active volcano, Mt. Asama, and the other originates from a currently inactive volcano, Yatsugatake Mountains in Nagano, Japan. These rivers were investigated to understand the role of river water as a pollutant of rice and other aquatic plants (via irrigation) and aquatic animals. The results indicated that the behavior of toxic trace elements in river water are likely controlled by their interactions with particulate Fe, Al, and Ti compounds. The majority of Pb and Cd is transported as particulate matter with Fe, Al, and Ti, while the majority of As is transported in the dissolved form, predominantly as arsenate, with low abundance of particulate matter. Cs is transported either as the dissolved form or as particulate matter in both rivers. The investigated elements are transported in the rivers as particulate and dissolved forms, and the ratio of these forms is controlled by the pH and presence of particulate Fe, Al, and Ti phases in the river water. With respect to Cs in both rivers, the parameter governing the concentration and transportation of Cs, in the bimodal form (i.e., particulate and dissolved forms), through the river possibly shifts from sorption to pH by particulate Fe-Al-Ti, according to the abrupt increase in the concentration of Cs in the river. The chemical attraction of particulate Fe-Al-Ti for Cs is weaker than that for Pb and Cd, indicating that the lower electronegativity of Cs weakens the chemical attraction on a colloid for the competitive sorption with the other trace elements. The different relationships between As and Fe in the river and in the irrigation water and soil water, as well as those in paddy rice, suggested that As in paddy rice is not directly derived from As in the irrigation water from the river under flooding.

BUTIMBA: Intensifying the Hunt for Child TB in Swaziland through Household Contact Tracing

PubMed Central

Alonso Ustero, Pilar; Golin, Rachel; Anabwani, Florence; Mzileni, Bulisile; Sikhondze, Welile; Stevens, Robert

2017-01-01

Background Limited data exists to inform contact tracing guidelines in children and HIV-affected populations. We evaluated the yield and additionality of household contact and source case investigations in Swaziland, a TB/HIV high-burden setting, while prioritizing identification of childhood TB. Methods In partnership with 7 local TB clinics, we implemented standardized contact tracing of index cases (IC) receiving TB treatment. Prioritizing child contacts and HIV-affected households, screening officers screened contacts for TB symptoms and to identify risk factors associated with TB. We ascertained factors moderating the yield of contact tracing and measured the impact of our program by additional notifications. Results From March 2013 to November 2015, 3,258 ICs (54% bacteriologically confirmed; 70% HIV-infected; 85% adults) were enrolled leading to evaluation of 12,175 contacts (median age 18 years, IQR 24–42; 45% children; 9% HIV-infected). Among contacts, 196 TB cases (56% bacteriologically confirmed) were diagnosed resulting in a program yield of 1.6% for all forms of TB. The number needed to screen (NNS) to identify a bacteriologically confirmed TB case or all forms TB case traced from a child IC <5 years was respectively 62% and 40% greater than the NNS for tracing from an adult IC. In year one, we demonstrated a 32% increase in detection of bacteriologically confirmed child TB. Contacts were more likely to have TB if <5 years (OR = 2.0), HIV-infected (OR = 4.9), reporting ≥1 TB symptoms (OR = 7.7), and sharing a bed (OR = 1.7) or home (OR = 1.4) with the IC. There was a 1.4 fold increased chance of detecting a TB case in households known to be HIV-affected. Conclusion Contact tracing prioritizing children is not only feasible in a TB/HIV high-burden setting but contributes to overall case detection. Our findings support WHO guidelines prioritizing contact tracing among children and HIV-infected populations while highlighting potential to integrate TB and HIV case finding. PMID:28107473

Penetrative trace fossils from the late Ediacaran of Mongolia: early onset of the agronomic revolution.

PubMed

Oji, Tatsuo; Dornbos, Stephen Q; Yada, Keigo; Hasegawa, Hitoshi; Gonchigdorj, Sersmaa; Mochizuki, Takafumi; Takayanagi, Hideko; Iryu, Yasufumi

2018-02-01

The Cambrian radiation of complex animals includes a dramatic increase in the depth and intensity of bioturbation in seafloor sediment known as the 'agronomic revolution'. This bioturbation transition was coupled with a shift in dominant trace fossil style from horizontal surficial traces in the late Precambrian to vertically penetrative trace fossils in the Cambrian. Here we show the existence of the first vertically penetrative trace fossils from the latest Ediacaran: dense occurrences of the U-shaped trace fossil Arenicolites from late Precambrian marine carbonates of Western Mongolia. Their Ediacaran age is established through stable carbon isotope chemostratigraphy and their occurrence stratigraphically below the first appearance of the trace fossil Treptichnus pedum . These Arenicolites are large in diameter, penetrate down to at least 4 cm into the sediment, and were presumably formed by the activity of bilaterian animals. They are preserved commonly as paired circular openings on bedding planes with maximum diameters ranging up to almost 1 cm, and as U- and J-shaped tubes in vertical sections of beds. Discovery of these complex penetrative trace fossils demonstrates that the agronomic revolution started earlier than previously considered.

Penetrative trace fossils from the late Ediacaran of Mongolia: early onset of the agronomic revolution

PubMed Central

Dornbos, Stephen Q.; Yada, Keigo; Hasegawa, Hitoshi; Gonchigdorj, Sersmaa; Mochizuki, Takafumi; Takayanagi, Hideko; Iryu, Yasufumi

2018-01-01

The Cambrian radiation of complex animals includes a dramatic increase in the depth and intensity of bioturbation in seafloor sediment known as the ‘agronomic revolution’. This bioturbation transition was coupled with a shift in dominant trace fossil style from horizontal surficial traces in the late Precambrian to vertically penetrative trace fossils in the Cambrian. Here we show the existence of the first vertically penetrative trace fossils from the latest Ediacaran: dense occurrences of the U-shaped trace fossil Arenicolites from late Precambrian marine carbonates of Western Mongolia. Their Ediacaran age is established through stable carbon isotope chemostratigraphy and their occurrence stratigraphically below the first appearance of the trace fossil Treptichnus pedum. These Arenicolites are large in diameter, penetrate down to at least 4 cm into the sediment, and were presumably formed by the activity of bilaterian animals. They are preserved commonly as paired circular openings on bedding planes with maximum diameters ranging up to almost 1 cm, and as U- and J-shaped tubes in vertical sections of beds. Discovery of these complex penetrative trace fossils demonstrates that the agronomic revolution started earlier than previously considered. PMID:29515908

Penetrative trace fossils from the late Ediacaran of Mongolia: early onset of the agronomic revolution

NASA Astrophysics Data System (ADS)

Oji, Tatsuo; Dornbos, Stephen Q.; Yada, Keigo; Hasegawa, Hitoshi; Gonchigdorj, Sersmaa; Mochizuki, Takafumi; Takayanagi, Hideko; Iryu, Yasufumi

2018-02-01

The Cambrian radiation of complex animals includes a dramatic increase in the depth and intensity of bioturbation in seafloor sediment known as the `agronomic revolution'. This bioturbation transition was coupled with a shift in dominant trace fossil style from horizontal surficial traces in the late Precambrian to vertically penetrative trace fossils in the Cambrian. Here we show the existence of the first vertically penetrative trace fossils from the latest Ediacaran: dense occurrences of the U-shaped trace fossil Arenicolites from late Precambrian marine carbonates of Western Mongolia. Their Ediacaran age is established through stable carbon isotope chemostratigraphy and their occurrence stratigraphically below the first appearance of the trace fossil Treptichnus pedum. These Arenicolites are large in diameter, penetrate down to at least 4 cm into the sediment, and were presumably formed by the activity of bilaterian animals. They are preserved commonly as paired circular openings on bedding planes with maximum diameters ranging up to almost 1 cm, and as U- and J-shaped tubes in vertical sections of beds. Discovery of these complex penetrative trace fossils demonstrates that the agronomic revolution started earlier than previously considered.

Risks of using EDTA as an agent for trace metals dosing in anaerobic digestion of olive mill solid waste.

PubMed

Serrano, A; Pinto-Ibieta, F; Braga, A F M; Jeison, D; Borja, R; Fermoso, F G

2017-12-01

Low concentrations of trace elements in many organic wastes recommend their supplementation in order to avoid potential limitations. Different chelating agents have been used to ensure an adequate trace metal pool in the soluble fraction, by forming dissolved complexes. Ethylenediaminetetraacetic acid (EDTA) is probably the most common, although several negative effects could be associated with its usage. Biomethane potential tests were performed using Olive Mill Solid Waste as the substrate, supplementing different combinations of Fe, Co, Ni, Ba, always under the presence of EDTA. Results show that Ni and Co slightly recovered biodegradability. However, Ba supplementation resulted in worsening the methane yield coefficient in all cases. High concentration of EDTA led to decrease in the activity of anaerobic digestion. High availability of EDTA induces the capture of trace metals like Co or Ni, key trace metals for anaerobic biomass activity. While supplementing trace metals, the addition of Ba and/or EDTA must be carefully considered.

Genetic lineage tracing identifies in situ Kit-expressing cardiomyocytes

PubMed Central

Liu, Qiaozhen; Yang, Rui; Huang, Xiuzhen; Zhang, Hui; He, Lingjuan; Zhang, Libo; Tian, Xueying; Nie, Yu; Hu, Shengshou; Yan, Yan; Zhang, Li; Qiao, Zengyong; Wang, Qing-Dong; Lui, Kathy O; Zhou, Bin

2016-01-01

Cardiac cells marked by c-Kit or Kit, dubbed cardiac stem cells (CSCs), are in clinical trials to investigate their ability to stimulate cardiac regeneration and repair. These studies were initially motivated by the purported cardiogenic activity of these cells. Recent lineage tracing studies using Kit promoter to drive expression of the inducible Cre recombinase showed that these CSCs had highly limited cardiogenic activity, inadequate to support efficient cardiac repair. Here we reassess the lineage tracing data by investigating the identity of cells immediately after Cre labeling. Our instant lineage tracing approach identifies Kit-expressing cardiomyocytes, which are labeled immediately after tamoxifen induction. In combination with long-term lineage tracing experiments, these data reveal that the large majority of long-term labeled cardiomyocytes are pre-existing Kit-expressing cardiomyocytes rather than cardiomyocytes formed de novo from CSCs. This study presents a new interpretation for the contribution of Kit+ cells to cardiomyocytes and shows that Kit genetic lineage tracing over-estimates the cardiogenic activity of Kit+ CSCs. PMID:26634606

Are memory traces localized or distributed?

PubMed

Thompson, R F

1991-01-01

Evidence supports the view that "memory traces" are formed in the hippocampus and in the cerebellum in classical conditioning of discrete behavioral responses (e.g. eyeblink conditioning). In the hippocampus, learning results in long-lasting increases in excitability of pyramidal neurons that appear to be localized to these neurons (i.e. changes in membrane properties and receptor function). However, these learning-altered pyramidal neurons are distributed widely throughout CA3 and CA1. Although it plays a key role in certain aspects of classical conditioning, the hippocampus is not necessary for learning and memory of the basic conditioned responses. The cerebellum and its associated brain stem circuitry, on the other hand, does appear to be essential (necessary and sufficient) for learning and memory of the conditioned response. Evidence to date is most consistent with a localized trace in the interpositus nucleus and multiple localized traces in cerebellar cortex, each involving relatively large ensembles of neurons. Perhaps "procedural" memory traces are relatively localized and "declarative" traces more widely distributed.

Newly-formed emotional memories guide selective attention processes: Evidence from event-related potentials.

PubMed

Schupp, Harald T; Kirmse, Ursula; Schmälzle, Ralf; Flaisch, Tobias; Renner, Britta

2016-06-20

Emotional cues can guide selective attention processes. However, emotional stimuli can both activate long-term memory representations reflecting general world knowledge and engage newly formed memory representations representing specific knowledge from the immediate past. Here, the self-completion feature of associative memory was utilized to assess the regulation of attention processes by newly-formed emotional memory. First, new memory representations were formed by presenting pictures depicting a person either in an erotic pose or as a portrait. Afterwards, to activate newly-built memory traces, edited pictures were presented showing only the head region of the person. ERP recordings revealed the emotional regulation of attention by newly-formed memories. Specifically, edited pictures from the erotic compared to the portrait category elicited an early posterior negativity and late positive potential, similar to the findings observed for the original pictures. A control condition showed that the effect was dependent on newly-formed memory traces. Given the large number of new memories formed each day, they presumably make an important contribution to the regulation of attention in everyday life.

Newly-formed emotional memories guide selective attention processes: Evidence from event-related potentials

PubMed Central

Schupp, Harald T.; Kirmse, Ursula; Schmälzle, Ralf; Flaisch, Tobias; Renner, Britta

2016-01-01

Emotional cues can guide selective attention processes. However, emotional stimuli can both activate long-term memory representations reflecting general world knowledge and engage newly formed memory representations representing specific knowledge from the immediate past. Here, the self-completion feature of associative memory was utilized to assess the regulation of attention processes by newly-formed emotional memory. First, new memory representations were formed by presenting pictures depicting a person either in an erotic pose or as a portrait. Afterwards, to activate newly-built memory traces, edited pictures were presented showing only the head region of the person. ERP recordings revealed the emotional regulation of attention by newly-formed memories. Specifically, edited pictures from the erotic compared to the portrait category elicited an early posterior negativity and late positive potential, similar to the findings observed for the original pictures. A control condition showed that the effect was dependent on newly-formed memory traces. Given the large number of new memories formed each day, they presumably make an important contribution to the regulation of attention in everyday life. PMID:27321471

Cycling of oxyanion-forming trace elements in groundwaters from a freshwater deltaic marsh

NASA Astrophysics Data System (ADS)

Telfeyan, Katherine; Breaux, Alexander; Kim, Jihyuk; Kolker, Alexander S.; Cable, Jaye E.; Johannesson, Karen H.

2018-05-01

Pore waters and surface waters were collected from a freshwater system in southeastern Louisiana to investigate the geochemical cycling of oxyanion-forming trace elements (i.e., Mo, W, As, V). A small bayou (Bayou Fortier) receives input from a connecting lake (Lac des Allemands) and groundwater input at the head approximately 5 km directly south of the Mississippi River. Marsh groundwaters exchange with bayou surface water but are otherwise relatively isolated from outside hydrologic forcings, such as tides, storms, and effects from local navigation canals. Rather, redox processes in the marsh groundwaters appear to drive changes in trace element concentrations. Elevated dissolved S(-II) concentrations in marsh groundwaters suggest greater reducing conditions in the late fall and winter as compared to the spring and late summer. The data suggest that reducing conditions in marsh groundwaters initiate the dissolution of Fe(III)/Mn(IV) oxide/hydroxide minerals, which releases adsorbed and/or co-precipitated trace elements into solution. Once in solution, the fate of these elements is determined by complexation with aqueous species and precipitation with iron sulfide minerals. The trace elements remain soluble in the presence of Fe(III)- and SO42-- reducing conditions, suggesting that either kinetic limitations or complexation with aqueous ligands obfuscates the correlation between V and Mo sequestration in sediments with reducing or euxinic conditions.

PT -symmetric currents of a Bose-Einstein condensate in a triple well

NASA Astrophysics Data System (ADS)

Haag, Daniel; Dast, Dennis; Cartarius, Holger; Wunner, Günter

2015-11-01

We study the case of PT -symmetric perturbations of Hermitian Hamiltonians with degenerate eigenvalues using the example of a triple-well system. The degeneracy complicates the question of whether or not a stationary current through such a system can be established, i.e., whether or not the PT -symmetric states are stable. It is shown that this is only the case for perturbations that do not couple to any of the degenerate states. The physical explanation for the inhibition of stable currents is discussed. However, introducing an on-site interaction restores the capability to support stable currents.

Harnessing molecular excited states with Lanczos chains.

PubMed

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-24

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Survey of methods for calculating sensitivity of general eigenproblems

NASA Technical Reports Server (NTRS)

Murthy, Durbha V.; Haftka, Raphael T.

1987-01-01

A survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non-Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.

Hybrid normed ideal perturbations of n-tuples of operators I

NASA Astrophysics Data System (ADS)

Voiculescu, Dan-Virgil

2018-06-01

In hybrid normed ideal perturbations of n-tuples of operators, the normed ideal is allowed to vary with the component operators. We begin extending to this setting the machinery we developed for normed ideal perturbations based on the modulus of quasicentral approximation and an adaptation of our non-commutative generalization of the Weyl-von Neumann theorem. For commuting n-tuples of hermitian operators, the modulus of quasicentral approximation remains essentially the same when Cn- is replaced by a hybrid n-tuple Cp1,…- , … , Cpn- , p1-1 + ⋯ + pn-1 = 1. The proof involves singular integrals of mixed homogeneity.

The Quantum Phase-Dynamical Properties of the Squeezed Vacuum State Intensity-Couple Interacting with the Atom

NASA Technical Reports Server (NTRS)

Fan, An-Fu; Sun, Nian-Chun; Zhou, Xin

1996-01-01

The Phase-dynamical properties of the squeezed vacuum state intensity-couple interacting with the two-level atom in an ideal cavity are studied using the Hermitian phase operator formalism. Exact general expressions for the phase distribution and the associated expectation value and variance of the phase operator have been derived. we have also obtained the analytic results of the phase variance for two special cases-weakly and strongly squeezed vacuum. The results calculated numerically show that squeezing has a significant effect on the phase properties of squeezed vacuum.

Non-Hermitian engineering of single mode two dimensional laser arrays

PubMed Central

Teimourpour, Mohammad H.; Ge, Li; Christodoulides, Demetrios N.; El-Ganainy, Ramy

2016-01-01

A new scheme for building two dimensional laser arrays that operate in the single supermode regime is proposed. This is done by introducing an optical coupling between the laser array and lossy pseudo-isospectral chains of photonic resonators. The spectrum of this discrete reservoir is tailored to suppress all the supermodes of the main array except the fundamental one. This spectral engineering is facilitated by employing the Householder transformation in conjunction with discrete supersymmetry. The proposed scheme is general and can in principle be used in different platforms such as VCSEL arrays and photonic crystal laser arrays. PMID:27698355

Relativistic Coulomb Problem for Z Larger than 137

NASA Astrophysics Data System (ADS)

Alhaidari, A. D.

We propose a relativistic one-parameter Hermitian theory for the Coulomb problem with an electric charge greater than 137. In the nonrelativistic limit, the theory becomes identical to the Schrödinger-Coulomb problem for all Z. Moreover, it agrees with the Dirac-Coulomb problem to order (αZ)2, where α is the fine structure constant. The vacuum in the theory is stable and does not suffer from the "charged vacuum" problem for all Z. Moreover, transition between positive and negative energy states could be eliminated. The relativistic bound states energy spectrum and corresponding spinor wave functions are obtained.

Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism

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

Ramos, J. J.; White, R. L.

The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are then given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.

Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential.

PubMed

Akemann, G; Bloch, J; Shifrin, L; Wettig, T

2008-01-25

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.

Nonlinear behavior of shells of revolution under cyclic loading.

NASA Technical Reports Server (NTRS)

Levine, H. S.; Armen, H., Jr.; Winter, R.; Pifko, A.

1973-01-01

A large deflection elastic-plastic analysis is presented applicable to orthotropic axisymmetric plates and shells of revolution subjected to monotonic and cyclic loading conditions. The analysis is based on the finite-element method. It employs a new higher order, fully compatible, doubly curved orthotropic shell-of-revolution element using cubic Hermitian expansions for both meridional and normal displacements. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening theory, which predicts an ideal Bauschinger effect. Numerous sample problems involving monotonic and cyclic loading conditions are analyzed.

Calculation of transmission probability by solving an eigenvalue problem

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Varga, Kálmán

2010-11-01

The electron transmission probability in nanodevices is calculated by solving an eigenvalue problem. The eigenvalues are the transmission probabilities and the number of nonzero eigenvalues is equal to the number of open quantum transmission eigenchannels. The number of open eigenchannels is typically a few dozen at most, thus the computational cost amounts to the calculation of a few outer eigenvalues of a complex Hermitian matrix (the transmission matrix). The method is implemented on a real space grid basis providing an alternative to localized atomic orbital based quantum transport calculations. Numerical examples are presented to illustrate the efficiency of the method.

Harnessing molecular excited states with Lanczos chains

NASA Astrophysics Data System (ADS)

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O.; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-01

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism

DOE PAGES

Ramos, J. J.; White, R. L.

2018-03-01

The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are then given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.

Base norms and discrimination of generalized quantum channels

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

Jenčová, A.

2014-02-15

We introduce and study norms in the space of hermitian matrices, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels, and networks. We further introduce generalized quantum decision problems and show that the maximal average payoffs of decision procedures are again given by these norms. We also study optimality of decision procedures, in particular, we obtain a necessary and sufficient condition under which an optimal 1-tester for discrimination of quantum channels exists, such that the input state is maximally entangled.

Electric discharge for treatment of trace contaminants

NASA Technical Reports Server (NTRS)

Flamm, D. L.; Wydeven, T. J. (Inventor)

1978-01-01

A radio frequency glow discharge reactor is described for removing trace oxidizable contaminants from an oxygen bearing atmosphere. The reaction chamber is defined by an inner metal electrode facing a dielectric backed by an outer conductive electrode. In one embodiment, a conductive liquid forms the conductor of an outer electrode and cools the dielectric. A resonator coupled to a variable radio frequency source generates the high voltages for creating a glow discharge in the chamber at a predetermined pressure whereby the trace contaminants are oxidized into a few simple non-toxic products that may be easily recovered. The corresponding process for removal of trace contaminants from an oxygen-bearing atmosphere with high efficiency independent of the concentration level is also disclosed.

[Temporal changes in conscious and unconscious trace phenomena in six to seven-year-old children].

PubMed

Fedotchev, A I

1975-01-01

Development in time of unconscious trace reactions as well as a change in the time of reproduction of verbal material in natural conditions was studied by the conditioned reflex to time method on 107 school children aged from six to seven years and on 35 subjects of the same age from a kindergarten. It has been found that in schoolchildren the transfer of trace reactions to long-term storage is completed faster, and their voluntary acts in the course of conscious reproduction of an interstimuli intervals are more adequate than in the kindergarten children of the same age. The trace phenomena formed in natural conditions and in the laboratory experiment develop in time in a similar way. The change in time of conscious trace phenomena is of a more complex nature than of the unconscious phenomena. The practical significance of the data obtained is noted.

Outlines of a multiple trace theory of temporal preparation.

PubMed

Los, Sander A; Kruijne, Wouter; Meeter, Martijn

2014-01-01

We outline a new multiple trace theory of temporal preparation (MTP), which accounts for behavior in reaction time (RT) tasks in which the participant is presented with a warning stimulus (S1) followed by a target stimulus (S2) that requires a speeded response. The theory assumes that during the foreperiod (FP; the S1-S2 interval) inhibition is applied to prevent premature response, while a wave of activation occurs upon the presentation of S2. On each trial, these actions are stored in a separate memory trace, which, jointly with earlier formed memory traces, starts contributing to preparation on subsequent trials. We show that MTP accounts for classic effects in temporal preparation, including mean RT-FP functions observed under a variety of FP distributions and asymmetric sequential effects. We discuss the advantages of MTP over other accounts of these effects (trace-conditioning and hazard-based explanations) and suggest a critical experiment to empirically distinguish among them.

Consumer-producer relationships for trace metals in Chorthippus brunneus (Thunberg. )

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

Johnson, M.S.

1986-08-01

The behavior of trace metals in terrestrial food chains is a subject of ecological interest, particularly in polluted environments where the potential exists for bioconcentration of metals known to be essential in trace amounts for normal plant and animal metabolism, as well as those with no known metabolic function but recognized toxicological properties. Laboratory studies of food chain relationships afford a means by which direct comparisons can be made between trace metals as a basis for interpretation of data collected from wild plant and animal populations. This study compares the behavior of three trace elements, copper, zinc and cadmium, inmore » terms of their assimilation under experimental conditions by the herbivorous common field grasshopper, Chorthippus brunneus (Thunberg.). This voracious orthopteran is widely distributed in Britain and is particularly prominent in the restricted invertebrate community of some metal smelter-affected grasslands where it forms important seasonal prey for insectivorous small mammals.« less

Multi-Dimensional Damage Detection

NASA Technical Reports Server (NTRS)

Gibson, Tracy L. (Inventor); Williams, Martha K. (Inventor); Roberson, Luke B. (Inventor); Lewis, Mark E. (Inventor); Snyder, Sarah J. (Inventor); Medelius, Pedro J. (Inventor)

2016-01-01

Methods and systems may provide for a structure having a plurality of interconnected panels, wherein each panel has a plurality of detection layers separated from one another by one or more non-detection layers. The plurality of detection layers may form a grid of conductive traces. Additionally, a monitor may be coupled to each grid of conductive traces, wherein the monitor is configured to detect damage to the plurality of interconnected panels in response to an electrical property change with respect to one or more of the conductive traces. In one example, the structure is part of an inflatable space platform such as a spacecraft or habitat.

Further developments in oxidation of methane traces with radiofrequency discharge

NASA Technical Reports Server (NTRS)

Flamm, D. L.; Wydeven, T. J.

1977-01-01

The radiofrequency discharge, previously shown to oxidize trace levels of methane in oxygen, was studied with contaminated air at 50, 600, and 760 torr. As with oxygen, the concentration of methane traces could be reduced by several orders of magnitude, and no organic reaction products were detected in the effluent; however, substantial concentrations of NOx (0.1-6%) were formed during treatment. The concentration of NOx was decreased by using a large diameter electrode. There is evidence that the process will oxidize N2 and NO as well as organic impurities in oxygen or oxygen/inert gas atmospheres.

On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for C*-Dynamical Systems

NASA Astrophysics Data System (ADS)

Fathizadeh, Farzad; Gabriel, Olivier

2016-02-01

The analog of the Chern-Gauss-Bonnet theorem is studied for a C^*-dynamical system consisting of a C^*-algebra A equipped with an ergodic action of a compact Lie group G. The structure of the Lie algebra g of G is used to interpret the Chevalley-Eilenberg complex with coefficients in the smooth subalgebra A subset A as noncommutative differential forms on the dynamical system. We conformally perturb the standard metric, which is associated with the unique G-invariant state on A, by means of a Weyl conformal factor given by a positive invertible element of the algebra, and consider the Hermitian structure that it induces on the complex. A Hodge decomposition theorem is proved, which allows us to relate the Euler characteristic of the complex to the index properties of a Hodge-de Rham operator for the perturbed metric. This operator, which is shown to be selfadjoint, is a key ingredient in our construction of a spectral triple on A and a twisted spectral triple on its opposite algebra. The conformal invariance of the Euler characteristic is interpreted as an indication of the Chern-Gauss-Bonnet theorem in this setting. The spectral triples encoding the conformally perturbed metrics are shown to enjoy the same spectral summability properties as the unperturbed case.

Heavy and Light Quarks with Lattice Chiral Fermions

NASA Astrophysics Data System (ADS)

Liu, K. F.; Dong, S. J.

The feasibility of using lattice chiral fermions which are free of O(a) errors for both the heavy and light quarks is examined. The fact that the effective quark propagators in these fermions have the same form as that in the continuum with the quark mass being only an additive parameter to a chirally symmetric anti-Hermitian Dirac operator is highlighted. This implies that there is no distinction between the heavy and light quarks and no mass dependent tuning of the action or operators as long as the discretization error O(m2a2) is negligible. Using the overlap fermion, we find that the O(m2a2) (and O(ma2)) errors in the dispersion relations of the pseudoscalar and vector mesons and the renormalization of the axial-vector current and scalar density are small. This suggests that the applicable range of ma may be extended to ~0.56 with only 5% error, which is a factor of ~2.4 larger than the corresponding range of the improved Wilson action. We show that the generalized Gell-Mann-Oakes-Renner relation with unequal masses can be utilized to determine the finite ma corrections in the renormalization of the matrix elements for the heavy-light decay constants and semileptonic decay constants of the B/D meson.

Spectral and entropic characterizations of Wigner functions: applications to model vibrational systems.

PubMed

Luzanov, A V

2008-09-07

The Wigner function for the pure quantum states is used as an integral kernel of the non-Hermitian operator K, to which the standard singular value decomposition (SVD) is applied. It provides a set of the squared singular values treated as probabilities of the individual phase-space processes, the latter being described by eigenfunctions of KK(+) (for coordinate variables) and K(+)K (for momentum variables). Such a SVD representation is employed to obviate the well-known difficulties in the definition of the phase-space entropy measures in terms of the Wigner function that usually allows negative values. In particular, the new measures of nonclassicality are constructed in the form that automatically satisfies additivity for systems composed of noninteracting parts. Furthermore, the emphasis is given on the geometrical interpretation of the full entropy measure as the effective phase-space volume in the Wigner picture of quantum mechanics. The approach is exemplified by considering some generic vibrational systems. Specifically, for eigenstates of the harmonic oscillator and a superposition of coherent states, the singular value spectrum is evaluated analytically. Numerical computations are given for the nonlinear problems (the Morse and double well oscillators, and the Henon-Heiles system). We also discuss the difficulties in implementation of a similar technique for electronic problems.

A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

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

Haut, T. S.; Babb, T.; Martinsson, P. G.

2015-06-16

Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existingmore » methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.« less

Rule-Based Runtime Verification

NASA Technical Reports Server (NTRS)

Barringer, Howard; Goldberg, Allen; Havelund, Klaus; Sen, Koushik

2003-01-01

We present a rule-based framework for defining and implementing finite trace monitoring logics, including future and past time temporal logic, extended regular expressions, real-time logics, interval logics, forms of quantified temporal logics, and so on. Our logic, EAGLE, is implemented as a Java library and involves novel techniques for rule definition, manipulation and execution. Monitoring is done on a state-by-state basis, without storing the execution trace.

Reverse ray tracing for transformation optics.

PubMed

Hu, Chia-Yu; Lin, Chun-Hung

2015-06-29

Ray tracing is an important technique for predicting optical system performance. In the field of transformation optics, the Hamiltonian equations of motion for ray tracing are well known. The numerical solutions to the Hamiltonian equations of motion are affected by the complexities of the inhomogeneous and anisotropic indices of the optical device. Based on our knowledge, no previous work has been conducted on ray tracing for transformation optics with extreme inhomogeneity and anisotropicity. In this study, we present the use of 3D reverse ray tracing in transformation optics. The reverse ray tracing is derived from Fermat's principle based on a sweeping method instead of finding the full solution to ordinary differential equations. The sweeping method is employed to obtain the eikonal function. The wave vectors are then obtained from the gradient of that eikonal function map in the transformed space to acquire the illuminance. Because only the rays in the points of interest have to be traced, the reverse ray tracing provides an efficient approach to investigate the illuminance of a system. This approach is useful in any form of transformation optics where the material property tensor is a symmetric positive definite matrix. The performance and analysis of three transformation optics with inhomogeneous and anisotropic indices are explored. The ray trajectories and illuminances in these demonstration cases are successfully solved by the proposed reverse ray tracing method.

Distribution of arsenic, selenium, and other trace elements in high pyrite Appalachian coals: evidence for multiple episodes of pyrite formation

USGS Publications Warehouse

Diehl, S.F.; Goldhaber, M.B.; Koenig, A.E.; Lowers, H.A.; Ruppert, L.F.

2012-01-01

Pennsylvanian coals in the Appalachian Basin host pyrite that is locally enriched in potentially toxic trace elements such as As, Se, Hg, Pb, and Ni. A comparison of pyrite-rich coals from northwestern Alabama, eastern Kentucky, and West Virginia reveals differences in concentrations and mode of occurrence of trace elements in pyrite. Pyrite occurs as framboids, dendrites, or in massive crystalline form in cell lumens or crosscutting veins. Metal concentrations in pyrite vary over all scales, from microscopic to mine to regional, because trace elements are inhomogeneously distributed in the different morphological forms of pyrite, and in the multiple generations of sulfide mineral precipitates. Early diagenetic framboidal pyrite is usually depleted in As, Se, and Hg, and enriched in Pb and Ni, compared to other pyrite forms. In dendritic pyrite, maps of As distribution show a chemical gradient from As-rich centers to As-poor distal branches, whereas Se concentrations are highest at the distal edges of the branches. Massive crystalline pyrite that fills veins is composed of several generations of sulfide minerals. Pyrite in late-stage veins commonly exhibits As-rich growth zones, indicating a probable epigenetic hydrothermal origin. Selenium is concentrated at the distal edges of veins. A positive correlation of As and Se in pyrite veins from Kentucky coals, and of As and Hg in pyrite-filled veins from Alabama coals, suggests coprecipitation of these elements from the same fluid. In the Kentucky coal samples (n = 18), As and Se contents in pyrite-filled veins average 4200 ppm and 200 ppm, respectively. In Alabama coal samples, As in pyrite-filled veins averages 2700 ppm (n = 34), whereas As in pyrite-filled cellular structures averages 6470 ppm (n = 35). In these same Alabama samples, Se averages 80 ppm in pyrite-filled veins, but was below the detection limit in cell structures. In samples of West Virginia massive pyrite, As averages 1700 ppm, and Se averages 270 ppm (n = 24). The highest concentration of Hg (≤ 102 ppm) is in Alabama pyrite veins. Improved detailed descriptions of sulfide morphology, sulfide mineral paragenesis, and trace-element concentration and distribution allow more informed predictions of: (1) the relative rate of release of trace elements during weathering of pyrite in coals, and (2) the relative effectiveness of various coal-cleaning procedures of removing pyrite. For example, trace element-rich pyrite has been shown to be more soluble than stoichiometric pyrite, and fragile fine-grained pyrite forms such as dendrites and framboids are more susceptible to dissolution and disaggregation but less amenable to removal during coal cleaning.

(Quasi)-convexification of Barta's (multi-extrema) bounding theorem: Inf_x\\big(\\ssty\\frac{H\\Phi(x)}{\\Phi(x)} \\big) \\le E_gr \\le Sup_x \\big(\\ssty\\frac{H\\Phi(x)}{\\Phi(x)} \\big)

NASA Astrophysics Data System (ADS)

Handy, C. R.

2006-03-01

There has been renewed interest in the exploitation of Barta's configuration space theorem (BCST) (Barta 1937 C. R. Acad. Sci. Paris 204 472) which bounds the ground-state energy, Inf_x\\big({{H\\Phi(x)}\\over {\\Phi(x)}} \\big ) \\leq E_gr \\leq Sup_x \\big({{H\\Phi(x)}\\over {\\Phi(x)}}\\big) , by using any Φ lying within the space of positive, bounded, and sufficiently smooth functions, {\\cal C} . Mouchet's (Mouchet 2005 J. Phys. A: Math. Gen. 38 1039) BCST analysis is based on gradient optimization (GO). However, it overlooks significant difficulties: (i) appearance of multi-extrema; (ii) inefficiency of GO for stiff (singular perturbation/strong coupling) problems; (iii) the nonexistence of a systematic procedure for arbitrarily improving the bounds within {\\cal C} . These deficiencies can be corrected by transforming BCST into a moments' representation equivalent, and exploiting a generalization of the eigenvalue moment method (EMM), within the context of the well-known generalized eigenvalue problem (GEP), as developed here. EMM is an alternative eigenenergy bounding, variational procedure, overlooked by Mouchet, which also exploits the positivity of the desired physical solution. Furthermore, it is applicable to Hermitian and non-Hermitian systems with complex-number quantization parameters (Handy and Bessis 1985 Phys. Rev. Lett. 55 931, Handy et al 1988 Phys. Rev. Lett. 60 253, Handy 2001 J. Phys. A: Math. Gen. 34 5065, Handy et al 2002 J. Phys. A: Math. Gen. 35 6359). Our analysis exploits various quasi-convexity/concavity theorems common to the GEP representation. We outline the general theory, and present some illustrative examples.

Non-Hermitian localization in biological networks.

PubMed

Amir, Ariel; Hatano, Naomichi; Nelson, David R

2016-04-01

We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N, the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to 90^{∘} rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias-dependent shape of this hole tracks the bias-independent contours of constant localization length. We treat the large-N limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's law" (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

Application of Hermitian time-dependent coupled-cluster response Ansätze of second order to excitation energies and frequency-dependent dipole polarizabilities

NASA Astrophysics Data System (ADS)

Wälz, Gero; Kats, Daniel; Usvyat, Denis; Korona, Tatiana; Schütz, Martin

2012-11-01

Linear-response methods, based on the time-dependent variational coupled-cluster or the unitary coupled-cluster model, and truncated at the second order according to the Møller-Plesset partitioning, i.e., the TD-VCC[2] and TD-UCC[2] linear-response methods, are presented and compared. For both of these methods a Hermitian eigenvalue problem has to be solved to obtain excitation energies and state eigenvectors. The excitation energies thus are guaranteed always to be real valued, and the eigenvectors are mutually orthogonal, in contrast to response theories based on “traditional” coupled-cluster models. It turned out that the TD-UCC[2] working equations for excitation energies and polarizabilities are equivalent to those of the second-order algebraic diagrammatic construction scheme ADC(2). Numerical tests are carried out by calculating TD-VCC[2] and TD-UCC[2] excitation energies and frequency-dependent dipole polarizabilities for several test systems and by comparing them to the corresponding values obtained from other second- and higher-order methods. It turns out that the TD-VCC[2] polarizabilities in the frequency regions away from the poles are of a similar accuracy as for other second-order methods, as expected from the perturbative analysis of the TD-VCC[2] polarizability expression. On the other hand, the TD-VCC[2] excitation energies are systematically too low relative to other second-order methods (including TD-UCC[2]). On the basis of these results and an analysis presented in this work, we conjecture that the perturbative expansion of the Jacobian converges more slowly for the TD-VCC formalism than for TD-UCC or for response theories based on traditional coupled-cluster models.

Non-Hermitian localization in biological networks

NASA Astrophysics Data System (ADS)

Amir, Ariel; Hatano, Naomichi; Nelson, David R.

2016-04-01

We explore the spectra and localization properties of the N -site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N , the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to 90∘ rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias-dependent shape of this hole tracks the bias-independent contours of constant localization length. We treat the large-N limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's law" (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

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.

Automated method for tracing leading and trailing processes of migrating neurons in confocal image sequences

NASA Astrophysics Data System (ADS)

Kerekes, Ryan A.; Gleason, Shaun S.; Trivedi, Niraj; Solecki, David J.

2010-03-01

Segmentation, tracking, and tracing of neurons in video imagery are important steps in many neuronal migration studies and can be inaccurate and time-consuming when performed manually. In this paper, we present an automated method for tracing the leading and trailing processes of migrating neurons in time-lapse image stacks acquired with a confocal fluorescence microscope. In our approach, we first locate and track the soma of the cell of interest by smoothing each frame and tracking the local maxima through the sequence. We then trace the leading process in each frame by starting at the center of the soma and stepping repeatedly in the most likely direction of the leading process. This direction is found at each step by examining second derivatives of fluorescent intensity along curves of constant radius around the current point. Tracing terminates after a fixed number of steps or when fluorescent intensity drops below a fixed threshold. We evolve the resulting trace to form an improved trace that more closely follows the approximate centerline of the leading process. We apply a similar algorithm to the trailing process of the cell by starting the trace in the opposite direction. We demonstrate our algorithm on two time-lapse confocal video sequences of migrating cerebellar granule neurons (CGNs). We show that the automated traces closely approximate ground truth traces to within 1 or 2 pixels on average. Additionally, we compute line intensity profiles of fluorescence along the automated traces and quantitatively demonstrate their similarity to manually generated profiles in terms of fluorescence peak locations.

Isotope-Labeled Composition B for Tracing Detonation Signatures

NASA Astrophysics Data System (ADS)

Manner, Virginia; Podlesak, David; Huber, Rachel; Amato, Ronald; Giambra, Anna; Bowden, Patrick; Hartline, Ernest; Dattelbaum, Dana

2017-06-01

To better understand how solid carbon forms and evolves during detonation, we have prepared Composition B with 13 C and 15 N-labeled 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) and 2,4,6-trinitrotoluene (TNT) in order to trace the formation of soot from the carbon and nitrogen atoms in these explosives. Isotope-labeling of explosives has been performed in the recent past for a variety of reasons, including environmental remediation and reaction mechanism studies. Because it is expensive and time consuming to prepare these materials, and our detection equipment only requires trace amounts of isotopes, we have prepared fully-labeled materials and substituted them into unlabeled RDX and TNT at less than the 1% level. We will discuss the preparation and full characterization of this labeled Composition B, the detonation tests performed, along with the results of the post-detonation soot analysis. Various detonation models predict differing amounts and forms of carbon and nitrogen; these isotopically-labeled precursors have allowed these models to be tested.

Enhancing biogas production from vinasse in sugarcane biorefineries: Effects of urea and trace elements supplementation on process performance and stability.

PubMed

Janke, Leandro; Leite, Athaydes F; Batista, Karla; Silva, Witan; Nikolausz, Marcell; Nelles, Michael; Stinner, Walter

2016-10-01

In this study, the effects of nitrogen, phosphate and trace elements supplementation were investigated in a semi-continuously operated upflow anaerobic sludge blanket system to enhance process stability and biogas production from sugarcane vinasse. Phosphate in form of KH2PO4 induced volatile fatty acids accumulation possibly due to potassium inhibition of the methanogenesis. Although nitrogen in form of urea increased the reactor's alkalinity, the process was overloaded with an organic loading rate of 6.1gCODL(-1)d(-1) and a hydraulic retention time of 3.6days. However, by supplementing urea and trace elements a stable operation even at an organic loading rate of 9.6gCODL(-1)d(-1) and a hydraulic retention time of 2.5days was possible, resulting in 79% higher methane production rate with a stable specific methane production of 239mLgCOD(-1). Copyright © 2016 Elsevier Ltd. All rights reserved.

Network-wide reorganization of procedural memory during NREM sleep revealed by fMRI

PubMed Central

Vahdat, Shahabeddin; Fogel, Stuart; Benali, Habib; Doyon, Julien

2017-01-01

Sleep is necessary for the optimal consolidation of newly acquired procedural memories. However, the mechanisms by which motor memory traces develop during sleep remain controversial in humans, as this process has been mainly investigated indirectly by comparing pre- and post-sleep conditions. Here, we used functional magnetic resonance imaging and electroencephalography during sleep following motor sequence learning to investigate how newly-formed memory traces evolve dynamically over time. We provide direct evidence for transient reactivation followed by downscaling of functional connectivity in a cortically-dominant pattern formed during learning, as well as gradual reorganization of this representation toward a subcortically-dominant consolidated trace during non-rapid eye movement (NREM) sleep. Importantly, the putamen functional connectivity within the consolidated network during NREM sleep was related to overnight behavioral gains. Our results demonstrate that NREM sleep is necessary for two complementary processes: the restoration and reorganization of newly-learned information during sleep, which underlie human motor memory consolidation. DOI: http://dx.doi.org/10.7554/eLife.24987.001 PMID:28892464

Evaluation of frictional melting on the basis of trace element analyses of fault rocks

NASA Astrophysics Data System (ADS)

Ishikawa, T.; Ujiie, K.

2016-12-01

Pseudotachylytes (solidified frictional melts produced during seismic slip) found in exhumed accretionary complexes are considered to have formed originally at seismogenic depths, and help our understanding of the dynamics of earthquake faulting in subduction zones. The frictional melting should affect rock chemistry. Actually, major element compositions of unaltered pseudotachylyte matrix in the Shimanto accretionary complex are reported to be similar to that of illite, implying disequilibrium melting in the slip zone (Ujiie et al., 2007). Bulk-rock trace element analyses of the pseudotachylyte-bearing fault rocks also revealed their shift to the clay-mineral-like compositions (Honda et al., 2011). Toward better understanding of the frictional melting using chemical means, we carried out detailed major and trace element analyses for pseudotachylyte-bearing dark veins and surrounding host rocks from the Mugi area of the Shimanto accretionary complex (Ujiie et al., 2007). About one milligram each of samples was collected from a rock chip along the microstructure by using the PC-controlled micro-drilling apparatus, and then analyzed by ICP-MS. Host rocks showed a series of compositional trends controlled by mixing of detrital sedimentary components. Unaltered part of the pseudotachylyte vein, on the other hand, showed striking enrichment of fluid-immobile trace elements, consistent with selective melting of fine-grained, clay-rich matrix of the fault rock. Importantly, completely altered parts of the dark veins exhibit essentially the same characteristics as the unaltered part, indicating that the trace element composition of the pseudotachylyte is well preserved even after considerable alteration in the later stages. These results demonstrate that trace element and structural analyses are useful to detect preexistence of pseudotachylytes resulting from selective frictional melting of clay minerals. It has been controversial that pseudotachylytes are rarely formed or rarely preserved. Trace element analyses on clay-rich localized slipping zones shed light on this topic. References: Ujiie et al. (2007) J. Struct. Geol. 29, 599-613; Honda et al. (2011) GRL 38, L06310.

Inert Reassessment Document for Sodium Molybdate - CAS No. 7631-95-0

EPA Pesticide Factsheets

Sodium molybdate is a soluble sodium salt form of molybdenum, a naturallyoccurringelement that is present in the earth's crust and in soils at background concentrations of1-2 mgkg. Molybdenum is an essential trace element for virtually all life forms.

Some Remarks about Semiclassical Trace Invariants and Quantum Normal Forms

NASA Astrophysics Data System (ADS)

Guillemin, Victor; Paul, Thierry

2010-02-01

In this paper we explore the connection between semi-classical and quantum Birkhoff canonical forms (BCF) for Schrödinger operators. In particular we give a “non-symbolic” operator theoretic derivation of the quantum Birkhoff canonical form and provide an explicit recipe for expressing the quantum BCF in terms of the semi-classical BCF.

Isotopic and elemental chemistry of sedimentary pyrite: A combined analytical and statistical approach to a novel planetary biosignature

NASA Astrophysics Data System (ADS)

Figueroa, M. C.; Gregory, D. D.; Lyons, T. W.; Williford, K. H.

2017-12-01

Life processes affect trace element abundances in pyrite such that sedimentary and hydrothermal pyrite have significantly different trace element signatures. Thus, we propose that these biogeochemical data could be used to identify pyrite that formed biogenetically either early in our planet's history or on other planets, particularly Mars. The potential for this approach is elevated because pyrite is common in diverse sedimentary settings, and its trace element content can be preserved despite secondary overprints up to greenschist facies, thus minimizing the concerns about remobilization that can plague traditional whole rock studies. We are also including in-situ sulfur isotope analysis to further refine our understanding of the complex signatures of ancient pyrite. Sulfur isotope data can point straightforwardly to the involvement of life, because pyrite in sediments is inextricably linked to bacterial sulfate reduction and its diagnostic isotopic expressions. In addition to analyzing pyrite of known biological origin formed in the modern and ancient oceans under a range of conditions, we are building a data set for pyrite formed by hydrothermal and metamorphic processes to minimize the risk of false positives in life detection. We have used Random Forests (RF), a machine learning statistical technique with proven efficiency for classifying large geological datasets, to classify pyrite into biotic and abiotic end members. Coupling the trace element and sulfur isotope data from our analyses with a large existing dataset from diverse settings has yielded 4500 analyses with 18 different variables. Our initial results reveal the promise of the RF approach, correctly identifying biogenic pyrite 97 percent of the time. We will continue to couple new in-situ S-isotope and trace element analyses of biogenic pyrite grains from modern and ancient environments, using cutting-edge microanalytical techniques, with new data from high temperature settings. Our ultimately goal is a refined search tool with straightforward application in the search for early life on Earth and distant life recorded in meteorites, returned samples, and in situ measurements.

Petrogenesis of High-CaO Lavas Recovered from Hawaii Scientific Drilling Project

NASA Astrophysics Data System (ADS)

Huang, S.

2015-12-01

Mauna Kea tholeiitic lavas recovered from Hawaii Scientific Drilling Project (HSDP) can be divided into three groups based on their major element compositions: High-SiO2, Low-SiO2, and High-CaO groups. Detailed geochemical and isotopic studies have been focused on the High- and Low-SiO2 group lavas, and High-CaO lavas were not well studied because they were not included in the original reference suite samples. Here we report trace element compositions determined on a suite of High-CaO glasses, and use these data to constrain the petrogenesis of High-CaO lavas. When normalized to Low-SiO2 lavas, High-CaO lavas form a U-shaped trace element pattern. That is, High-CaO lavas are enriched in both the most (Nb, Th) and the least (Sc, V) incompatible elements. This trace element difference is best explained if High-CaO parental magma represents a mixture of low degree partial melt of the Low-SiO2 mantle source and a mafic cumulate component. This mafic cumulate must be clinopyroxene-rich, and it could be delaminated mafic cumulate formed under arcs during continent formation, lower continental crust, or lower oceanic crust.Mauna Kea tholeiitic lavas recovered from Hawaii Scientific Drilling Project (HSDP) can be divided into three groups based on their major element compositions: High-SiO2, Low-SiO2, and High-CaO groups. Detailed geochemical and isotopic studies have been focused on the High- and Low-SiO2 group lavas, and High-CaO lavas were not well studied because they were not included in the original reference suite samples. Here we report trace element compositions determined on a suite of High-CaO glasses, and use these data to constrain the petrogenesis of High-CaO lavas. When normalized to Low-SiO2 lavas, High-CaO lavas form a U-shaped trace element pattern. That is, High-CaO lavas are enriched in both the most (Nb, Th) and the least (Sc, V) incompatible elements. This trace element difference is best explained if High-CaO parental magma represents a mixture of low degree partial melt of the Low-SiO2 mantle source and a mafic cumulate component. This mafic cumulate must be clinopyroxene-rich, and it could be delaminated mafic cumulate formed under arcs during continent formation, lower continental crust, or lower oceanic crust.

Measuring Trace Hydrocarbons in Silanes

NASA Technical Reports Server (NTRS)

Lesser, L. A.

1984-01-01

Technique rapid and uses standard analytical equipment. Silane gas containing traces of hydrocarbons injected into carrier gas of moist nitrogen having about 0.2 percent water vapor. Carrier, water and silane pass through short column packed with powdered sodium hydroxide which combines moisture and silane to form nonvolatile sodium silicate. Carrier gas free of silane but containing nonreactive hydrocarbons, pass to silica-gel column where chromatographic separation takes place. Hydrocarbons measured by FID.

Large-sized out-of-plane stretchable electrodes based on poly-dimethylsiloxane substrate

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

Chou, Namsun; Lee, Jongho; Research Institute for Solar and Sustainable Energies

2014-12-15

This paper describes a reliable fabrication method of stretchable electrodes based on poly-dimethylsiloxane (PDMS) substrate. The electrode traces and pads were formed in out-of-plane structures to improve the flexibility and stretchability of the electrode array. The suspended traces and pads were attached to the PDMS substrate via parylene posts that were located nearby the traces and under the pads. As only conventional micro-electro-mechanical systems techniques were used, the out-of-plane electrode arrays were clearly fabricated at wafer level with high yield and reliability. Also, bi-layer out-of-plane electrodes were formed through additional fabrication steps in addition to mono-layer out-of-plane electrodes. The mechanicalmore » characteristics such as the stretchability, flexibility, and foldability of the fabricated electrodes were evaluated, resulting in stable electrical connection of the metal traces with up to 32.4% strain and up to 360° twist angle over 25 mm. The durability in stretched condition was validated by cyclic stretch test with 10% and 20% strain, resulting in electrical disconnection at 8600 cycles when subjected to 20% strain. From these results, it is concluded that the proposed fabrication method produced highly reliable, out-of-plane and stretchable electrodes, which would be used in various flexible and stretchable electronics applications.« less

The petrology and geochemistry of impact melts, granulites, and hornfelses from consortium breccia 61175

NASA Technical Reports Server (NTRS)

Winzer, S. R.; Meyerhoff, M.; Nava, D. F.; Schuhmann, S.; Philpotts, J. A.; Lindstrom, D. J.; Lum, R. K. L.; Lindstrom, M. M.; Schuhmann, P.

1977-01-01

The matrix and 58 clasts from breccia 61175 were analyzed for major, minor, and trace elements. The matrix is anorthositic and has lithophile trace element abundances 20 to 40 times chondrite. Clasts comprise impact melt rocks, xenocryst and xenolith-free very high aluminum (VHA) and anorthositic basalts, anorthosite, anorthosite-norite-troctolite granulites, and hornfelses. The VHA and anorthositic basalts are considered to be impact melts, and the hornfelses were probably formed by incorporation of breccias or preexisting melt rocks into a melt sheet prior to cooling. The range of melt-rock lithophile trace element abundances might indicate more than one melt sheet.

Biological forcing controls the chemistry of reef-building coral skeleton

NASA Astrophysics Data System (ADS)

Meibom, Anders; Mostefaoui, Smail; Cuif, Jean-Pierre; Dauphin, Yannicke; Houlbreque, Fanny; Dunbar, Robert; Constantz, Brent

2007-01-01

We present analyses of major elements C and Ca and trace elements N, S, Mg and Sr in a Porites sp. exoskeleton with a spatial resolution better than ˜150 nm. Trace element variations are evaluated directly against the ultra-structure of the skeleton and are ascribed to dynamic biological forcing. Individual growth layers in the bulk fibrous aragonite skeleton form on sub-daily timescales. Magnesium concentration variations are dramatically correlated with the growth layers, but are uncorrelated with Sr concentration variations. Observed (sub)seasonal relationships between water temperature and skeletal trace-element chemistry are secondary, mediated by sensitive biological processes to which classical thermodynamic formalism does not apply.

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

Lee, Gregory L.; Arnold, Dorian; LeGendre, Matthew

STAT is a light weight debugging tool that gathers and merges stack traces from all of the processes in a parallel application. STAT uses the MRNet tree based overlay network to broadcast commands from the tool front-end to the STAT daemons and for the front-end to gather the traces from the STAT daemons. As the traces propagate through the MRNet network tree, they are merged across all tasks to form a similar function call patterns and to delineate a small set of equivalence classes. A representative task from each of these classes can then be fed into a full featuremore » debugger like TolalView for root cause analysis.« less

The Fine Transverse Structure of a Vortex Flow Beyond the Edge of a Disc Rotating in a Stratified Fluid

NASA Astrophysics Data System (ADS)

Chashechkin, Yu. D.; Bardakov, R. N.

2018-02-01

By the methods of schlieren visualization, the evolution of elements of the fine structure of transverse vortex loops formed in the circular vortex behind the edge of a disk rotating in a continuously stratified fluid is traced for the first time. An inhomogeneous distribution of the density of a table-salt solution in a basin was formed by the continuous-squeezing method. The development of periodic perturbations at the outer boundary of the circular vortex and their transformation at the vortex-loop vertex are traced. A slow change in the angular size of the structural elements in the supercritical-flow mode is noted.

Geochemical Constraints on the Size of the Moon — Forming Giant Impact

NASA Astrophysics Data System (ADS)

Piet, H.; Badro, J.; Gillet, P.

2018-05-01

We use the partitioning of siderophile trace elements to model the geochemical influence of the Moon-forming giant impact on Earth’s mantle during core formation. We find the size of the impactor to be 15% of Earth mass or smaller.

Recovery of Trace and Heavy Metals from Coal Combustion Residues for Reuse and Safe Disposal: A Review

NASA Astrophysics Data System (ADS)

Kumar, Ashvani; Samadder, Sukha Ranjan; Elumalai, Suresh Pandian

2016-09-01

The safe disposal of coal combustion residues (CCRs) will remain a major public issue as long as coal is used as a fuel for energy production. Both dry and wet disposal methods of CCRs create serious environmental problems. The dry disposal method creates air pollution initially, and the wet disposal method creates water pollution as a result of the presence of trace and heavy metals. These leached heavy metals from fly ash may become more hazardous when they form toxic compounds such as arsenic sulfite (As2S3) and lead nitrate (N2O6Pb). The available studies on trace and heavy metals present in CCRs cannot ensure environmentally safe utilization. In this work, a novel approach has been offered for the retrieval of trace and heavy metals from CCRs. If the proposed method becomes successful, then the recovered trace and heavy metals may become a resource and environmentally safe use of CCRs may be possible.

Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies.

PubMed

Mostafazadeh, Ali

2009-06-05

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic waveguide.

Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at Real Energies

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

Mostafazadeh, Ali

2009-06-05

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic waveguide.

Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions

NASA Astrophysics Data System (ADS)

Valchev, T. I.

2016-02-01

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m + n)/S(U(m) × U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schrödinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.

Dannie Heineman Prize for Mathematical Physics: Applying mathematical techniques to solve important problems in quantum theory

NASA Astrophysics Data System (ADS)

Bender, Carl

2017-01-01

The theory of complex variables is extremely useful because it helps to explain the mathematical behavior of functions of a real variable. Complex variable theory also provides insight into the nature of physical theories. For example, it provides a simple and beautiful picture of quantization and it explains the underlying reason for the divergence of perturbation theory. By using complex-variable methods one can generalize conventional Hermitian quantum theories into the complex domain. The result is a new class of parity-time-symmetric (PT-symmetric) theories whose remarkable physical properties have been studied and verified in many recent laboratory experiments.

Nonlinear behavior of shells of revolution under cyclic loading

NASA Technical Reports Server (NTRS)

Levine, H. S.; Armen, H., Jr.; Winter, R.; Pifko, A.

1972-01-01

A large deflection elastic-plastic analysis is presented, applicable to orthotropic axisymmetric plates and shells of revolution subjected to monotonic and cyclic loading conditions. The analysis is based on the finite-element method. It employs a new higher order, fully compatible, doubly curved orthotropic shell-of-revolution element using cubic Hermitian expansions for both meridional and normal displacements. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening theory, which predicts an ideal Bauschinger effect. Numerous sample problems involving monotonic and cyclic loading conditions are analyzed. The monotonic results are compared with other theoretical solutions.

Power-law scaling of extreme dynamics near higher-order exceptional points

NASA Astrophysics Data System (ADS)

Zhong, Q.; Christodoulides, D. N.; Khajavikhan, M.; Makris, K. G.; El-Ganainy, R.

2018-02-01

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time (PT ) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other physical systems as well.

Competing role of interactions in synchronisation of exciton-polariton condensates

NASA Astrophysics Data System (ADS)

Khan, Saeed A.; Türeci, Hakan E.

2017-10-01

We present a theoretical study of synchronisation dynamics of incoherently pumped exciton-polariton condensates in coupled polariton traps. Our analysis is based on a coupled-mode theory for the generalised Gross-Pitaevskii equation, which employs an expansion in non-Hermitian, pump-dependent modes appropriate for the pumped geometry. We find that polariton-polariton and reservoir-polariton interactions play competing roles and lead to qualitatively different synchronised phases of the coupled polariton modes as pumping power is increased. Crucially, these interactions can also act against each other to hinder synchronisation. We map out a phase diagram and discuss the general characteristics of these phases using a generalised Adler equation.

Multigrid for Staggered Lattice Fermions

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

Brower, Richard C.; Clark, M. A.; Strelchenko, Alexei

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

Solving complex band structure problems with the FEAST eigenvalue algorithm

NASA Astrophysics Data System (ADS)

Laux, S. E.

2012-08-01

With straightforward extension, the FEAST eigenvalue algorithm [Polizzi, Phys. Rev. B 79, 115112 (2009)] is capable of solving the generalized eigenvalue problems representing traveling-wave problems—as exemplified by the complex band-structure problem—even though the matrices involved are complex, non-Hermitian, and singular, and hence outside the originally stated range of applicability of the algorithm. The obtained eigenvalues/eigenvectors, however, contain spurious solutions which must be detected and removed. The efficiency and parallel structure of the original algorithm are unaltered. The complex band structures of Si layers of varying thicknesses and InAs nanowires of varying radii are computed as test problems.

A technique for plasma velocity-space cross-correlation

NASA Astrophysics Data System (ADS)

Mattingly, Sean; Skiff, Fred

2018-05-01

An advance in experimental plasma diagnostics is presented and used to make the first measurement of a plasma velocity-space cross-correlation matrix. The velocity space correlation function can detect collective fluctuations of plasmas through a localized measurement. An empirical decomposition, singular value decomposition, is applied to this Hermitian matrix in order to obtain the plasma fluctuation eigenmode structure on the ion distribution function. A basic theory is introduced and compared to the modes obtained by the experiment. A full characterization of these modes is left for future work, but an outline of this endeavor is provided. Finally, the requirements for this experimental technique in other plasma regimes are discussed.

Numerical radius and zero pattern of matrices

NASA Astrophysics Data System (ADS)

Nikiforov, Vladimir

2008-01-01

Let A be an n×n complex matrix and r be the maximum size of its principal submatrices with no off-diagonal zero entries. Suppose A has zero main diagonal and x is a unit n-vector. Then, letting ||A|| be the Frobenius norm of A, we show that2[less-than-or-equals, slant](1-1/2r-1/2n)||A||2. This inequality is tight within an additive term O(rn-2). If the matrix A is Hermitian, then2[less-than-or-equals, slant](1-1/r)||A||2. This inequality is sharp; moreover, it implies the Turán theorem for graphs.

Quasi-kernel polynomials and convergence results for quasi-minimal residual iterations

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1992-01-01

Recently, Freund and Nachtigal have proposed a novel polynominal-based iteration, the quasi-minimal residual algorithm (QMR), for solving general nonsingular non-Hermitian linear systems. Motivated by the QMR method, we have introduced the general concept of quasi-kernel polynomials, and we have shown that the QMR algorithm is based on a particular instance of quasi-kernel polynomials. In this paper, we continue our study of quasi-kernel polynomials. In particular, we derive bounds for the norms of quasi-kernel polynomials. These results are then applied to obtain convergence theorems both for the QMR method and for a transpose-free variant of QMR, the TFQMR algorithm.

Comment on ‘Numerical estimates of the spectrum for anharmonic PT symmetric potentials’

NASA Astrophysics Data System (ADS)

Amore, Paolo; Fernández, Francisco M.

2013-04-01

We show that the authors of the commented paper (Bowen et al 2012 Phys. Scr. 85 065005) draw their conclusions from the eigenvalues of truncated Hamiltonian matrices that do not converge as the matrix dimension increases. In some of the studied examples, the authors missed the real positive eigenvalues that already converge towards the exact eigenvalues of the non-Hermitian operators and focused their attention on the complex ones that do not. We also show that the authors misread Bender's argument about the eigenvalues of the harmonic oscillator with boundary conditions in the complex-x plane (Bender 2007 Rep. Prog. Phys. 70 947).

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

Cartarius, Holger; Moiseyev, Nimrod; Department of Physics and Minerva Center for Nonlinear Physics of Complex Systems, Technion-Israel Institute of Technology, Haifa, 32000

The unique time signature of the survival probability exactly at the exceptional point parameters is studied here for the hydrogen atom in strong static magnetic and electric fields. We show that indeed the survival probability S(t)=|<{psi}(0)|{psi}(t)>|{sup 2} decays exactly as |1-at|{sup 2}e{sup -{Gamma}{sub E}{sub P}t/({Dirac_h}/2{pi})}, where {Gamma}{sub EP} is associated with the decay rate at the exceptional point and a is a complex constant depending solely on the initial wave packet that populates exclusively the two almost degenerate states of the non-Hermitian Hamiltonian. This may open the possibility for a first experimental detection of exceptional points in a quantum system.

Temporal patterns of inputs to cerebellum necessary and sufficient for trace eyelid conditioning.

PubMed

Kalmbach, Brian E; Ohyama, Tatsuya; Mauk, Michael D

2010-08-01

Trace eyelid conditioning is a form of associative learning that requires several forebrain structures and cerebellum. Previous work suggests that at least two conditioned stimulus (CS)-driven signals are available to the cerebellum via mossy fiber inputs during trace conditioning: one driven by and terminating with the tone and a second driven by medial prefrontal cortex (mPFC) that persists through the stimulus-free trace interval to overlap in time with the unconditioned stimulus (US). We used electric stimulation of mossy fibers to determine whether this pattern of dual inputs is necessary and sufficient for cerebellar learning to express normal trace eyelid responses. We find that presenting the cerebellum with one input that mimics persistent activity observed in mPFC and the lateral pontine nuclei during trace eyelid conditioning and another that mimics tone-elicited mossy fiber activity is sufficient to produce responses whose properties quantitatively match trace eyelid responses using a tone. Probe trials with each input delivered separately provide evidence that the cerebellum learns to respond to the mPFC-like input (that overlaps with the US) and learns to suppress responding to the tone-like input (that does not). This contributes to precisely timed responses and the well-documented influence of tone offset on the timing of trace responses. Computer simulations suggest that the underlying cerebellar mechanisms involve activation of different subsets of granule cells during the tone and during the stimulus-free trace interval. These results indicate that tone-driven and mPFC-like inputs are necessary and sufficient for the cerebellum to learn well-timed trace conditioned responses.

Worthwhile optical method for free-form mirrors qualification

NASA Astrophysics Data System (ADS)

Sironi, G.; Canestrari, R.; Toso, G.; Pareschi, G.

2013-09-01

We present an optical method for free-form mirrors qualification developed by the Italian National Institute for Astrophysics (INAF) in the context of the ASTRI (Astrofisica con Specchi a Tecnologia Replicante Italiana) Project which includes, among its items, the design, development and installation of a dual-mirror telescope prototype for the Cherenkov Telescope Array (CTA) observatory. The primary mirror panels of the telescope prototype are free-form concave mirrors with few microns accuracy required on the shape error. The developed technique is based on the synergy between a Ronchi-like optical test performed on the reflecting surface and the image, obtained by means of the TraceIT ray-tracing proprietary code, a perfect optics should generate in the same configuration. This deflectometry test allows the reconstruction of the slope error map that the TraceIT code can process to evaluate the measured mirror optical performance at the telescope focus. The advantages of the proposed method is that it substitutes the use of 3D coordinates measuring machine reducing production time and costs and offering the possibility to evaluate on-site the mirror image quality at the focus. In this paper we report the measuring concept and compare the obtained results to the similar ones obtained processing the shape error acquired by means of a 3D coordinates measuring machine.

Storytelling and German Culture.

ERIC Educational Resources Information Center

Cooper, Connie S. Eigenmann

The genre of fairytales, one structured form of storytelling, has been labeled "Marchen." German culture is orally transmitted in this generic form, and can be traced to a collection of 210 fairytales, the Grimm brothers'"Kinder-und Taus-Marchen," first published shortly after 1800. For this study, research questions were posed…

Constructivism in the Art Classroom: Praxis and Policy

ERIC Educational Resources Information Center

Thompson, Christine Marmé

2015-01-01

Constructivist thought and practice connect easily with forms of art education that emphasize choice and student agency. This article traces the contemporary forms of constructivism that vie with more structured pedagogical approaches in American schools and recommends policies and procedures that may preserve the qualities of constructivist…

Sensational Roots: The Police Court Heritage.

ERIC Educational Resources Information Center

Francke, Warren

Part of a broader inquiry into "Investigative Exposure in the Nineteenth Century: The Journalistic Heritage of the Muckrakers," this study traces the evolving reportorial techniques and literary style that gave journalism its form--a form combining strengths and flaws, freedom and inhibitions. Before nineteenth century police court reporting was…

What forms of life could have arisen in the ancient conditions of Mars?

NASA Astrophysics Data System (ADS)

Vidmachenko, A. P.

2017-05-01

The first geological era of Mars - Phyllocyanic - began about 4.5 billion years ago and continued 500-700 million years. Then Mars was similar to the ancient Earth with dense atmosphere and water on the surface. That is he planet was once much more suitable for the existence of life. Then appeared simple forms of life on Earth, and we believe, that the same could happen on Mars. But it is likely that if once life appeared on Mars, it did not disappear without a trace. It could move from the surface of the planet to its interior, to be conserved there in relict fossils, and possibly, survived there in some very simple forms, that then covered by powerful soil emissions. Therefore, its traces should search under the ground in those layers of sedimentary rocks that are refers to the first Phyllocyanic geological epoch.

Nano-delivery of trace minerals for marine fish larvae: influence on skeletal ossification, and the expression of genes involved in intestinal transport of minerals, osteoblast differentiation, and oxidative stress response.

PubMed

Terova, Genciana; Rimoldi, Simona; Izquierdo, Marisol; Pirrone, Cristina; Ghrab, Wafa; Bernardini, Giovanni

2018-06-17

Currently, the larviculture of many marine fish species with small-sized larvae depends for a short time after hatching, on the supply of high-quality live zooplankton to ensure high survival and growth rates. During the last few decades, the research community has made great efforts to develop artificial diets, which can completely substitute live prey. However, studies aimed at determining optimal levels of minerals in marine larvae compound feeds and the potential of novel delivery vectors for mineral acquisition has only very recently begun. Recently, the agro-food industry has developed several nano-delivery systems, which could be used for animal feed, too. Delivery through nano-encapsulation of minerals and feed additives would protect the bioactive molecules during feed manufacturing and fish feeding and allow an efficient acquisition of active substances into biological system. The idea is that dietary minerals in the form of nanoparticles may enter cells more easily than their larger counterparts enter and thus speed up their assimilation in fish. Accordingly, we evaluated the efficacy of early weaning diets fortified with organic, inorganic, or nanoparticle forms of trace minerals (Se, Zn, and Mn) in gilthead seabream (Sparus aurata) larvae. We tested four experimental diets: a trace mineral-deficient control diet, and three diets supplemented with different forms of trace minerals. At the end of the feeding trial, larvae growth performance and ossification, and the level of expression of six target genes (SLC11A2β, dmt1, BMP2, OC, SOD, GPX), were evaluated. Our data demonstrated that weaning diets supplemented with Mn, Se, and Zn in amino acid-chelated (organic) or nanoparticle form were more effective than diets supplemented with inorganic form of minerals to promote bone mineralization, and prevent skeletal anomalies in seabream larvae. Furthermore, nanometals markedly improved larval stress resistance in comparison to inorganic minerals and upregulated mRNA copy number of OC gene. The expression of this gene was strongly correlated with mineralization degree, thus confirming its potency as a good marker of bone mineralization in gilthead seabream larvae.

Weathering of the New Albany Shale, Kentucky: II. Redistribution of minor and trace elements

USGS Publications Warehouse

Tuttle, M.L.W.; Breit, G.N.; Goldhaber, M.B.

2009-01-01

During weathering, elements enriched in black shale are dispersed in the environment by aqueous and mechanical transport. Here a unique evaluation of the differential release, transport, and fate of Fe and 15 trace elements during progressive weathering of the Devonian New Albany Shale in Kentucky is presented. Results of chemical analyses along a weathering profile (unweathered through progressively weathered shale to soil) describe the chemically distinct pathways of the trace elements and the rate that elements are transferred into the broader, local environment. Trace elements enriched in the unweathered shale are in massive or framboidal pyrite, minor sphalerite, CuS and NiS phases, organic matter and clay minerals. These phases are subject to varying degrees and rates of alteration along the profile. Cadmium, Co, Mn, Ni, and Zn are removed from weathered shale during sulfide-mineral oxidation and transported primarily in aqueous solution. The aqueous fluxes for these trace elements range from 0.1 g/ha/a (Cd) to 44 g/ha/a (Mn). When hydrologic and climatic conditions are favorable, solutions seep to surface exposures, evaporate, and form Fe-sulfate efflorescent salts rich in these elements. Elements that remain dissolved in the low pH (<4) streams and groundwater draining New Albany Shale watersheds become fixed by reactions that increase pH. Neutralization of the weathering solution in local streams results in elements being adsorbed and precipitated onto sediment surfaces, resulting in trace element anomalies. Other elements are strongly adsorbed or structurally bound to solid phases during weathering. Copper and U initially are concentrated in weathering solutions, but become fixed to modern plant litter in soil formed on New Albany Shale. Molybdenum, Pb, Sb, and Se are released from sulfide minerals and organic matter by oxidation and accumulate in Fe-oxyhydroxide clay coatings that concentrate in surface soil during illuviation. Chromium, Ti, and V are strongly correlated with clay abundance and considered to be in the structure of illitic clay. Illite undergoes minimal alteration during weathering and is concentrated during illuvial processes. Arsenic concentration increases across the weathering profile and is associated with the succession of secondary Fe(III) minerals that form with progressive weathering. Detrital fluxes of particle-bound trace elements range from 0.1 g/ha/a (Sb) to 8 g/ha/a (Mo). Although many of the elements are concentrated in the stream sediments, changes in pH and redox conditions along the sediment transport path could facilitate their release for aqueous transport.

Speciations of trace metals in the Danube alluvial sediments within an oil refinery.

PubMed

Relić, Dubravka; Dordević, Dragana; Popović, Aleksandar; Blagojević, Tamara

2005-07-01

A sequential extraction procedure was applied to identify forms of Ni, Zn, Pb and Cu with Fe- and Mn-oxides associated in alluvial sediments of the River Danube within Pancevo Oil Refinery (Serbia). The five steps of the sequential extraction procedure partitioned metals into: CH(3)COONH(4) extractable (S1); NH(2)OH.HCl carbonate extractable and easily reducible (S2); (NH(4))(2)C(2)O(2)/H(2)C(2)O(2) moderately reducible (S3); H(2)O(2)-HNO(3) organic extractable (S4); and HCl acid soluble residue (S5). Extracted concentrations of trace metals, analyzed after all five steps, were found to be (mg kg(-1)) for Mn: 656, Fe: 26734, Ni: 32.3, Zn: 72.8, Pb: 13.4 and Cu: 27.0. Most of the elements were found in acid soluble residue, characterizing stable compounds in sediments. Non-residual fractions of trace metals (sum of the first four fractions) were analyzed because they are more bioavailable than the residual amount. Correlation analysis and two multivariate analysis methods (principal component and cluster analysis) were used to understand and visualize the associations between the non-residual fractions of trace metals and certain forms, more or less crystalline of Fe- and Mn-oxides within the analyzed sediments, since Fe- and Mn-oxides play an important role in trace metal sorption within aquatic systems, especially within the Danube alluvium where the fluctuations of groundwater are very frequent and the level of groundwater could come close to surface.

Detecting Runtime Anomalies in AJAX Applications through Trace Analysis

DTIC Science & Technology

2011-08-10

statements by adding the instrumentation to the GWT UI classes, leaving the user code untouched. Some content management frameworks such as Drupal [12...Google web toolkit.” http://code.google.com/webtoolkit/. [12] “Form generation – drupal api.” http://api.drupal.org/api/group/form_api/6. 9

The Jerusarema Dance of Zimbabwe.

ERIC Educational Resources Information Center

Asante, Kariamu Welsh

1985-01-01

Traces the historical development of the Jerusarema, a traditional dance of the Shona of Zimbabwe, from its origins as a form of military defense to its present role in recreation and ceremony. Describes the Jerusarema, classifies it in relation to other African dance forms, and discusses how it is learned. (KH)

Fate of the CHBrsub2O radical in air

NASA Technical Reports Server (NTRS)

Bayes, K. D.; Friedl, R. F.

2003-01-01

Trace amounts of bromoform in air have been photolyzed at 266 and 303 nm to form Br atoms and CHBr2 radicals. The Br concentration as a funtion of time is followed by resonance fluorescence. The CHBr2 radicals react with O2 in the air to form peroxy radicals.

Determining the physical and chemical processes behind four caldera-forming eruptions in rapid succession in the San Juan caldera cluster, Colorado, USA

NASA Astrophysics Data System (ADS)

Curry, A. C.; Caricchi, L.; Lipman, P. W.

2017-12-01

A primary goal of volcanology is to understand the frequency and magnitude of large, explosive volcanic eruptions to mitigate their impact on society. Recent studies show that the average magma flux and the time between magma injections into a given magmatic-volcanic system fundamentally control the frequency and magnitude of volcanic eruptions, yet these parameters are unknown for many volcanic regions on Earth. We focus on major and trace element chemistry of individual phases and whole-rock samples, initial zircon ID-TIMS analyses, and zircon SIMS oxygen isotope analyses of four caldera-forming ignimbrites from the San Juan caldera cluster in the Southern Rocky Mountain volcanic field, Colorado, to determine the physical and chemical processes leading to large eruptions. We collected outflow samples along stratigraphy of the three caldera-forming ignimbrites of the San Luis caldera complex: the Rat Creek Tuff ( 150 km3), Cebolla Creek Tuff ( 250 km3), and Nelson Mountain Tuff (>500 km3); and we collected samples of both outflow and intracaldera facies of the Snowshoe Mountain Tuff (>500 km3), which formed the Creede caldera. Single-crystal sanidine 40Ar/39Ar ages show that these large eruptions occurred in rapid succession between 26.91 ± 0.02 Ma (Rat Creek Tuff) and 26.87 ± 0.02 Ma (Snowshoe Mountain Tuff), providing an opportunity to investigate the temporal evolution of magmatic systems feeding large, explosive volcanic eruptions. Major and trace element analyses show that the first and last eruption of the San Luis caldera complex (Rat Creek Tuff and Nelson Mountain Tuff) are rhyolitic to dacitic ignimbrites, whereas the Cebolla Creek Tuff and Snowshoe Mountain Tuff are crystal-rich, dacitic ignimbrites. Trace elements show enrichment in light rare-earth elements (LREEs) over heavy rare-earth elements (HREEs), and whereas the trace element patterns are similar for each caldera cycle, trace element values for each ignimbrite show variability in HREE concentrations. This variability indicates that these large eruptions sampled a magmatic system with some degree of internal heterogeneity. These results have implications for the chemical and physical processes, such as magmatic flux and injection periodicity, leading to the formation of large magmatic systems prior to large, explosive eruptions.

Trace gas emissions from the marine biosphere.

PubMed

Liss, Peter S

2007-07-15

A wide variety of trace gases (e.g. dimethyl sulphide, organohalogens, ammonia, non-methane and oxygenated hydrocarbons, volatile oxygenated organics and nitrous oxide) are formed in marine waters by biological and photochemical processes. This leads in many, but not all, cases to supersaturation of the water relative to marine air concentrations and a net flux of trace gas to the atmosphere. Since the gases are often in their reduced forms in the water, once in the atmosphere they are subject to oxidation by photolysis or radical attack to form chemically reactive species that can affect the oxidizing capacity of the air. They can also lead to the formation of new particles or the growth of existing ones that can then contribute to both direct and indirect (via the formation of cloud condensation nuclei) aerosol effects on climate. These cycles are discussed with respect to their impacts on the chemistry of the atmosphere, climate and human health. This whole topic was the subject of an extensive review (Nightingale & Liss 2003 In Treatise in geochemistry (eds H. D. Holland & K. K. Turekian), pp. 49-81) and what will be attempted here is a brief update of the earlier paper. There is no attempt to be comprehensive either in terms of gases covered or to give a complete review of all the recent literature. It is a personal view of recent advances both from my own research group as well as significant work from others. Questions raised at the meeting 'Trace gas biogeochemistry and global change' are dealt with at appropriate places in the text (rather than at the end of the piece). Discussion of each of the gases or group of gases is given in the following separate sections.

Method and system for pipeline communication

DOEpatents

Richardson,; John, G [Idaho Falls, ID

2008-01-29

A pipeline communication system and method includes a pipeline having a surface extending along at least a portion of the length of the pipeline. A conductive bus is formed to and extends along a portion of the surface of the pipeline. The conductive bus includes a first conductive trace and a second conductive trace with the first and second conductive traces being adapted to conformally couple with a pipeline at the surface extending along at least a portion of the length of the pipeline. A transmitter for sending information along the conductive bus on the pipeline is coupled thereto and a receiver for receiving the information from the conductive bus on the pipeline is also couple to the conductive bus.

Micro-PIXE analysis of trace element concentrations of natural rubies from different locations in Myanmar

NASA Astrophysics Data System (ADS)

Sanchez, J. L.; Osipowicz, T.; Tang, S. M.; Tay, T. S.; Win, T. T.

1997-07-01

The trace element concentrations found in geological samples can shed light on the formation process. In the case of gemstones, which might be of artificial or natural origin, there is also considerable interest in the development of methods that provide identification of the origin of a sample. For rubies, trace element concentrations present in natural samples were shown previously to be significant indicators of the region of origin [S.M. Tang et al., Appl. Spectr. 42 (1988) 44, and 43 (1989) 219]. Here we report the results of micro-PIXE analyses of trace element (Ti, V, Cr, Fe, Cu and Ga) concentrations of a large set ( n = 130) of natural rough rubies from nine locations in Myanmar (Burma). The resulting concentrations are subjected to statistical analysis. Six of the nine groups form clusters when the data base is evaluated using tree clustering and principal component analysis.

Concept and analytical basis for revistas - A fast, flexible computer/graphic system for generating periodic satellite coverage patterns

NASA Technical Reports Server (NTRS)

King, J. C.

1976-01-01

The generation of satellite coverage patterns is facilitated by three basic strategies: use of a simplified physical model, permitting rapid closed-form calculation; separation of earth rotation and nodal precession from initial geometric analyses; and use of symmetries to construct traces of indefinite length by repetitive transposition of basic one-quadrant elements. The complete coverage patterns generated consist of a basic nadir trace plus a number of associated off-nadir traces, one for each sensor swath edge to be delineated. Each trace is generated by transposing one or two of the basic quadrant elements into a circle on a nonrotating earth model sphere, after which the circle is expanded into the actual 'helical' pattern by adding rotational displacements to the longitude coordinates. The procedure adapts to the important periodic coverage cases by direct insertion of the characteristic integers N and R (days and orbital revolutions, respectively, per coverage period).

Effect of Ocean Acidification on Organic and Inorganic Speciation of Trace Metals.

PubMed

Stockdale, Anthony; Tipping, Edward; Lofts, Stephen; Mortimer, Robert J G

2016-02-16

Rising concentrations of atmospheric carbon dioxide are causing acidification of the oceans. This results in changes to the concentrations of key chemical species such as hydroxide, carbonate and bicarbonate ions. These changes will affect the distribution of different forms of trace metals. Using IPCC data for pCO2 and pH under four future emissions scenarios (to the year 2100) we use a chemical speciation model to predict changes in the distribution of organic and inorganic forms of trace metals. Under a scenario where emissions peak after the year 2100, predicted free ion Al, Fe, Cu, and Pb concentrations increase by factors of up to approximately 21, 2.4, 1.5, and 2.0 respectively. Concentrations of organically complexed metal typically have a lower sensitivity to ocean acidification induced changes. Concentrations of organically complexed Mn, Cu, Zn, and Cd fall by up to 10%, while those of organically complexed Fe, Co, and Ni rise by up to 14%. Although modest, these changes may have significance for the biological availability of metals given the close adaptation of marine microorganisms to their environment.

Analysis of minerals containing dissolved traces of the fluid phase components water and carbon dioxide

NASA Technical Reports Server (NTRS)

Freund, Friedemann

1991-01-01

Substantial progress has been made towards a better understanding of the dissolution of common gas/fluid phase components, notably H2O and CO2, in minerals. It has been shown that the dissolution mechanisms are significantly more complex than currently believed. By judiciously combining various solid state analytical techniques, convincing evidence was obtained that traces of dissolved gas/fluid phase components undergo, at least in part, a redox conversion by which they split into reduced H2 and and reduced C on one hand and oxidized oxygen, O(-), on the other. Analysis for 2 and C as well as for any organic molecules which may form during the process of co-segregation are still impeded by the omnipresent danger of extraneous contamination. However, the presence of O(-), an unusual oxidized form of oxygen, has been proven beyond a reasonable doubt. The presence of O(-) testifies to the fact that a redox reaction must have taken place in the solid state involving the dissolved traces of gas/fluid phase components. Detailed information on the techniques used and the results obtained are given.

Water in Earth's mantle: Hydrogen analysis of mantle olivine, pyroxenes and garnet using the SIMS

NASA Technical Reports Server (NTRS)

Kurosawa, Masanori; Yurimoto, Hisayoshi; Sueno, Shigeho

1993-01-01

Hydrogen (or water) in the Earth's interior plays a key role in the evolution and dynamics of the planet. However, the abundance and the existence form of the hydrogen have scarcely been clear in practice. Hydrogen in the mantle was incorporated in the interior during the formation of the Earth. The incorporated hydrogen was hardly possible to concentrate locally inside the Earth considering its high mobility and high reactivity. The hydrogen, preferably, could be distributed homogeneously over the mantle and the core by the subsequent physical and chemical processes. Therefore, hydrogen in the mantle could be present in the form of trace hydrogen in nominally anhydrous mantle minerals. The hydrogen and the other trace elements in mantle olivines, orthopyroxenes, clinopyroxenes, and garnets were determined using secondary ion mass spectrometry (SIMS) for elucidating (1) the exact hydrogen contents, (2) the correlation between the hydrogen and the other trace elements, (3) the dependence of the hydrogen contents on the depth, and (4) the dependence of the whole rock water contents on the depth.

Trace elements in hydrothermal quartz: Relationships to cathodoluminescent textures and insights into vein formation

USGS Publications Warehouse

Rusk, B.G.; Lowers, H.A.; Reed, M.H.

2008-01-01

High-resolution electron microprobe maps show the distribution of Ti, Al, Ca, K, and Fe among quartz growth zones revealed by scanning electron microscope-cathodoluminescence (SEM-CL) from 12 hydrothermal ore deposits formed between ???100 and e1750 ??C. The maps clearly show the relationships between trace elements and CL intensity in quartz. Among all samples, no single trace element consistently correlates with variations in CL intensity. However in vein quartz from five porphyry-Cu (Mo-Au) deposits, CL intensity always correlates positively with Ti concentrations, suggesting that Ti is a CL activator in quartz formed at >400 ??C. Ti concentrations in most rutile-bearing vein quartz from porphyry copper deposits indicate reasonable formation temperatures of 2000 ppm, but in high-temperature quartz, Al concentrations are consistently in the range of several hundred ppm. Aluminum concentrations in quartz refl ect the Al solubility in hydrothermal fluids, which is strongly dependent on pH. Aluminum concentrations in quartz therefore reflect fluctuations in pH that may drive metal-sulfide precipitation in hydrothermal systems. ?? 2008 The Geological Society of America.

Assessment of serum trace elements and electrolytes in children with childhood and atypical autism.

PubMed

Skalny, Anatoly V; Simashkova, Natalia V; Klyushnik, Tatiana P; Grabeklis, Andrei R; Radysh, Ivan V; Skalnaya, Margarita G; Nikonorov, Alexandr A; Tinkov, Alexey A

2017-09-01

The existing data demonstrate a significant interrelation between ASD and essential and toxic trace elements status of the organism. However, data on trace element homeostasis in particular ASD forms are insufficient. Therefore, the objective of the present study was to assess the level of trace elements and electrolytes in serum of children with childhood and atypical autism. A total of 48 children with ASD (24 with childhood and 24 with atypical autism) and age- and sex-adjusted controls were examined. Serum trace elements and electrolytes were assessed using inductively-coupled plasma mass spectrometry. The obtained data demonstrate that children with ASD unspecified are characterized by significantly lower Ni, Cr, and Se levels as compared to the age- and sex-matched controls. At the same time, significantly decreased serum Ni and Se concentrations were detected in patients with childhood autism. In turn, children with atypical autism were characterized by more variable serum trace element spectrum. In particular, atypical autism is associated with lower serum Al, As, Ni, Cr, Mn, and Se levels in comparison to the control values. Moreover, Al and Mn concentration in this group was also lower than that in childhood autism patients. Generally, the obtained data demonstrate lower levels of both essential and toxic trace elements in atypical autism group, being indicative of profound alteration of trace elements metabolism. However, further detailed metabolic studies are required to reveal critical differences in metabolic pathways being responsible for difference in trace element status and clinical course of the disease. Copyright © 2016 Elsevier GmbH. All rights reserved.

Astronomy and the camera obscura

NASA Astrophysics Data System (ADS)

Feist, M.

2000-02-01

The camera obscura (from Latin meaning darkened chamber) is a simple optical device with a long history. In the form considered here, it can be traced back to 1550. It had its heyday during the Victorian era when it was to be found at the seaside as a tourist attraction or sideshow. It was also used as an artist's drawing aid and, in 1620, the famous astronomer-mathematician, Johannes Kepler used a small tent camera obscura to trace the scenery.

Wireless Sensing System Using Open-circuit, Electrically-conductive Spiral-trace Sensor

NASA Technical Reports Server (NTRS)

Woodard, Stanley E. (Inventor); Taylor, Bryant D. (Inventor)

2013-01-01

A wireless sensing system includes a sensor made from an electrical conductor shaped to form an open-circuit, electrically-conductive spiral trace having inductance and capacitance. In the presence of a time-varying magnetic field, the sensor resonates to generate a harmonic response having a frequency, amplitude and bandwidth. A magnetic field response recorder wirelessly transmits the time-varying magnetic field to the sensor and wirelessly detects the sensor's response frequency, amplitude and bandwidth.

Changes in magma storage conditions following caldera collapse at Okataina Volcanic Center, New Zealand

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

Rubin, Allison; Cooper, Kari M.; Leever, Marissa

Large silicic volcanic centers produce both small rhyolitic eruptions and catastrophic caldera-forming eruptions. Although changes in trace element and isotopic compositions within eruptions following caldera collapse have been observed at rhyolitic volcanic centers such as Yellowstone and Long Valley, much still remains unknown about the ways in which magma reservoirs are affected by caldera collapse. We present 238U– 230Th age, trace element, and Hf isotopic data from individual zircon crystals from four eruptions from the Okataina Volcanic Center, Taupo Volcanic Zone, New Zealand, in order to assess changes in trace element and isotopic composition of the reservoir following the 45-kamore » caldera-forming Rotoiti eruption. Our data indicate that (1) mixing of magmas derived from crustal melts and mantle melts takes place within the shallow reservoir; (2) while the basic processes of melt generation likely did not change significantly between pre- and post-caldera rhyolites, post-caldera zircons show increased trace element and isotopic heterogeneity that suggests a decrease in the degree of interconnectedness of the liquid within the reservoir following collapse; and (3) post-caldera eruptions from different vents indicate different storage times of the amalgamated melt prior to eruption. Furthermore, these data further suggest that the timescales needed to generate large volumes of eruptible melt may depend on the timescales needed to increase interconnectedness and achieve widespread homogenization throughout the reservoir.« less

Catalytic solid substrate room temperature phosphorimetry for the determination of trace rhamnose based on its condensation reaction with calcein

NASA Astrophysics Data System (ADS)

Liu, Jia-Ming; Lin, Li-Ping; Wang, Hong-Xin; Lin, Shao-Qin; Zhang, Li-Hong; Cai, Wen-Lian; Lin, Xuan; Pan, You-Zhu; Wang, Xin-Xing; Li, Zhi-Ming; Jiao, Li; Cui, Ma-Lin

2011-12-01

Calcein (R) could not only emit strong and stable room temperature phosphorescence (RTP) on filter paper using I - as perturber, but also could be oxidized by H 2O 2 to form a non-phosphorescence compound (R'), resulting in the quenching of RTP signal of R. Moreover, the ortho-hydrogen of phenolic hydroxyl in R took condensation reaction with rhamnose (Rha) to produce non-phosphorescence compound (R-Rha) causing the RTP signal of R to further quench, and R-Rha was oxidized by H 2O 2 to form R' and Rha, bringing about the sharp RTP signal quenching of R. Thus, a new solid substrate room temperature phosphorimetry (SSRTP) for the determination of trace Rha based on its strong catalytic effect on H 2O 2 oxidizing R has been established, with the detection limit (LD) of 7.8 zg spot -1 (corresponding concentration: 2.0 × 10 -17 g ml -1, sample volume: 0.40 μl spot -1). This method has been applied to determine trace Rha in cigarettes and jujubes, with the results coinciding well with those determined by a high performance liquid chromatography (HPLC). The component of R-Rha also was analyzed by means of HPLC, mass spectrometer and nuclear magnetic resonance (NMR) measurements. The mechanism of catalytic SSRTP for the determination of trace Rha was discussed.

Changes in magma storage conditions following caldera collapse at Okataina Volcanic Center, New Zealand

DOE PAGES

Rubin, Allison; Cooper, Kari M.; Leever, Marissa; ...

2015-12-15

Large silicic volcanic centers produce both small rhyolitic eruptions and catastrophic caldera-forming eruptions. Although changes in trace element and isotopic compositions within eruptions following caldera collapse have been observed at rhyolitic volcanic centers such as Yellowstone and Long Valley, much still remains unknown about the ways in which magma reservoirs are affected by caldera collapse. We present 238U– 230Th age, trace element, and Hf isotopic data from individual zircon crystals from four eruptions from the Okataina Volcanic Center, Taupo Volcanic Zone, New Zealand, in order to assess changes in trace element and isotopic composition of the reservoir following the 45-kamore » caldera-forming Rotoiti eruption. Our data indicate that (1) mixing of magmas derived from crustal melts and mantle melts takes place within the shallow reservoir; (2) while the basic processes of melt generation likely did not change significantly between pre- and post-caldera rhyolites, post-caldera zircons show increased trace element and isotopic heterogeneity that suggests a decrease in the degree of interconnectedness of the liquid within the reservoir following collapse; and (3) post-caldera eruptions from different vents indicate different storage times of the amalgamated melt prior to eruption. Furthermore, these data further suggest that the timescales needed to generate large volumes of eruptible melt may depend on the timescales needed to increase interconnectedness and achieve widespread homogenization throughout the reservoir.« less

Thermodynamic framework for the ground state of a simple quantum system

NASA Astrophysics Data System (ADS)

Souza, Andre M. C.; Nobre, Fernando D.

2017-01-01

The ground state of a two-level system (associated with probabilities p and 1 -p , respectively) defined by a general Hamiltonian H ̂=Ĥ0+λ V ̂ is studied. The simple case characterized by λ =0 , whose Hamiltonian Ĥ0 is represented by a diagonal matrix, is well established and solvable within Boltzmann-Gibbs statistical mechanics; in particular, it follows the third law of thermodynamics, presenting zero entropy (SBG=0 ) at zero temperature (T =0 ). Herein it is shown that the introduction of a perturbation λ V ̂ (λ >0 ) in the Hamiltonian may lead to a nontrivial ground state, characterized by an entropy S [p ] (with S [p ] ≠SBG[p ] ), if the Hermitian operator V ̂ is represented by a 2 ×2 matrix, defined by nonzero off-diagonal elements V12=V21=-z , where z is a real positive number. Hence, this new term in the Hamiltonian, presenting V12≠0 , may produce physically significant changes in the ground state, and especially, it allows for the introduction of an effective temperature θ (θ ∝λ z ), which is shown to be a parameter conjugated to the entropy S . Based on this, one introduces an infinitesimal heatlike quantity, δ Q =θ d S , leading to a consistent thermodynamic framework, and by proposing an infinitesimal form for the first law, a Carnot cycle and thermodynamic potentials are obtained. All results found are very similar to those of usual thermodynamics, through the identification T ↔θ , and particularly the form for the efficiency of the proposed Carnot Cycle. Moreover, S also follows a behavior typical of a third law, i.e., S →0 , when θ →0 .

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

NASA Astrophysics Data System (ADS)

Garmon, Savannah; Ordonez, Gonzalo

2017-06-01

It has been reported in the literature that the survival probability P(t) near an exceptional point where two eigenstates coalesce should generally exhibit an evolution P (t ) ˜t2e-Γ t, in which Γ is the decay rate of the coalesced eigenstate; this has been verified in a microwave billiard experiment [B. Dietz et al., Phys. Rev. E 75, 027201 (2007)]. However, the heuristic effective Hamiltonian that is usually employed to obtain this result ignores the possible influence of the continuum threshold on the dynamics. By contrast, in this work we employ an analytical approach starting from the microscopic Hamiltonian representing two simple models in order to show that the continuum threshold has a strong influence on the dynamics near exceptional points in a variety of circumstances. To report our results, we divide the exceptional points in Hermitian open quantum systems into two cases: at an EP2A two virtual bound states coalesce before forming a resonance, anti-resonance pair with complex conjugate eigenvalues, while at an EP2B two resonances coalesce before forming two different resonances. For the EP2B, which is the case studied in the microwave billiard experiment, we verify that the survival probability exhibits the previously reported modified exponential decay on intermediate time scales, but this is replaced with an inverse power law on very long time scales. Meanwhile, for the EP2A the influence from the continuum threshold is so strong that the evolution is non-exponential on all time scales and the heuristic approach fails completely. When the EP2A appears very near the threshold, we obtain the novel evolution P (t ) ˜1 -C1√{t } on intermediate time scales, while further away the parabolic decay (Zeno dynamics) on short time scales is enhanced.

On the M-function and Borg-Marchenko theorems for vector-valued Sturm-Liouville equations

NASA Astrophysics Data System (ADS)

Andersson, E.

2003-12-01

We will consider a vector-valued Sturm-Liouville equation of the form R[U]≔-(PU')'+QU=λWU, x∈[0,b), with P-1, W, Q∈Lloc1([0,b))m×m being Hermitian and under some additional conditions on P-1 and W. We give an elementary deduction of the leading order term asymptotics for the Titchmarsh-Weyl M-function corresponding to this equation. In the special case of P=W=I, Q∈L1([0,∞))m×m and the Neumann boundary conditions at 0, we will also prove that M=(1/√-λ )(I+R)(I-R)-1, where R=limn→∞ Rn=∑n=1∞Qn, for recursively defined sequences {Rn} and {Qn}. If Q∈Lloc1([0,b))m×m, 0

Thermodynamic framework for the ground state of a simple quantum system.

PubMed

Souza, Andre M C; Nobre, Fernando D

2017-01-01

The ground state of a two-level system (associated with probabilities p and 1-p, respectively) defined by a general Hamiltonian H[over ̂]=H[over ̂]_{0}+λV[over ̂] is studied. The simple case characterized by λ=0, whose Hamiltonian H[over ̂]_{0} is represented by a diagonal matrix, is well established and solvable within Boltzmann-Gibbs statistical mechanics; in particular, it follows the third law of thermodynamics, presenting zero entropy (S_{BG}=0) at zero temperature (T=0). Herein it is shown that the introduction of a perturbation λV[over ̂] (λ>0) in the Hamiltonian may lead to a nontrivial ground state, characterized by an entropy S[p] (with S[p]≠S_{BG}[p]), if the Hermitian operator V[over ̂] is represented by a 2×2 matrix, defined by nonzero off-diagonal elements V_{12}=V_{21}=-z, where z is a real positive number. Hence, this new term in the Hamiltonian, presenting V_{12}≠0, may produce physically significant changes in the ground state, and especially, it allows for the introduction of an effective temperature θ (θ∝λz), which is shown to be a parameter conjugated to the entropy S. Based on this, one introduces an infinitesimal heatlike quantity, δQ=θdS, leading to a consistent thermodynamic framework, and by proposing an infinitesimal form for the first law, a Carnot cycle and thermodynamic potentials are obtained. All results found are very similar to those of usual thermodynamics, through the identification T↔θ, and particularly the form for the efficiency of the proposed Carnot Cycle. Moreover, S also follows a behavior typical of a third law, i.e., S→0, when θ→0.

Alleviation of environmental risks associated with severely contaminated mine tailings using amendments: Modeling of trace element speciation, solubility, and plant accumulation.

PubMed

Pardo, Tania; Bes, Cleménce; Bernal, Maria Pilar; Clemente, Rafael

2016-11-01

Tailings are considered one of the most relevant sources of contamination associated with mining activities. Phytostabilization of mine spoils may need the application of the adequate combination of amendments to facilitate plant establishment and reduce their environmental impact. Two pot experiments were set up to assess the capability of 2 inorganic materials (calcium carbonate and a red mud derivate, ViroBind TM ), alone or in combination with organic amendments, for the stabilization of highly acidic trace element-contaminated mine tailings using Atriplex halimus. The effects of the treatments on tailings and porewater physico-chemical properties and trace-element accumulation by the plants, as well as the processes governing trace elements speciation and solubility in soil solution and their bioavailability were modeled. The application of the amendments increased tailings pH and decreased (>99%) trace elements solubility in porewater, but also changed the speciation of soluble Cd, Cu, and Pb. All the treatments made A. halimus growth in the tailings possible; organic amendments increased plant biomass and nutritional status, and reduced trace-element accumulation in the plants. Tailings amendments modified trace-element speciation in porewater (favoring the formation of chlorides and/or organo-metallic forms) and their solubility and plant uptake, which were found to be mainly governed by tailing/porewater pH, electrical conductivity, and organic carbon content, as well as soluble/available trace-element concentrations. Environ Toxicol Chem 2016;35:2874-2884. © 2016 SETAC. © 2016 SETAC.

a Baseline Study of Physico-Chemical Parameters and Trace Metals in Waters of Manakudy, South-West Coast of India

NASA Astrophysics Data System (ADS)

Subramanian, M.; Muthumanikkam, J.

2013-05-01

The transport of trace metals from the land to ocean has a number of different routes and efficiencies. The sources of toxic elements into the rivers to be debouched into the sea through estuaries are either weathered naturally from the soils and rocks or introduced anthropogenically from point or non-point sources, in labile form or in particulate form. However, recent studies indicate that the transport of trace elements to the aquatic environment is much more complex than what has been thought. The chemistry and ecology of an estuarine system are entirely different from the fluvial as well as the marine system. Estuarine environment is characterized by a constantly changing mixture of salt and freshwater. In the present study area Manakudy estuary is situated about 8 kilometres north west of Kanyakumari (Latitude N 08 05 21.8 and Longitude E 077 29 03.7). To gain a better understanding of the geochemical behavior of physico-chemical parameters and trace elements in the estuary and to examine variations in associated chemical changes, 20 water samples were collected throughout the Manakudy estuary, a minor river in south-western India. These samples, collected in typical dry season during 2012, were analyzed for physico-chemical parameters, dissolved major and trace elements. Our results show that dissolved Na, Mg, Ca and Cl behave conservatively along the salinity gradient. The concentration of nutrients is normal and they are due to the higher organic activity in soils as well as faster rates of chemical weathering reaction in the source region. The concentration of major ions is due to tidal influence and it increases with salinity and the nutrients do behave non-conservatively due to biogenic removal. The conservative behaviour of the trace metals with salinity has been strongly affected by the introduction of these metals by external sources. Even though the trace metals in the contaminated water have been removed and incorporated in sediments due to flocculation, the concentration of these metals did not decrease. S.MUTHUSAMY M.sc.,M.phil., RESEARCH SCHOLAR UNIVERSITY OF MADRAS CHENNAI,TAMILNADU INDIA

Nanogeochemistry of hydrothermal magnetite

NASA Astrophysics Data System (ADS)

Deditius, Artur P.; Reich, Martin; Simon, Adam C.; Suvorova, Alexandra; Knipping, Jaayke; Roberts, Malcolm P.; Rubanov, Sergey; Dodd, Aaron; Saunders, Martin

2018-06-01

Magnetite from hydrothermal ore deposits can contain up to tens of thousands of parts per million (ppm) of elements such as Ti, Si, V, Al, Ca, Mg, Na, which tend to either structurally incorporate into growth and sector zones or form mineral micro- to nano-sized particles. Here, we report micro- to nano-structural and chemical data of hydrothermal magnetite from the Los Colorados iron oxide-apatite deposit in Chile, where magnetite displays both types of trace element incorporation. Three generations of magnetites (X-Z) were identified with concentrations of minor and trace elements that vary significantly: SiO2, from below detection limit (bdl) to 3.1 wt%; Al2O3, 0.3-2.3 wt%; CaO, bdl-0.9 wt%; MgO, 0.02-2.5 wt%; TiO2, 0.1-0.4 wt%; MnO, 0.04-0.2 wt%; Na2O, bdl-0.4 wt%; and K2O, bdl-0.4 wt%. An exception is V2O3, which is remarkably constant, ranging from 0.3 to 0.4 wt%. Six types of crystalline nanoparticles (NPs) were identified by means of transmission electron microscopy in the trace element-rich zones, which are each a few micrometres wide: (1) diopside, (2) clinoenstatite; (3) amphibole, (4) mica, (5) ulvöspinel, and (6) Ti-rich magnetite. In addition, Al-rich nanodomains, which contain 2-3 wt% of Al, occur within a single crystal of magnetite. The accumulation of NPs in the trace element-rich zones suggest that they form owing to supersaturation from a hydrothermal fluid, followed by entrapment during continuous growth of the magnetite surface. It is also concluded that mineral NPs promote exsolution of new phases from the mineral host, otherwise preserved as structurally bound trace elements. The presence of abundant mineral NPs in magnetite points to a complex incorporation of trace elements during growth, and provides a cautionary note on the interpretation of micron-scale chemical data of magnetite.

Origins of diamond-forming fluids: An isotopic and trace element study of diamonds and silicates from diamondiferous xenoliths

NASA Astrophysics Data System (ADS)

Laiginhas, Fernando; Pearson, D. Graham; McNeill, John; Gurney, John; Nowell, Geoff; Ottley, Chris

2010-05-01

While there is increasing understanding of the age of formation and nature of "gem" diamonds, significant debate revolves around the nature of the fluids/melts from which they form. Stable C and N isotopes have been shown to be highly variable and yet the role of subduction-related fluids remains strongly debated. Recent studies on fibrous diamonds have yielded new trace and major element data (e.g., Weiss et al., 2009) that, together with new radiogenic isotope data (Klein BenDavid et al., 2010) indicate such diamonds grow from fluids that comprise mixtures of hydrous silicic, hydrous saline and carbonatitic fluids, derived from different source components of asthenospheric and lithospheric origin. However, until now such data has been lacking from gem diamonds. Using a new laser-based technique (McNeill et al., 2009), we have analysed a suite of diamonds plus co-existing host silicates from several diamondiferous xenoliths (6 harzburgites, 1 eclogite) from the Finsch and Newlands kimberlites in order to try to understand the fluid compositions that produce gem diamonds and better understand their effects of their mantle wall rocks. Diamonds from the xenoliths show a wide variety of trace element enrichment levels. While the eclogitic diamond shows similar trace element systematics to some of the harzburgitic diamonds there are significant differences within the harzburgitic diamonds from different xenoliths, with those from Finsch being significantly enriched in Ba, Sr and Pb relative to other elements. Nd isotope data on the host silicates is variable and dominantly unradiogenic, indicative of long-term enrichment typically associated with the source of some diamond-forming fluids. We will present Sr isotopic data on host silicates and diamond fluids to constrain whether the "gem" diamonds require the complex sources of fluids that characterise the growth of fibrous diamonds. 1) Y. Weiss, R. Kessel, W.L. Griffin, I. Kiflawi, O. Klein-BenDavid, D.R. Bell, J.W. Harris and O. Navon (2009). A new model for the evolution of diamond-forming fluids: Evidence from microinclusion-bearing diamonds from Kankan, Guinea. Lithos 112, Supp. 2: 660-674. 2) O. Klein-BenDavid, D.G. Pearson, G.M. Nowell, C. Ottley, J.C.R. McNeill, P. Cartigny (2010). Mixed fluid sources involved in diamond growth constrained by Sr-Nd-Pb-C-N isotopes and trace elements. EPSL 289, 1-2: 123-133. 3) J. McNeill, D.G. Pearson, O. Klein-BenDavid, G.M. Nowell, C.J. Ottley and I. Chinn (2009). Quantitative analysis of trace element concentrations in some gem-quality diamonds. J. Phys.: Condens. Matter 21: 364207 (13pp).

Electrochemical Sample Matrix Elimination for Trace Level Potentiometric Detection with Polymeric Membrane Ion-Selective Electrodes

PubMed Central

Chumbimuni-Torres, Karin Y.; Calvo-Marzal, Percy; Wang, Joseph; Bakker, Eric

2008-01-01

Potentiometric sensors are today sufficiently well understood and optimized to reach ultra-trace level (sub-nanomolar) detection limits for numerous ions. In many cases of practical relevance, however, a high electrolyte background hampers the attainable detection limits. A particularly difficult sample matrix for potentiometric detection is seawater, where the high saline concentration forms a major interfering background and reduces the activity of most trace metals by complexation. This paper describes for the first time a hyphenated system for the online electrochemically modulated preconcentration and matrix elimination (EMPM) of trace metals, combined with a downstream potentiometric detection with solid contact polymeric membrane ion-selective microelectrodes. Following the preconcentration at the bismuth coated electrodes, the deposited metals are oxidized and released to a medium favorable to potentiometric detection, in this case calcium nitrate. Matrix interferences arising from the saline sample medium are thus circumvented. This concept is successfully evaluated with cadmium as a model trace element and offers potentiometric detection down to low parts per billion levels in samples containing 0.5 M NaCl background electrolyte. PMID:18570385

Designing quantum information processing via structural physical approximation.

PubMed

Bae, Joonwoo

2017-10-01

In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.

Designing quantum information processing via structural physical approximation

NASA Astrophysics Data System (ADS)

Bae, Joonwoo

2017-10-01

In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.

Numerical Analysis of Stress Concentration in Isotropic and Laminated Plates with Inclined Elliptical Holes

NASA Astrophysics Data System (ADS)

Khechai, Abdelhak; Tati, Abdelouahab; Belarbi, Mohamed Ouejdi; Guettala, Abdelhamid

2018-03-01

The design of high-performance composite structures frequently includes discontinuities to reduce the weight and fastener holes for joining. Understanding the behavior of perforated laminates is necessary for structural design. In the current work, stress concentrations taking place in laminated and isotropic plates subjected to tensile load are investigated. The stress concentrations are obtained using a recent quadrilateral finite element of four nodes with 32 DOFs. The present finite element (PE) is a combination of two finite elements. The first finite element is a linear isoparametric membrane element and the second is a high precision Hermitian element. One of the essential objectives of the current investigation is to confirm the capability and efficiency of the PE for stress determination in perforated laminates. Different geometric parameters, such as the cutout form, sizes and cutout orientations, which have a considerable effect on the stress values, are studied. Using the present finite element formulation, the obtained results are found to be in good agreement with the analytical findings, which validates the capability and the efficiency of the proposed formulation. Finally, to understand the material parameters effect such as the orientation of fibers and degree of orthotropy ratio on the stress values, many figures are presented using different ellipse major to minor axis ratio. The stress concentration values are considerably affected by increasing the orientation angle of the fibers and degree of orthotropy.

Holographic hierarchy in the Gaussian matrix model via the fuzzy sphere

NASA Astrophysics Data System (ADS)

Garner, David; Ramgoolam, Sanjaye

2013-10-01

The Gaussian Hermitian matrix model was recently proposed to have a dual string description with worldsheets mapping to a sphere target space. The correlators were written as sums over holomorphic (Belyi) maps from worldsheets to the two-dimensional sphere, branched over three points. We express the matrix model correlators by using the fuzzy sphere construction of matrix algebras, which can be interpreted as a string field theory description of the Belyi strings. This gives the correlators in terms of trivalent ribbon graphs that represent the couplings of irreducible representations of su(2), which can be evaluated in terms of 3j and 6j symbols. The Gaussian model perturbed by a cubic potential is then recognised as a generating function for Ponzano-Regge partition functions for 3-manifolds having the worldsheet as boundary, and equipped with boundary data determined by the ribbon graphs. This can be viewed as a holographic extension of the Belyi string worldsheets to membrane worldvolumes, forming part of a holographic hierarchy linking, via the large N expansion, the zero-dimensional QFT of the Matrix model to 2D strings and 3D membranes. Note that if, after removing the white vertices, the graph contains a blue edge connecting to the same black vertex at both ends, then the triangulation generated from the black edges will contain faces that resemble cut discs. These faces are triangles with two of the edges identified.

Quantum and electromagnetic propagation with the conjugate symmetric Lanczos method.

PubMed

Acevedo, Ramiro; Lombardini, Richard; Turner, Matthew A; Kinsey, James L; Johnson, Bruce R

2008-02-14

The conjugate symmetric Lanczos (CSL) method is introduced for the solution of the time-dependent Schrodinger equation. This remarkably simple and efficient time-domain algorithm is a low-order polynomial expansion of the quantum propagator for time-independent Hamiltonians and derives from the time-reversal symmetry of the Schrodinger equation. The CSL algorithm gives forward solutions by simply complex conjugating backward polynomial expansion coefficients. Interestingly, the expansion coefficients are the same for each uniform time step, a fact that is only spoiled by basis incompleteness and finite precision. This is true for the Krylov basis and, with further investigation, is also found to be true for the Lanczos basis, important for efficient orthogonal projection-based algorithms. The CSL method errors roughly track those of the short iterative Lanczos method while requiring fewer matrix-vector products than the Chebyshev method. With the CSL method, only a few vectors need to be stored at a time, there is no need to estimate the Hamiltonian spectral range, and only matrix-vector and vector-vector products are required. Applications using localized wavelet bases are made to harmonic oscillator and anharmonic Morse oscillator systems as well as electrodynamic pulse propagation using the Hamiltonian form of Maxwell's equations. For gold with a Drude dielectric function, the latter is non-Hermitian, requiring consideration of corrections to the CSL algorithm.

Webinar on the Removal of Uranium from Drinking Water by Small System Treatment Technology

EPA Science Inventory

Abstract: Radionuclides, such as uranium (U), occur naturally as trace elements in rocks and soils and thus can be found in dissolved forms in ground waters. Uranium has four oxidation states (+3, +4, +5, and +6) and is a very reactive element forming a variety of stable complexe...

Earth's first stable continents did not form by subduction

NASA Astrophysics Data System (ADS)

Johnson, Tim; Brown, Michael; Gardiner, Nicholas; Kirkland, Christopher; Smithies, Hugh

2017-04-01

The geodynamic setting in which Earth's first stable cratonic nuclei formed remains controversial. Most exposed Archaean continental crust comprises rocks of the tonalite-trondhjemite-granodiorite (TTGs) series that were produced from partial melting of low magnesium basaltic source rocks and have 'arc-like' trace element signatures that resemble continental crust produced in modern supra-subduction zone settings. The East Pilbara Terrane, Western Australia, is amongst the oldest fragments of preserved continental crust of Earth. Low magnesium basalts of the Paleoarchaean Coucal Formation, at the base of the Pilbara Supergroup, have trace element compositions consistent with the putative source rocks for TTGs. These basalts may be remnants of the ≥35 km-thick pre-3.5 Ga plateau-like basaltic crust that is predicted to have formed if mantle temperatures were much hotter than today. Using phase equilibria modelling of an average uncontaminated Coucal basalt, we confirm their suitability as TTG source rocks. The results suggest that TTGs formed by 20-30% melting along high geothermal gradients (≥700 °C/GPa), which accord with apparent geotherms recorded by >95% of Archaean rocks worldwide. Moreover, the trace element composition of the Coucal basalts demonstrates that they were derived from an earlier generation of mafic/ultramafic rocks, and that the arc-like signature in Archaean TTGs was inherited through an ancestral source lineage. The protracted multistage process required for production and stabilisation of Earth's first continents, coupled with the high geothermal gradients, are incompatible with modern-style subduction and favour a stagnant lid regime in the early Archaean.

Spontaneous PT-Symmetry Breaking for Systems of Noncommutative Euclidean Lie Algebraic Type

NASA Astrophysics Data System (ADS)

Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah

2015-11-01

We propose a noncommutative version of the Euclidean Lie algebra E 2. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra.

Floquet protocols of adiabatic state flips and reallocation of exceptional points

NASA Astrophysics Data System (ADS)

Halpern, Dashiell; Li, Huanan; Kottos, Tsampikos

2018-04-01

We introduce the notion of adiabatic state flip of a Floquet Hamiltonian associated with a non-Hermitian system that it is subjected to two driving schemes with clear separation of time scales. The fast (Floquet) modulation scheme is utilized to reallocate the exceptional points in the parameter space of the system and redefine the topological features of an adiabatic cyclic modulation associated with the slow driving scheme. Such topological reorganization can be used in order to control the adiabatic transport between two eigenmodes of the Floquet Hamiltonian. The proposed scheme provides a degree of reconfigurability of adiabatic state transfer which can find applications in system control in photonics and microwave domains.

QCD dirac operator at nonzero chemical potential: lattice data and matrix model.

PubMed

Akemann, Gernot; Wettig, Tilo

2004-03-12

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at a nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.

Quasibound states in a triple Gaussian potential

NASA Astrophysics Data System (ADS)

Reichl, L. E.; Porter, Max D.

2018-04-01

We derive the transmission probabilities and delay times, and identify quasibound state structures in an open quantum system consisting of three Gaussian potential energy peaks, a system whose classical scattering dynamics we show to be chaotic. Such open quantum systems can serve as models for nanoscale quantum devices and their wave dynamics are similar to electromagnetic wave dynamics in optical microcavities. We use a quantum web to determine energy regimes for which the system exhibits the quantum manifestations of chaos, and we show that the classical scattering dynamics contains a significant amount of chaos. We also derive an exact expression for the non-Hermitian Hamiltonian whose eigenvalues give quasibound state energies and lifetimes of the system.

Recursive inverse factorization.

PubMed

Rubensson, Emanuel H; Bock, Nicolas; Holmström, Erik; Niklasson, Anders M N

2008-03-14

A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.

Coherent perfect absorption in one-sided reflectionless media

PubMed Central

Wu, Jin-Hui; Artoni, M.; La Rocca, G. C.

2016-01-01

In optical experiments one-sided reflectionless (ORL) and coherent perfect absorption (CPA) are unusual scattering properties yet fascinating for their fundamental aspects and for their practical interest. Although these two concepts have so far remained separated from each other, we prove that the two phenomena are indeed strictly connected. We show that a CPA–ORL connection exists between pairs of points lying along lines close to each other in the 3D space-parameters of a realistic lossy atomic photonic crystal. The connection is expected to be a generic feature of wave scattering in non-Hermitian optical media encompassing, as a particular case, wave scattering in parity-time (PT) symmetric media. PMID:27759020

Fingerprints of exceptional points in the survival probability of resonances in atomic spectra

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Moiseyev, Nimrod

2011-07-01

The unique time signature of the survival probability exactly at the exceptional point parameters is studied here for the hydrogen atom in strong static magnetic and electric fields. We show that indeed the survival probability S(t)=|<ψ(0)|ψ(t)>|2 decays exactly as |1-at|2e-ΓEPt/ℏ, where ΓEP is associated with the decay rate at the exceptional point and a is a complex constant depending solely on the initial wave packet that populates exclusively the two almost degenerate states of the non-Hermitian Hamiltonian. This may open the possibility for a first experimental detection of exceptional points in a quantum system.

Uncertainty Relation on Generalized Skew Information with aMonotone Pair

NASA Astrophysics Data System (ADS)

Liu, Jun-Tong; Wang, Qing-Wen; Li, Lei

2017-08-01

In this paper, we first define a generalized ( f, g)-skew information |I_{ ρ }^{(f, g)} |(A) and two related quantity |J_{ ρ }^{(f, g)} |(A) and |U_{ ρ }^{(f, g)} |(A) for any non-Hermitian Hilbert-Schmidt operator A and a density operator ρ on a Hilbert space H and discuss some properties of them. And then, we obtain the following uncertainty relation in terms of |U_{ ρ }^{(f, g)} |(A): |U_{ ρ}^{(f, g)}|(A)|U_{ ρ}^{(f, g)}|(B)≥ β_{(f, g)}|Tr( f(ρ)g(ρ)[A, B]0)|2, which is a generalization of a known uncertainty relation in Ko and Yoo (J. Math. Anal. Appl. 383, 208-214, 11).

Petrographic and geochemical contrasts and environmentally significant trace elements in marine-influenced coal seams, Yanzhou mining area, China

USGS Publications Warehouse

Liu, Gaisheng; Yang, P.; Peng, Z.; Chou, C.-L.

2004-01-01

The Yanzhou mining area in west Shandong Province, China contains coals of Permian and Carboniferous age. The 31 and 32 seams of the Permian Shanxi Formation and seams 6, 15-17 of the Carboniferous Taiyuan Formation were analyzed for coal petrology, mineralogy and geochemical parameters. The parameters indicate that the coal is high volatile bituminous in rank. The coal is characterized by high vitrinite and low to medium inertinite and liptinite contents. These properties may be related to evolution of the coal forming environment from more reducing conditions in a marine influenced lower delta plain environment for the early Taiyuan coals to more oxidizing paleoenvironments in an upper delta plain for the upper Shanxi coal seams. The major mineral phases present in the coal are quartz, kaolinite, pyrite and calcite. Sulfur is one of the hazardous elements in coal. The major forms of sulfur in coal are pyritic, organic and sulfate sulfur. Pyritic and organic sulfur generally account for the bulk of the sulfur in coal. Elemental sulfur also occurs in coal, but only in trace to minor amounts. In this paper, the distribution and concentration of sulfur in the Yanzhou mining district are analyzed, and the forms of sulfur are studied. The sulfur content of the Taiyuan coal seams is considerably higher than that of the Shanxi coals. Organic sulfur content is positively correlated to total and pyritic sulfur. The vertical variation of Cu, Zn, Pb, As, Th, U and sulfur contents in coal seam 3 of the Shanxi Formation in the Xinglongzhuang mine show that all these trace elements, with the exception of Th, are enriched in the top and bottom plies of the seam, and that their concentrations are also relatively high in the dirt bands within the seam. The pyritic sulfur is positively correlated with total sulfur, and both are enriched in the top, bottom and parting plies of the seam. The concentrations of the trace elements are closely related to sulfur and ash contents. Most of the trace elements are correlated with the ash content, and may be associated with the mineral matter in the coal. ?? 2004 Elsevier Ltd. All rights reserved.

Tracing Multiple Generations of Active Galactic Nucleau Feedback in the Core of Abell 262

DTIC Science & Technology

2009-06-01

Virgo cluster reveal a series of filaments, which trace regions that are thought 1481 Report Documentation Page Form ApprovedOMB No. 0704-0188 Public...L. Sarazin4, L. D. Anderson3, Gopal-Krishna5, E. M. Douglass3, and N. E. Kassim1 1 Naval Research Laboratory, 4555 Overlook Avenue SW, Code 7213...Washington, DC 20375, USA 2 Interferometrics Inc., 13454 Sunrise Valley Drive, Suite 240, Herndon, VA 20171, USA 3 Institute for Astrophysical Research

A preliminary study on ice shape tracing with a laser light sheet

NASA Technical Reports Server (NTRS)

Mercer, Carolyn R.; Vargas, Mario; Oldenburg, John R.

1993-01-01

Preliminary work towards the development of an automated method of measuring the shape of ice forming on an airfoil during wind tunnel tests has been completed. A thin sheet of light illuminated the front surfaces of rime, glaze, and mixed ice shapes and a solid-state camera recorded images of each. A maximum intensity algorithm extracted the profiles of the ice shapes and the results were compared to hand tracings. Very good general agreement was found in each case.

Trace Element Abundances in an Unusual Hibonite-Perovskite Refractory Inclusion from Allende

NASA Technical Reports Server (NTRS)

Mane, Prajkta; Wadhwa, M.; Keller, L. P.

2013-01-01

Calcium-aluminum-rich refractory inclusions (CAIs) are thought to be the first-formed solids in the Solar protoplanetary disk and can provide information about the earliest Solar System processes (e.g., [1]). A hibonite-perovskitebearing CAI from the Allende CV3 chondrite (SHAL, [2]) contains a single of 500 micrometers hibonite grain and coarse-grained perovskite. The mineralogy and oxygen isotopic composition of this CAI shows similarities with FUN inclusions, especially HAL [2]. Here we present trace element abundances in SHAL.

Nebulization Reflux Concentrator

NASA Technical Reports Server (NTRS)

Cofer, Wesley R., III; Collins, V. G.

1986-01-01

Nebulization reflux concentrator extracts and concentrates trace quantities of water-soluble gases for subsequent chemical analysis. Hydrophobic membrane and nebulizing nozzles form scrubber for removing trace quantities of soluble gases or other contaminants from atmosphere. Although hydrophobic membrane virtually blocks all transport of droplets, it offers little resistance to gas flow; hence, device permits relatively large volumes of gas scrubbed efficiently with very small volumes of liquid. This means analyzable quantities of contaminants concentrate in extracting solutions in much shorter times than with conventional techniques.

A comparison of measures of riverbed form for evaluating distributions of benthic fishes

USGS Publications Warehouse

Wildhaber, Mark L.; Lamberson, Peter J.; Galat, David L.

2003-01-01

A method to quantitatively characterize the bed forms of a large river and a preliminary test of the relationship between bed-form characteristics and catch per unit area of benthic fishes is presented. We used analog paper recordings of bathymetric data from the Missouri River and fish data collected from 1996 to 1998 at both the segment (???101-102-km) and macrohabitat (???10-1-100-km) spatial scales. Bed-form traces were transformed to digital data with image analysis software. The slope, mean residual, and SD of the residuals of the regression of depth versus distance along the bottom, as well as mean depth, were estimated for each trace. These four metrics were compared with sinuosity, fractal dimension, critical scale, and maximum mean angle for the same traces. Mean depth and sinuosity differed among segments and macrohabitats. Fractal-based measures of the relative depth of bottom troughs (critical scale) and smoothness (maximum mean angle) differed among segments. Statistics-based measures of the relative depth of bottom troughs (mean residual) and smoothness (SD of the residuals) differed among macrohabitats. Sites with shovelnose sturgeon Scaphirhynchus platorynchus were shallower and smoother than sites without shovelnose sturgeon. When compared with sites without sicklefin chub Macrhybopsis meeki, sites with sicklefin chub were shallower, had shallower troughs, and sloped more out of the flow of the river. Sites with sturgeon chub M. gelida were shallower, had shallower troughs, and were smoother than sites without sturgeon chub. Sites with and without channel catfish Ictalurus punctatus did not differ for any bed-form variables measured. Nonzero shovelnose sturgeon density increased with depth, whereas nonzero sturgeon chub density decreased with depth. Indices of bed-form structure demonstrated potential for describing the distribution and abundance of Missouri River benthic fishes. The observed fish patterns, though limited, provide valuable direction for future research into the habitat preferences of these fishes.

Trace element abundances in megacrysts and their host basalts - Constraints on partition coefficients and megacryst genesis

NASA Technical Reports Server (NTRS)

Irving, A. J.; Frey, F. A.

1984-01-01

Rare earth and other trace element abundances are determined in megacrysts of clinopyroxene, orthopyroxene, amphibole, mica, anorthoclase, apatite and zircon, as well as their host basalts, in an effort to gather data on mineral/melt trace element partitioning during the high pressure petrogenesis of basic rocks. Phase equilibria, major element partitioning and isotopic ratio considerations indicate that while most of the pyroxene and amphibole megacrysts may have been in equilibrium with their host magmas at high pressures, mica, anorthoclase, apatite, and zircon megacrysts are unlikely to have formed in equilibrium with their host basalts. It is instead concluded that they were precipitated from more evolved magmas, and have been mixed into their present hosts.

A comparison of partially specular radiosity and ray tracing for room acoustics modeling

NASA Astrophysics Data System (ADS)

Beamer, C. Walter; Muehleisen, Ralph T.

2005-04-01

Partially specular (PS) radiosity is an extended form of the general radiosity method. Acoustic radiosity is a form of bulk transfer of radiant acoustic energy. This bulk transfer is accomplished through a system of energy balance equations that relate the bulk energy transfer of each surface in the system to all other surfaces in the system. Until now acoustic radiosity has been limited to modeling only diffuse surface reflection. The new PS acoustic radiosity method can model all real surface types, diffuse, specular and everything in between. PS acoustic radiosity also models all real source types and distributions, not just point sources. The results of the PS acoustic radiosity method are compared to those of well known ray tracing programs. [Work supported by NSF.

Major, trace element and stable isotope geochemistry of synorogenic breccia bodies, Ellsworth Mountains, Antarctica

USGS Publications Warehouse

Craddock, J.P.; McGillion, M.S.; Webers, G.F.

2007-01-01

Cambrian carbonates in the Heritage Range of the Ellsworth Mountains, West Antarctica host a series of carbonate-rich breccia bodies that formed contemporaneously with the Permian Gondwanide orogen. The breccia bodies had a three-stage genesis, with the older breccias containing Cambrian limestone (and marble) clasts supported by calcite, whereas the younger breccias are nearly clast-free and composed entirely of matrix calcite. Breccia clasts, calcite matrix and detrital matrix samples were analyzed using x-ray fluorescence (major and trace elements), x-ray diffraction, and stable isotopes (C, O) and suggest that the breccias formed as part of a closed geochemical system, at considerable depth, within the Cambrian limestone host as the Ellsworth Mountains deformed into a fold-and-thrust belt along the margin of Gondwana

Analysis of transferred fragrance and its forensic implications.

PubMed

Gherghel, Simona; Morgan, Ruth M; Blackman, Christopher S; Karu, Kersti; Parkin, Ivan P

2016-12-01

Perfumes are widely used by many people in developed countries, and a large number of both men and women wear perfumes on a daily basis. Analysis of perfume trace materials from clothing is not commonly employed within forensic casework, yet as a form of trace evidence it has the potential to provide valuable intelligence. In order to appreciate the value of trace evidence there is a fundamental need for an evidence base that can both offer insight into how a trace material behaves under different scenarios and activities, and from which inferences can be made. With this purpose a gas chromatography-mass spectrometry method for trace analysis of perfumes was developed. This paper presents two different series of experiments that investigate the dynamics of perfume transfer as a factor of perfume ageing time, and as a factor of perfume contact time. Empirical data showed that both perfume ageing time, and perfume contact time play a key role in the number of perfume components transferred. These studies have implication for forensic protocols, specifically for perfume trace evidence collection, analysis, interpretation, and presentation, and there is potentially great value in analysing perfumes from clothing exhibits in forensic enquiries that involve close contact between individuals, such as sexual assaults. Copyright © 2016 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Leveraging Semantic Labels for Multi-level Abstraction in Medical Process Mining and Trace Comparison.

PubMed

Leonardi, Giorgio; Striani, Manuel; Quaglini, Silvana; Cavallini, Anna; Montani, Stefania

2018-05-21

Many medical information systems record data about the executed process instances in the form of an event log. In this paper, we present a framework, able to convert actions in the event log into higher level concepts, at different levels of abstraction, on the basis of domain knowledge. Abstracted traces are then provided as an input to trace comparison and semantic process discovery. Our abstraction mechanism is able to manage non trivial situations, such as interleaved actions or delays between two actions that abstract to the same concept. Trace comparison resorts to a similarity metric able to take into account abstraction phase penalties, and to deal with quantitative and qualitative temporal constraints in abstracted traces. As for process discovery, we rely on classical algorithms embedded in the framework ProM, made semantic by the capability of abstracting the actions on the basis of their conceptual meaning. The approach has been tested in stroke care, where we adopted abstraction and trace comparison to cluster event logs of different stroke units, to highlight (in)correct behavior, abstracting from details. We also provide process discovery results, showing how the abstraction mechanism allows to obtain stroke process models more easily interpretable by neurologists. Copyright © 2018. Published by Elsevier Inc.

On Asymptotic Properties of a Number Theoretic Function Arising out of a Spin Chain Modelin Statistical Mechanics

NASA Astrophysics Data System (ADS)

Kallies, J.; Özlük, A.; Peter, M.; Snyder, C.

Let Let N be a positive integer and define Φ(N) as the number of matrices, C, which are products of A and B, where both A and B must occur, such that the trace, Tr(C)=N. It has been conjectured that see [10]. In this note we consider the summatory function and show that

On the phase form of a deformation quantization with separation of variables

NASA Astrophysics Data System (ADS)

Karabegov, Alexander

2016-06-01

Given a star product with separation of variables on a pseudo-Kähler manifold, we obtain a new formal (1, 1)-form from its classifying form and call it the phase form of the star product. The cohomology class of a star product with separation of variables equals the class of its phase form. We show that the phase forms can be arbitrary and they bijectively parametrize the star products with separation of variables. We also describe the action of a change of the formal parameter on a star product with separation of variables, its formal Berezin transform, classifying form, phase form, and canonical trace density.

27 CFR 17.161 - General.

Code of Federal Regulations, 2010 CFR

2010-04-01

... form is prescribed for these records, but the data required to be shown shall be clearly recorded and organized to enable appropriate TTB officers to trace each operation or transaction, monitor compliance with...

27 CFR 17.161 - General.

Code of Federal Regulations, 2012 CFR

2012-04-01

... form is prescribed for these records, but the data required to be shown shall be clearly recorded and organized to enable appropriate TTB officers to trace each operation or transaction, monitor compliance with...

27 CFR 17.161 - General.

Code of Federal Regulations, 2011 CFR

2011-04-01

... form is prescribed for these records, but the data required to be shown shall be clearly recorded and organized to enable appropriate TTB officers to trace each operation or transaction, monitor compliance with...

27 CFR 17.161 - General.

Code of Federal Regulations, 2013 CFR

2013-04-01

... form is prescribed for these records, but the data required to be shown shall be clearly recorded and organized to enable appropriate TTB officers to trace each operation or transaction, monitor compliance with...

27 CFR 17.161 - General.

Code of Federal Regulations, 2014 CFR

2014-04-01

... form is prescribed for these records, but the data required to be shown shall be clearly recorded and organized to enable appropriate TTB officers to trace each operation or transaction, monitor compliance with...

Balancing single- and multi-reference correlation in the chemiluminescent reaction of dioxetanone using the anti-Hermitian contracted Schrödinger equation.

PubMed

Greenman, Loren; Mazziotti, David A

2011-05-07

Direct computation of energies and two-electron reduced density matrices (2-RDMs) from the anti-Hermitian contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)], it is shown, recovers both single- and multi-reference electron correlation in the chemiluminescent reaction of dioxetanone especially in the vicinity of the conical intersection where strong correlation is important. Dioxetanone, the light-producing moiety of firefly luciferin, efficiently converts chemical energy into light by accessing its excited-state surface via a conical intersection. Our previous active-space 2-RDM study of dioxetanone [L. Greenman and D. A. Mazziotti, J. Chem. Phys. 133, 164110 (2010)] concluded that correlating 16 electrons in 13 (active) orbitals is required for realistic surfaces without correlating the remaining (inactive) orbitals. In this paper we pursue two complementary goals: (i) to correlate the inactive orbitals in 2-RDMs along dioxetanone's reaction coordinate and compare these results with those from multireference second-order perturbation theory (MRPT2) and (ii) to assess the size of the active space-the number of correlated electrons and orbitals-required by both MRPT2 and ACSE for accurate energies and surfaces. While MRPT2 recovers very different amounts of correlation with (4,4) and (16,13) active spaces, the ACSE obtains a similar amount of correlation energy with either active space. Nevertheless, subtle differences in excitation energies near the conical intersection suggest that the (16,13) active space is necessary to determine both energetic details and properties. Strong electron correlation is further assessed through several RDM-based metrics including (i) total and relative energies, (ii) the von Neumann entropy based on the 1-electron RDM, as well as the (iii) infinity and (iv) squared Frobenius norms based on the cumulant 2-RDM.

Application and development of the Schwinger multichannel scattering theory and the partial differential equation theory of electron-molecule scattering

NASA Technical Reports Server (NTRS)

Weatherford, Charles A.

1993-01-01

One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.

Flow of essential elements in subcellular fractions during oxidative stress.

PubMed

Lago, Larissa; Nunes, Emilene A; Vigato, Aryane A; Souza, Vanessa C O; Barbosa, Fernando; Sato, João R; Batista, Bruno L; Cerchiaro, Giselle

2017-02-01

Essential trace elements are commonly found in altered concentrations in the brains of patients with neurodegenerative diseases. Many studies in trace metal determination and quantification are conducted in tissue, cell culture or whole brain. In the present investigation, we determined by ICP-MS Fe, Cu, Zn, Ca, Se, Co, Cr, Mg, and Mn in organelles (mitochondria, nuclei) and whole motor neuron cell cultured in vitro. We performed experiments using two ways to access oxidative stress: cell treatments with H 2 O 2 or Aβ-42 peptide in its oligomeric form. Both treatments caused accumulation of markers of oxidative stress, such as oxidized proteins and lipids, and alteration in DNA. Regarding trace elements, cells treated with H 2 O 2 showed higher levels of Zn and lower levels of Ca in nuclei when compared to control cells with no oxidative treatments. On the other hand, cells treated with Aβ-42 peptide in its oligomeric form showed higher levels of Mg, Ca, Fe and Zn in nuclei when compared to control cells. These differences showed that metal flux in cell organelles during an intrinsic external oxidative condition (H 2 O 2 treatment) are different from an intrinsic external neurodegenerative treatment.

Mercury species, selenium, metallothioneins and glutathione in two dolphins from the southeastern Brazilian coast: Mercury detoxification and physiological differences in diving capacity.

PubMed

Kehrig, Helena A; Hauser-Davis, Rachel A; Seixas, Tercia G; Pinheiro, Ana Beatriz; Di Beneditto, Ana Paula M

2016-06-01

In the present study, the concentration of trace elements, total mercury (Hg) and selenium (Se) and mercury forms (MeHg, Hginorg and HgSe) in the vulnerable coastal dolphins Pontoporia blainvillei and Sotalia guianensis were appraised and compared, using metallothioneins (MT) and glutathione (GSH) as biomarkers for trace element exposure. The trace element concentrations varied between muscle and liver tissues, with liver of all dolphin specimens showing higher Hg and Se concentrations than those found in muscle. Hg, MeHg and Hginorg molar concentrations showed a clear increase with Se molar concentrations in the liver of both dolphins, and Se concentrations were higher than those of Hg on a molar basis. Se plays a relevant role in the detoxification of MeHg in the hepatic tissue of both dolphins, forming Hg-Se amorphous crystals in liver. In contrast, MT were involved in the detoxification process of Hginorg in liver. GSH levels in P. blainvillei and S. guianensis muscle tissue suggest that these dolphins have different diving capacities. Muscle Hg concentrations were associated to this tripeptide, which protects dolphin cells against Hg stress. Copyright © 2016 Elsevier Ltd. All rights reserved.

Probabilistic evaluation of n traces with no putative source: A likelihood ratio based approach in an investigative framework.

PubMed

De March, I; Sironi, E; Taroni, F

2016-09-01

Analysis of marks recovered from different crime scenes can be useful to detect a linkage between criminal cases, even though a putative source for the recovered traces is not available. This particular circumstance is often encountered in the early stage of investigations and thus, the evaluation of evidence association may provide useful information for the investigators. This association is evaluated here from a probabilistic point of view: a likelihood ratio based approach is suggested in order to quantify the strength of the evidence of trace association in the light of two mutually exclusive propositions, namely that the n traces come from a common source or from an unspecified number of sources. To deal with this kind of problem, probabilistic graphical models are used, in form of Bayesian networks and object-oriented Bayesian networks, allowing users to intuitively handle with uncertainty related to the inferential problem. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Al-26, Pu-244, Ti-50, REE, and trace element abundances in hibonite grains from CM and CV meteorites

NASA Technical Reports Server (NTRS)

Fahey, A. J.; Mckeegan, K. D.; Zinner, E.; Goswami, J. N.

1987-01-01

Hibonites from the CM meteorites Murchison, Murray, and Cold Bokkeveld, and hibonites and Ti-rich pyroxene from the CV chondrite Allende are studied. Electron microprobe measurements of major element concentrations and track and ion probe measurements of Mg and Ti isotopic ratios, rare earth elements (REEs), and trace element abundances are analyzed. Correlations between isotopic anomalies in Ti, Al-26, Pu-244, and Mg-26(asterisk) are examined. Ti isotopic anomalies are compared with REE and trace element abundance patterns. Reasons for the lack of Al-26 in the hibonites are investigated and discussed. It is observed that there is no correlation between the Ti isotopic compositions, and the presence of Mg-26(asterisk), Pu-244, and REE and trace element patterns in individual hibonite samples. The data reveal that hibonites are not interstellar dust grains but formed on a short time scale and in localized regions of the early solar system.

Report of the U.S. Geological Survey's evaluation program for standard reference samples distributed in April 1993; T-123 (trace constituents), T-125 (trace constituents), M-126 (major constituents, N-38 (nutrients), N-39 (nutrients), P-20 (low ionic strength, and Hg-16 (mercury)

USGS Publications Warehouse

Long, H.K.; Farrar, J.W.

1993-01-01

This report presents the results of the U.S. Geological Survey's analytical evaluation program for seven standard reference samples--T-123 (trace constituents), T-125 (trace constituents), M-126 (major constituents), N-38 (nutrients), N-39 (Nutrients), P-20 (precipitation-low ionic strength), and Hg-16 (mercury)--that were distributed in April 1993 to 175 laboratories registered in the U.S. Geological Survey sponsored interlaboratory testing program. Analytical data received from 131 of the laboratories were evaluated with respect to: overall laboratory performance and relative laboratory performance for each analyte in the 7 reference samples. Results of these evaluations are presented in tabular form. Also presented are tables and graphs summarizing the analytical data provided by each laboratory for each analyte in the seven standard reference samples. The most probable value for each analyte was determined using nonparametric statistics.

Cholinergic transmission in the dorsal hippocampus modulates trace but not delay fear conditioning.

PubMed

Pang, Min-Hee; Kim, Nam-Soo; Kim, Il-Hwan; Kim, Hyun; Kim, Hyun-Taek; Choi, June-Seek

2010-09-01

Although cholinergic mechanisms have been widely implicated in learning and memory processes, few studies have investigated the specific contribution of hippocampal cholinergic transmission during trace fear conditioning, a form of associative learning involving a temporal gap between two stimuli. Microinfusions of scopolamine, a muscarinic receptor antagonist, into the dorsal hippocampus (DH) produced dose-dependent impairment in the acquisition and expression of a conditioned response (CR) following trace fear conditioning with a tone conditioned stimulus (CS) and a footshock unconditioned stimulus (US) in rats. The same infusions, however, had no effect on delay conditioning, general activity, pain sensitivity or attentional modulation. Moreover, scopolamine infusions attenuated phosphorylation of extracellular signal-regulated kinase (ERK) in the amygdala, indicating that cholinergic signals in the DH are important for trace fear conditioning. Taken together, the current study provides evidence that cholinergic neurotransmission in the DH is essential for the cellular processing of CS-US association in the amygdala when the two stimuli are temporally disconnected. Copyright 2010 Elsevier Inc. All rights reserved.

Geochemistry of environmentally sensitive trace elements in Permian coals from the Huainan coalfield, Anhui, China

USGS Publications Warehouse

Chen, J.; Liu, Gaisheng; Jiang, M.; Chou, C.-L.; Li, H.; Wu, B.; Zheng, Lingyun; Jiang, D.

2011-01-01

To study the geochemical characteristics of 11 environmentally sensitive trace elements in the coals of the Permian Period from the Huainan coalfield, Anhui province, China, borehole samples of 336 coals, two partings, and four roof and floor mudstones were collected from mineable coal seams. Major elements and selected trace elements were determined by inductively coupled plasma optical emission spectrometry (ICP-OES), inductively coupled plasma mass spectrometry (ICP-MS), and hydride generation atomic absorption spectrometry (HAAS). The depositional environment, abundances, distribution, and modes of occurrence of trace elements were investigated. Results show that clay and carbonate minerals are the principal inorganic constituents in the coals. A lower deltaic plain, where fluvial channel systems developed successively, was the likely depositional environment of the Permian coals in the Huainan coalfield. All major elements have wider variation ranges than those of Chinese coals except for Mg and Fe. The contents of Cr, Co, Ni, and Se are higher than their averages for Chinese coals and world coals. Vertical variations of trace elements in different formations are not significant except for B and Ba. Certain roof and partings are distinctly higher in trace elements than underlying coal bench samples. The modes of occurrence of trace elements vary in different coal seams as a result of different coal-forming environments. Vanadium, Cr, and Th are associated with aluminosilicate minerals, Ba with carbonate minerals, and Cu, Zn, As, Se, and Pb mainly with sulfide minerals. ?? 2011 Elsevier B.V.

Trace elements in Gem-Quality Diamonds - Origin and evolution of diamond-forming fluid inclusions

NASA Astrophysics Data System (ADS)

Pearson, Graham; Krebs, Mandy; Stachel, Thomas; Woodland, Sarah; Chinn, Ingrid; Kong, Julie

2017-04-01

In the same way that melt inclusions in phenocrysts have expanded our idea of melt formation and evolution in basalts, studying fluids trapped in diamonds is providing important new constraints on the nature of diamond-forming fluids. Fibrous and cloudy diamonds trap a high but variable density of fluid inclusions and so have been extensively studied using major and trace element compositions. In contrast, constraining the nature of the diamond-forming fluid for high purity gem-quality diamonds has been restricted by the rarity of available high quality trace element data. This is due to the extremely low concentrations of impurities that gem diamonds contain - often in the ppt range. The recent discovery of fluids in gem diamonds showing similar major element chemistry to fluid-rich diamonds suggest that many diamonds may share a common spectrum of parental fluids. Here we test this idea further. Recent advances in analytical techniques, in particular the development of the "off-line" laser ablation pre-concentration approach, have allowed fully quantitative trace element data to be recovered from "fluid-poor", high quality gem diamonds. We present trace element data for gem diamonds from a variety of locations from Canada, S. Africa and Russia, containing either silicate or sulphide inclusions to examine possible paragenetic or genetic differences between fluids. REE abundance in the "gem" diamonds vary from 0.1 to 0.0001 x chondrite. To a first order, we observe the same spectrum of trace element compositions in the gem diamonds as that seen in fluid-rich "fibrous" diamonds, supporting a common origin for the fluids. REE patterns range from extremely flat (Ce/Yb)n 2.5 to 5 (commonly in sulphide-bearing diamonds) to >70, the latter having significantly greater inter-element HFSE/LILE fractionation. In general, the fluids from the sulphide-bearing diamonds are less REE-enriched than the silicate-bearing diamonds, but the ranges overlap significantly. The very large range in REE fractionation mimics very closely that produced in high pressure (5-6 GPa) experimental melts of CO2-H2O fluxed peridotite. Hence, the elemental characteristics of the fluids could be reconciled by the diamonds growing from such melts over a range of T and hence F, with the sulphide-bearing diamonds generally being produced by larger fraction (higher T) melts that have reacted less with their wall rocks. It is also possible that the less REE enriched fluids are consistent with derivation from more reduced CH4-bearing fluids that have lower solute capacity than oxidised fluids. This option is being evaluated.

Drill Holes and Predation Traces versus Abrasion-Induced Artifacts Revealed by Tumbling Experiments

PubMed Central

Gorzelak, Przemysław; Salamon, Mariusz A.; Trzęsiok, Dawid; Niedźwiedzki, Robert

2013-01-01

Drill holes made by predators in prey shells are widely considered to be the most unambiguous bodies of evidence of predator-prey interactions in the fossil record. However, recognition of traces of predatory origin from those formed by abiotic factors still waits for a rigorous evaluation as a prerequisite to ascertain predation intensity through geologic time and to test macroevolutionary patterns. New experimental data from tumbling various extant shells demonstrate that abrasion may leave holes strongly resembling the traces produced by drilling predators. They typically represent singular, circular to oval penetrations perpendicular to the shell surface. These data provide an alternative explanation to the drilling predation hypothesis for the origin of holes recorded in fossil shells. Although various non-morphological criteria (evaluation of holes for non-random distribution) and morphometric studies (quantification of the drill hole shape) have been employed to separate biological from abiotic traces, these are probably insufficient to exclude abrasion artifacts, consequently leading to overestimate predation intensity. As a result, from now on, we must adopt more rigorous criteria to appropriately distinguish abrasion artifacts from drill holes, such as microstructural identification of micro-rasping traces. PMID:23505530

Contact tracing and antiviral prophylaxis in the early stages of a pandemic: the probability of a major outbreak.

PubMed

Ross, Joshua V; Black, Andrew J

2015-09-01

Antiviral prophylaxis forms a significant component of health management plans for many countries around the world. A number of studies have shown that the delays typically encountered in distributing these antivirals to households, following the first infectious case, can result in their efficacy being severely reduced. Here, we investigate the use of contact tracing as a method to reduce the delays and hence mitigate the reduction in efficacy of antivirals. We assess the usefulness of contact tracing in terms of the probability of a major outbreak. It is found, with parameter distributions appropriate to the 2009 H1N1 pandemic and distributions reflecting commonly experienced delays, that standard contact tracing renders an outbreak impossible approximately one in five times compared with approximately one in ten times in its absence. A contact-tracing efficiency of 50% would see further improvements with an outbreak being impossible approximately one in four times, and a reduction of the median probability of a major outbreak from 0.41 to below 0.27. © The authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Trace elemental analysis of bituminuos coals using the Heidelberg proton microprobe

USGS Publications Warehouse

Chen, J.R.; Kneis, H.; Martin, B.; Nobiling, R.; Traxel, K.; Chao, E.C.T.; Minkin, J.A.

1981-01-01

Trace elements in coal can occur as components of either the organic constituents (macerals) or the inorganic constituents (minerals). Studies of the concentrations and distribution of the trace elements are vital to understanding the geochemical millieu in which the coal was formed and in evaluating the attempts to recover rare but technologically valuable metals. In addition, information on the trace element concentrations is important in predicting the environmental impact of burning particular coals, as many countries move toward greater utilization of coal reserves for energy production. Traditionally, the optical and the electron microscopes and more recently the electron microprobe have been used in studying the components of coal. The proton-induced X-ray emission (PIXE) microprobe offers a new complementary approach with an order of magnitude or more better minimum detection limit. We present the first measurements with a PIXE microprobe of the trace element concentrations of bituminous coal samples. Elemental analyses of the coal macerals-vitrinite, exinite, and inertinite-are discussed for three coal samples from the Eastern U.S.A., three samples from the Western U.S.A., and one sample from the Peoples Republic of China. ?? 1981.

Mechanisms for trace metal enrichment at the surface microlayer in an estuarine salt marsh

USGS Publications Warehouse

Lion, Leonard W.

1982-01-01

The relative contributions of adsorption to particulate surfaces, complexation with surface-active organic ligands and uptake by micro-organisms were evaluated with respect to their importance in the surface microlayer enrichment (‘partitioning’) of Cd, Pb and Cu. The contributions of each process were inferred from field data in which partitioning of the dissolved and particulate forms of Cd, Pb and Cu, total and dissolved organic carbon, particles and total bacteria were observed. In the South San Francisco Bay estuary, particle enrichment appears to control trace metal partitioning. Trace metal association with the particulate phase and the levels of partitioning observed were in the order Pb > Cu > Cd and reflect the calculated equilibrium chemical speciation of these metals in computer-simulated seawater matrices.

Identification of detergents for forensic fiber analysis.

PubMed

Heider, Emily C; Mujumdar, Nirvani; Campiglia, Andres D

2016-11-01

Trace fibers are an important form of trace evidence, and identification of exogenous substances on textile fibers provides valuable information about the origin of the fiber. Laundering textiles can provide a unique fluorescent spectral signature of the whitening agent in the detergent that adsorbs to the fiber. Using fluorescence microscopy, the spectral characteristics of seven detergents adsorbed to single fibers drawn from laundered textiles were investigated, and principal component analysis of clusters was used to characterize the type of detergent on the fiber. On dyed nylon fibers, spectra from eight different detergent pairs could be resolved and washed validation fibers correctly classified. On dyed acrylic fibers, five different detergent pairs could be resolved and identified. Identification of the detergent type may prove useful in matching a trace fiber to its bulk specimen of origin.

Nighttime chemical evolution of aerosol and trace gases in a power plant plume: Implications for secondary organic nitrate and organosulfate aerosol formation, NO₃ radical chemistry, and N₂O₅ heterogeneous hydrolysis

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

Zaveri, Rahul A.; Berkowitz, Carl M.; Brechtel, Fred J.

Chemical evolution of aerosols and trace gases in the Salem Harbor power plant plume was monitored with the DOE G-1 aircraft on the night of July 30-31, 2002. Quasi-Lagrangian sampling in the plume at increasing downwind distances/processing times was guided by a constant-volume tetroon that was released near the power plant at sunset. While no evidence of fly ash particles was found, concentrations of particulate organics, sulfate, and nitrate were higher in the plume than in the nearby background air. These species were internally mixed and the particles were acidic, suggesting that particulate nitrate was in the form of organicmore » nitrate. The enhanced particulate organic and nitrate masses in the plume were inferred to be as secondary organic aerosol, possibly formed from the NO3 radical-initiated oxidation of isoprene and other trace organic gases in the presence of acidic sulfate particles. The enhanced particulate sulfate concentrations observed in the plume were attributed to direct emissions of gaseous SO3/H2SO4 from the power plant. Furthermore, concentration of nucleation mode particles was significantly higher in the plume than in background air, suggesting that some of the emitted H2SO4 had nucleated to form new particles. Spectromicroscopic analyses of particle samples suggested that some sulfate was likely in the form of organosulfates. Constrained Lagrangian model analysis of the aircraft and tetroon observations showed that heterogeneous hydrolysis of N2O5 was negligibly slow. These results have significant implications for several scientific and regulatory issues related to the impacts of power plant emissions on atmospheric chemistry, air quality, visibility, and climate.« less

Rare Earth Geochemistry of Rock Core form WY Reservoirs

DOE Data Explorer

Quillinan, Scott; Bagdonnas, Davin; McLaughlin, J. Fred; Nye, Charles

2016-10-01

These data include major, minor, trace and rare earth element concentration of geologic formations in Wyoming oil and gas fields. *Note - Link below contains updated version of spreadsheet (6/14/2017)

The Apollo 17 'melt sheet' - Chemistry, age and Rb/Sr systematics

NASA Technical Reports Server (NTRS)

Winzer, S. R.; Nava, D. F.; Schuhmann, S.; Philpotts, J. A.; Schuhmann, P. J.; Lum, R. K. L.; Lindstrom, M. M.; Lindstrom, D. J.

1977-01-01

Major, minor, and trace-element compositions, age data, and Rb/Sr systematics of Apollo 17 boulders have been compiled, and additional analyses performed on a norite breccia clast (77215) included in the Apollo 17, Station 7 boulder. The Apollo 17 boulders are found to be identical or nearly so in major, minor, and trace-element composition, suggesting that they all originated as an impact melt analogous to melt sheets found in larger terrestrial craters. The matrix dates (Ar-40/Ar-39) and Rb/Sr systematics available suggest that this impact melt formed by a single impact about 4 billion years ago. This impact excavated, shocked, brecciated, and melted norites, norite cumulates, and possibly anorthositic gabbros and dunites about 4.4 billion years old. The impact was likely a major one, possibly the Serenitatis basin-forming event.

Volcaniclastic habitats for early life on Earth and Mars: A case study from ˜3.5 Ga-old rocks from the Pilbara, Australia

NASA Astrophysics Data System (ADS)

Westall, Frances; Foucher, Frédéric; Cavalazzi, Barbara; de Vries, Sjoukje T.; Nijman, Wouter; Pearson, Victoria; Watson, Jon; Verchovsky, Alexander; Wright, Ian; Rouzaud, Jean-Noel; Marchesini, Daniele; Anne, Severine

2011-08-01

Within the context of present and future in situ missions to Mars to investigate its habitability and to search for traces of life, we studied the habitability and traces of past life in ˜3.5 Ga-old volcanic sands deposited in littoral environments an analogue to Noachian environments on Mars. The environmental conditions on Noachian Mars (4.1-3.7 Ga) and the Early Archaean (4.0-3.3 Ga) Earth were, in many respects, similar: presence of liquid water, dense CO 2 atmosphere, availability of carbon and bio-essential elements, and availability of energy. For this reason, information contained in Early Archaean terrestrial rocks concerning habitable conditions (on a microbial scale) and traces of past life are of relevance in defining strategies to be used to identify past habitats and past life on Mars. One such example is the 3.446 Ga-old Kitty's Gap Chert in the Pilbara Craton, NW. Australia. This formation consists of volcanic sediments deposited in a coastal mudflat environment and is thus a relevant analogue for sediments deposited in shallow water environments on Noachian Mars. Two main types of habitat are represented, a volcanic (lithic) habitat and planar stabilized sediment surfaces in sunlit shallow waters. The sediments hosted small (<1 μm in size) microorganisms that formed colonies on volcanic particle surfaces and in pore waters within the volcanic sediments, as well as biofilms on stabilised sediment surfaces. The microorganisms included coccoids, filaments and rare rod-shaped organisms associated with microbial polymer (EPS). The preserved microbial community was apparently dominated by chemotrophic organisms but some locally transported filaments and filamentous mat fragments indicate that possibly photosynthetic mats formed nearby. Both microorganisms and sediments were silicified during very early diagenesis. There are no macroscopic traces of fossilised life in these volcanic sediments and sophisticated instrumentation and specialized sample preparation techniques are required to establish the biogenicity and syngenicity of the traces of past life. The fact that the traces of life are cryptic, and the necessity of using sophisticated instrumentation, reinforces the challenges and difficulties of in situ robotic missions to identify past life on Mars. We therefore recommend the return of samples from Mars to Earth for a definitive search for traces of life.

A comparison of ZnO films deposited on indium tin oxide and soda lime glass under identical conditions

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

Deka, Angshuman; Nanda, Karuna Kar

2013-06-15

ZnO films have been grown via a vapour phase transport (VPT) on soda lime glass (SLG) and indium-tin oxide (ITO) coated glass. ZnO film on ITO had traces of Zn and C which gives them a dark appearance while that appears yellowish-white on SLG. X-ray photoelectron spectroscopy studies confirm the traces of C in the form of C-O. The photoluminescence studies reveal a prominent green luminescence band for ZnO film on ITO.

Iron active electrode and method of making same

DOEpatents

Jackovitz, John F.; Seidel, Joseph; Pantier, Earl A.

1982-10-26

An iron active electrode and method of preparing same in which iron sulfate is calcined in an oxidizing atmosphere at a temperature in the range of from about 600.degree. C. to about 850.degree. C. for a time sufficient to produce an iron oxide with a trace amount of sulfate. The calcined material is loaded into an electrically conductive support and then heated in a reducing atmosphere at an elevated temperature to produce activated iron having a trace amount of sulfide which is formed into an electrode plate.

Thermal cycler

DOEpatents

Benett, William J.; Andreski, John T.; Dzenitis, John M.; Makarewicz, Anthony J.; Hadley, Dean R.; Pannu, Satinderpall S.

2014-07-15

A thermalcycler includes a first thermalcycler body section having a first face and a second thermalcycler body section having a second face. A cavity is formed by the first face and the second face. A thermalcycling unit is positioned in the cavity. A heater trace unit is connected to a support section, to the first thermalcycler body section, to the second thermalcycler body section, and to the thermalcycling unit. The first thermalcycler body section and the second thermalcycler body section are positioned together against the support section to enclose the thermalcycling unit and the heater trace unit.

Characterization of Ultra-high Temperature Ceramics via Transmission Electron Microscopy Relevant ZrB2-based Composites, TaC-based Composites and Oxides Containing SiC Chopped Fibers

DTIC Science & Technology

2015-03-06

was formed by ZrO2 rounded grains containing W traces and covered by H3BO3 acicular crystals deriving from hydration of B2O3 after exposure to...TaSi2 grains tended to form large pockets as wide as 3-8 m. Other spurious phases formed upon decomposition of the additive, were identified as SiC

"Once-Upon-A-Time" Reconsidered: The Developmental Dialectic between Function and Form. Technical Report No. 36.

ERIC Educational Resources Information Center

Dyson, Anne Haas

A case study traces the evolution of "once-upon-a-time" in a child's classroom story writing, drawing upon data collected in a three-year study of writing development in an urban magnet school. The subject, Mitzi, is observed from kindergarten through second grade. The study assumes that stories are cultural discourse forms that serve…

Adaptive optics based non-null interferometry for optical free form surfaces test

NASA Astrophysics Data System (ADS)

Zhang, Lei; Zhou, Sheng; Li, Jingsong; Yu, Benli

2018-03-01

An adaptive optics based non-null interferometry (ANI) is proposed for optical free form surfaces testing, in which an open-loop deformable mirror (DM) is employed as a reflective compensator, to compensate various low-order aberrations flexibly. The residual wavefront aberration is treated by the multi-configuration ray tracing (MCRT) algorithm. The MCRT algorithm based on the simultaneous ray tracing for multiple system models, in which each model has different DM surface deformation. With the MCRT algorithm, the final figure error can be extracted together with the surface misalignment aberration correction after the initial system calibration. The flexible test for free form surface is achieved with high accuracy, without auxiliary device for DM deformation monitoring. Experiments proving the feasibility, repeatability and high accuracy of the ANI were carried out to test a bi-conic surface and a paraboloidal surface, with a high stable ALPAOTM DM88. The accuracy of the final test result of the paraboloidal surface was better than 1/20 Μ PV value. It is a successful attempt in research of flexible optical free form surface metrology and would have enormous potential in future application with the development of the DM technology.

Identifying common donors in DNA mixtures, with applications to database searches.

PubMed

Slooten, K

2017-01-01

Several methods exist to compute the likelihood ratio LR(M, g) evaluating the possible contribution of a person of interest with genotype g to a mixed trace M. In this paper we generalize this LR to a likelihood ratio LR(M 1 , M 2 ) involving two possibly mixed traces M 1 and M 2 , where the question is whether there is a donor in common to both traces. In case one of the traces is in fact a single genotype, then this likelihood ratio reduces to the usual LR(M, g). We explain how our method conceptually is a logical consequence of the fact that LR calculations of the form LR(M, g) can be equivalently regarded as a probabilistic deconvolution of the mixture. Based on simulated data, and using a semi-continuous mixture evaluation model, we derive ROC curves of our method applied to various types of mixtures. From these data we conclude that searches for a common donor are often feasible in the sense that a very small false positive rate can be combined with a high probability to detect a common donor if there is one. We also show how database searches comparing all traces to each other can be carried out efficiently, as illustrated by the application of the method to the mixed traces in the Dutch DNA database. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Trace Water as Prominent Factor to Induce Peptide Self-Assembly: Dynamic Evolution and Governing Interactions in Ionic Liquids.

PubMed

Wang, Juan; Yuan, Chengqian; Han, Yuchun; Wang, Yilin; Liu, Xiaomin; Zhang, Suojiang; Yan, Xuehai

2017-11-01

The interaction between water and biomolecules including peptides is of critical importance for forming high-level architectures and triggering life's functions. However, the bulk aqueous environment has limitations in detecting the kinetics and mechanisms of peptide self-assembly, especially relating to interactions of trace water. With ionic liquids (ILs) as a nonconventional medium, herein, it is discovered that trace amounts of water play a decisive role in triggering self-assembly of a biologically derived dipeptide. ILs provide a suitable nonaqueous environment, enabling us to mediate water content and follow the dynamic evolution of peptide self-assembly. The trace water is found to be involved in the assembly process of dipeptide, especially leading to the formation of stable noncovalent dipeptide oligomers in the early stage of nucleation, as evident by both experimental studies and theoretical simulations. The thermodynamics of the growth process is mainly governed by a synergistic effect of hydrophobic interaction and hydrogen bonds. Each step of assembly presents a different trend in thermodynamic energy. The dynamic evolution of assembly process can be efficiently mediated by changing trace water content. The decisive role of trace water in triggering and mediating self-assembly of biomolecules provides a new perspective in understanding supramolecular chemistry and molecular self-organization in biology. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Effect of Ground Patterns Size on FM-Band Cross-Talks between Two Parallel Signal Traces of Printed Circuit Boards for Vehicles

NASA Astrophysics Data System (ADS)

Iida, Michihira; Maeno, Tsuyoshi; Fujiwara, Osamu

It is well known that electromagnetic disturbances in vehicle-mounted radios are mainly caused by conducted noise currents flowing through wiring-harnesses from vehicle-mounted printed circuit boards (PCBs) with common ground patterns containing slits. To suppress the noise currents outflow from PCBs of these kinds, we previously measured noise currents outflow from simple two-layer PCBs having two parallel signal traces and different ground patterns with/without slits to reveal that making slits with open ends on the ground patterns in parallel with the traces can reduce the conducted noise currents. In the present study, with FDTD simulation, we investigated reduction effects of ground patterns size on the FM-band cross-talk noise levels between two parallel signal traces, by using four types of simple PCB models having different ground patterns formed in different numbers but containing the same planar dimension slits parallel to the traces, in addition to two types of PCB models with different ground patterns divided into two parts parallel to the traces. As a result, we found that the cross-talk noise currents for the above six types of PCBs decrease by 6.9-8.5dB compared to the PCB which has a plain ground with no slits. From this study, we got the finding that the contributing factor for the above mentioned cross-talk reduction relies on the reduction of mutual inductance between the two parallel traces. In addition, in case of this study, it is interesting to note that the noise currents outflow from PCBs can rather be suppressed when the size of the return ground of each signal trace is small.

Excess spontaneous emission in non-Hermitian optical systems. II. Laser oscillators

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

Siegman, A.E.

1989-02-01

When the Petermann excess-spontaneous-emission factor described in the accompanying paper (Siegman, preceding paper, Phys. Rev. A 39, 1253 (1989)) is taken into account, we find that the quantum-noise fluctuations or Schawlow-Townes fluctuations in the output spectrum of a laser oscillator will be multiplied by this excess noise factor. The excess spontaneous emission in a laser oscillator cannot be canceled by adjoint-mode-excitation techniques as it can be in a laser amplifier. The resulting noise enhancement can be very sizable (100 to 1000 times or more) in gain-guided laser oscillators, and especially in laser oscillators using geometrically unstable cavities with moderate tomore » high magnifications and Fresnel numbers.« less

Information Retrieval and Criticality in Parity-Time-Symmetric Systems.

PubMed

Kawabata, Kohei; Ashida, Yuto; Ueda, Masahito

2017-11-10

By investigating information flow between a general parity-time (PT-)symmetric non-Hermitian system and an environment, we find that the complete information retrieval from the environment can be achieved in the PT-unbroken phase, whereas no information can be retrieved in the PT-broken phase. The PT-transition point thus marks the reversible-irreversible criticality of information flow, around which many physical quantities such as the recurrence time and the distinguishability between quantum states exhibit power-law behavior. Moreover, by embedding a PT-symmetric system into a larger Hilbert space so that the entire system obeys unitary dynamics, we reveal that behind the information retrieval lies a hidden entangled partner protected by PT symmetry. Possible experimental situations are also discussed.

BFV approach to geometric quantization

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1994-12-01

A gauge-invariant approach to geometric quantization is developed. It yields a complete quantum description for dynamical systems with non-trivial geometry and topology of the phase space. The method is a global version of the gauge-invariant approach to quantization of second-class constraints developed by Batalin, Fradkin and Fradkina (BFF). Physical quantum states and quantum observables are respectively described by covariantly constant sections of the Fock bundle and the bundle of hermitian operators over the phase space with a flat connection defined by the nilpotent BVF-BRST operator. Perturbative calculation of the first non-trivial quantum correction to the Poisson brackets leads to the Chevalley cocycle known in deformation quantization. Consistency conditions lead to a topological quantization condition with metaplectic anomaly.

Spontaneous PT symmetry breaking in Dirac-Kronig-Penney crystals

NASA Astrophysics Data System (ADS)

Longhi, Stefano; Cannata, Francesco; Ventura, Alberto

2011-12-01

We introduce a non-Hermitian PT invariant extension of the Dirac-Kronig-Penney model, describing the motion of a Dirac quasiparticle in a locally periodic sequence of imaginary δ-Dirac barriers and wells, and propose its optical realization using superstructure fiber Bragg gratings with alternating regions of optical gain and absorption. For the infinite crystal, we determine the band structure and show that the PT phase is always broken. For a finite crystal, we derive analytical expressions for reflection and transmission probabilities, and show that the PT phase is unbroken below a finite threshold of the δ-barrier area. In the proposed optical realization, the onset of PT symmetry breaking in the finite crystal corresponds to the lasing condition for the grating superstructures.

Spectral singularity in composite systems and simulation of a resonant lasing cavity

NASA Astrophysics Data System (ADS)

Zhang, X. Z.; Li, G. R.; Song, Z.

2017-10-01

We investigate herein the existence of spectral singularities (SSs) in composite systems that consist of two separate scattering centers A and B embedded in one-dimensional free space, with at least one scattering center being non-Hermitian. We show that such composite systems have an SS at kc if the reflection amplitudes rA≤ft(kc\\right) and rB≤ft(kc\\right) of the two scattering centers satisfy the condition rR A≤ft(kc\\right) rLB≤ft(kc\\right) ei2kc≤ft(xB-xA\\right) =1 . We also extend the condition to the system with multi-scattering centers. As an application, we construct a simple system to simulate a resonant lasing cavity.

Basic modelling of transport in 2D wave-mechanical nanodots and billiards with balanced gain and loss mediated by complex potentials

NASA Astrophysics Data System (ADS)

Berggren, Karl-Fredrik; Tellander, Felix; Yakimenko, Irina

2018-05-01

Non-Hermitian quantum mechanics with parity-time (PT) symmetry is presently gaining great interest, especially within the fields of photonics and optics. Here, we give a brief overview of low-dimensional semiconductor nanodevices using the example of a quantum dot with input and output leads, which are mimicked by imaginary potentials for gain and loss, and how wave functions, particle flow, coalescence of levels and associated breaking of PT symmetry may be analysed within such a framework. Special attention is given to the presence of exceptional points and symmetry breaking. Related features for musical string instruments and ‘wolf-notes’ are outlined briefly with suggestions for further experiments.

Grassmann matrix quantum mechanics

DOE PAGES

Anninos, Dionysios; Denef, Frederik; Monten, Ruben

2016-04-21

We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit.more » In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.« less

Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2009-08-01

One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H ≠ H† is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our recent paper on bound states [Znojil M., SIGMA 5 (2009), 001, 19 pages, arXiv:0901.0700] is complemented by the text on scattering. An elementary example illustrates the feasibility of the resulting innovative theoretical recipe. A new family of the so called quasilocal inner products in Hilbert space is found to exist. Constructively, these products are all described in terms of certain non-equivalent short-range metric operators Θ ≠ I represented, in Runge-Kutta approximation, by (2R-1)-diagonal matrices.

Code Samples Used for Complexity and Control

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

The following sections are included: * MathematicaⓇ Code * Generic Chaotic Simulator * Vector Differential Operators * NLS Explorer * 2C++ Code * C++ Lambda Functions for Real Calculus * Accelerometer Data Processor * Simple Predictor-Corrector Integrator * Solving the BVP with the Shooting Method * Linear Hyperbolic PDE Solver * Linear Elliptic PDE Solver * Method of Lines for a Set of the NLS Equations * C# Code * Iterative Equation Solver * Simulated Annealing: A Function Minimum * Simple Nonlinear Dynamics * Nonlinear Pendulum Simulator * Lagrangian Dynamics Simulator * Complex-Valued Crowd Attractor Dynamics * Freeform Fortran Code * Lorenz Attractor Simulator * Complex Lorenz Attractor * Simple SGE Soliton * Complex Signal Presentation * Gaussian Wave Packet * Hermitian Matrices * Euclidean L2-Norm * Vector/Matrix Operations * Plain C-Code: Levenberg-Marquardt Optimizer * Free Basic Code: 2D Crowd Dynamics with 3000 Agents

Twist for Snyder space

NASA Astrophysics Data System (ADS)

Meljanac, Daniel; Meljanac, Stjepan; Mignemi, Salvatore; Pikutić, Danijel; Štrajn, Rina

2018-03-01

We construct the twist operator for the Snyder space. Our starting point is a non-associative star product related to a Hermitian realisation of the noncommutative coordinates originally introduced by Snyder. The corresponding coproduct of momenta is non-coassociative. The twist is constructed using a general definition of the star product in terms of a bi-differential operator in the Hopf algebroid approach. The result is given by a closed analytical expression. We prove that this twist reproduces the correct coproducts of the momenta and the Lorentz generators. The twisted Poincaré symmetry is described by a non-associative Hopf algebra, while the twisted Lorentz symmetry is described by the undeformed Hopf algebra. This new twist might be important in the construction of different types of field theories on Snyder space.

Geochemical study of stream waters affected by mining activities in the SE Spain

NASA Astrophysics Data System (ADS)

Garcia-Lorenzo, Maria Luz; Perez-Sirvent, Carmen; Martinez-Sanchez, Maria Jose; Bech, Jaime

2015-04-01

Water pollution by dissolved metals in mining areas has mainly been associated with the oxidation of sulphide-bearing minerals exposed to weathering conditions, resulting in low quality effluents of acidic pH and containing a high level of dissolved metals. According to transport process, three types of pollution could be established: a) Primary contamination, formed by residues placed close to the contamination sources; b) Secondary contamination, produced as a result of transport out of its production areas; c) Tertiary contamination. The aim of this work was to study trace element in water samples affected by mining activities and to apply the MINTEQ model for calculating aqueous geochemical equilibria. The studied area constituted an important mining centre for more than 2500 years, ceasing activity in 1991. The ore deposits of this zone have iron, lead and zinc as the main metal components. As a result, a lot of contaminations sources, formed by mining steriles, waste piles and foundry residues are present. For this study, 36 surficial water samples were collected after a rain episode in 4 different areas. In these samples, the trace element content was determined by by flame atomic absorption spectrometry (Fe and Zn), electrothermal atomization atomic absorption spectrometry (Pb and Cd), atomic fluorescence spectrometry (As) and ICP-MS for Al. MINTEQA2 is a geochemical equilibrium speciation model capable of computing equilibria among the dissolved, adsorbed, solid, and gas phases in an environmental setting and was applied to collected waters. Zone A: A5 is strongly influenced by tailing dumps and showed high trace element content. In addition, is influenced by the sea water and then showed high bromide, chloride, sodium and magnesium content, together with a basic pH. The MINTEQ model application suggested that Zn and Cd could precipitate as carbonate (hidrocincite, smithsonite and otavite). A9 also showed acid pH and high trace element content; is influenced by tailing dumps and also by waters from gully watercourses, transporting materials from Sierra Minera. The MINTEQ simulation showed that Pb and Ca could precipitate as sulphates (anglesite and gypsum). Waters affected by secondary contamination have been mixed with carbonate materials, present in the zone increasing the pH. Some elements have precipitated, such as Cu and Pb, while Cd, Zn and As are soluble. The MINTEQ model results showed that in A10 and A14, Al could precipitate as diaspore but also carbonates could be formed, particularly dolomite. These model in A12 sample showed that soluble Zn could precipitate as carbonate and Al as oxyhydroxide, similarly than in A13. A2 and A6 waters are affected by tertiary contamination and showed basic pH, soluble carbonates and lower trace element content. Only Zn, Cd and Al are present. The speciation model showed that in A2, Cd and Zn could precipitate as carbonates while Al as oxihydroxide. In A6, the model suggested that soluble Pb could precipitate as carbonate (hidrocerusite and cerusite) or as hydroxide; Al as diaspore, Ca as calcite and Fe as hematite. Zone B: All waters are strongly affected by mining activities and showed acid pH, high trace element content and high content of soluble sulphates. The MINTEQ results showed that in B8, Fe could precipitate as hydroxychloride and in B12 could form alunite. In B9, B10, B13 y B14, the model estimates the precipitation of anglesite, gypsum and Fe hydroxichloride (B9 and B10), diaspore in B13 and B14, and gypsum and Fe hydroxychloride in B13. All the sampling points collected in Zone C are affected by primary contamination, because there are a lot of tailing dumps. C1 showed high trace element content because is a reception point of a lot of tailing dumps. Water samples from C3 to C8 also had acid pH and high trace element content, particularly As, Zn and Cd. In addition, they showed high soluble sulphates. C2 water showed neutral pH, soluble carbonate and low trace element content because is influenced by a stabilised tailing dump. In all samples, except C2, the MINTEQ model showed that a lot of efflorescences could be formed, mainly sulphates. Zone D: All waters collected in this zone showed acid pH and high trace element content, mainly Zn, Cd and As. MINTEQ model results showed that elements could precipitate as jarosite but also anglesite in D8 and gypsum in D9, D11 and D12. D1 is affected by secondary contamination, which showed higher pH (still acid) and lower content in soluble salts and trace elements. The MINTEQ model suggested that Al could precipitate as diaspore, gibbsite and alunite. The applied model is an appropriate tool for the analysis of waters affected by mining activities. The obtained simulations confirm natural attenuation processes.

The effect of tissue structure and soil chemistry on trace element uptake in fossils

NASA Astrophysics Data System (ADS)

Hinz, Emily A.; Kohn, Matthew J.

2010-06-01

Trace element profiles for common divalent cations (Sr, Zn, Ba), rare-earth elements (REE), Y, U, and Th were measured in fossil bones and teeth from the c. 25 ka Merrell locality, Montana, USA, by using laser-ablation ICP-MS. Multiple traverses in teeth were transformed into 2-D trace element maps for visualizing structural influences on trace element uptake. Trace element compositions of different soils from the fossil site were also analyzed by solution ICP-MS, employing progressive leaches that included distilled H 2O, 0.1 M acetic acid, and microwave digestion in concentrated HCl-HNO 3. In teeth, trace element uptake in enamel is 2-4 orders of magnitude slower than in dentine, forming an effective trace element barrier. Uptake in dentine parallel to the dentine-enamel interface is enhanced by at least 2 orders of magnitude compared to transverse, causing trace element "plumes" down the tooth core. In bone, U, Ba and Sr are nearly homogeneous, implying diffusivities ˜5 orders of magnitude faster than in enamel and virtually complete equilibration with host soils. In contrast all REE show strong depletions inward, with stepwise linear segments in log-normal or inverse complementary error function plots; these data require a multi-medium diffusion model, with about 2 orders of magnitude difference in slowest vs. fastest diffusivities. Differences in REE diffusivities in bone (slow) vs. dentine (fast) reflect different partition coefficients ( Kd's). Although acid leaches and bulk digestion of soils yield comparable fossil-soil Kd's among different elements, natural solutions are expected to be neutral to slightly basic. Distilled H 2O leachates instead reveal radically different Kd's in bone for REE than for U-Sr-Ba, suggest orders of magnitude lower effective diffusivities for REE, and readily explain steep vs. flat profiles for REE vs. U-Sr-Ba, respectively. Differences among REE Kd's and diffusivities may explain inward changes in Ce anomalies. Acid washes and bulk soil compositions yield misleading Kd's for many trace elements, especially the REE, and H 2O-leaches are preferred. Patterns of trace element distributions indicate diagenetic alteration at all scales, including enamel, and challenge the use of trace elements in paleodietary studies.

39 CFR 3050.2 - Documentation of periodic reports.

Code of Federal Regulations, 2010 CFR

2010-07-01

... traced back to public documents or to primary data sources; and (3) Be submitted in a form, and be... Postal Service shall identify any input data that have changed, list any quantification techniques that...

Spatial distribution of trace metals in the Krka River, Croatia: an example of the self-purification.

PubMed

Cukrov, Neven; Cmuk, Petra; Mlakar, Marina; Omanović, Dario

2008-08-01

The spatial distribution of dissolved and total trace metals (Zn, Cd, Pb and Cu) in the Krka River (partly located in the Krka National Park) has been studied using a "clean" sampling, handling and analysis technique. Differential pulse anodic stripping voltammetry (DPASV) with a hanging mercury drop electrode (HMDE) has been used for trace metal analysis. The Krka River has been divided into the upper and lower flow region with respect to the metals concentration and main physico-chemical parameters. A significant increase in trace metal concentration as the result of the untreated waste water discharge downstream of Knin Town has been registered in the upper flow region. Due to a specific characteristic of the Krka, the so-called self-purification process, a decrease in the elevated trace metals concentration from the water column takes place at numerous small lakes formed by tufa barriers (at the end of the upper flow region). The clean groundwater input at the beginning of the lower flow region additionally contributes to the observed decrease in trace metals concentration in the Krka, maintaining them at a very low level in the remaining region of fresh-water flow. The determined median total concentrations were zinc 120-7400 ng l(-1), cadmium 3-8 ng l(-1), lead 11-250 ng l(-1) and copper 110-440 ng l(-1). Karst rivers, such as the Krka River, with extremely low natural concentrations of trace metals are highly sensitive to the anthropogenic influence. Therefore, such aquatic systems require implementation of strict protection regimes in the entire catchments area.

Trace metal accumulation in sediments and benthic macroinvertebrates before and after maintenance of a constructed wetland.

PubMed

O'Connor, Thomas P; Muthukrishnan, Swarna; Barshatzky, Kristen; Wallace, William

2012-04-01

Stormwater best management practices (BMPs) require regular maintenance. The impact on trace metal concentrations in a constructed stormwater wetland BMP on Staten Island, New York, was investigated by analyzing sediment concentrations and tissue residues of the dominant macroinvertebrates (Tubifex tubifex) prior and subsequent to maintenance. Trace metal concentrations were assessed using standard serial extraction (for sediment) and acid digestion (for tissue burdens) techniques, followed by quantitative determination using graphite furnace atomic absorption spectrometry and inductively coupled plasma optical emission spectrometry, respectively. The results suggest that disturbance of sediment during maintenance of the BMP resulted in an increase in the most mobile fraction of trace metals, especially those associated with finer grained sediments (< 63 tm), and as a consequence, measured metal concentrations in macroinvertebrates increased. Regressions of a subset of metal concentrations (copper, lead, and zinc) in sediment and the macroinvertebrate tissue burden samples generally increased as a result of maintenance. A follow-up sampling event 9 months after maintenance demonstrated that the most readily available form of trace metal in the BMP was reduced, which supports (1) long-term sequestration of metals in the BMP and (2) that elevated bioavailability following maintenance was potentially a transient feature of the disturbance. This study suggests that in the long-term, performing sediment removal might help reduce bioavailability of trace metal concentrations in both the BMP and the receiving water to which a BMP discharges. However, alternative practices might need to be implemented to reduce trace metal bioavailability in the short-term.

Monkeys have a limited form of short-term memory in audition

PubMed Central

Scott, Brian H.; Mishkin, Mortimer; Yin, Pingbo

2012-01-01

A stimulus trace may be temporarily retained either actively [i.e., in working memory (WM)] or by the weaker mnemonic process we will call passive short-term memory, in which a given stimulus trace is highly susceptible to “overwriting” by a subsequent stimulus. It has been suggested that WM is the more robust process because it exploits long-term memory (i.e., a current stimulus activates a stored representation of that stimulus, which can then be actively maintained). Recent studies have suggested that monkeys may be unable to store acoustic signals in long-term memory, raising the possibility that they may therefore also lack auditory WM. To explore this possibility, we tested rhesus monkeys on a serial delayed match-to-sample (DMS) task using a small set of sounds presented with ∼1-s interstimulus delays. Performance was accurate whenever a match or a nonmatch stimulus followed the sample directly, but it fell precipitously if a single nonmatch stimulus intervened between sample and match. The steep drop in accuracy was found to be due not to passive decay of the sample’s trace, but to retroactive interference from the intervening nonmatch stimulus. This “overwriting” effect was far greater than that observed previously in serial DMS with visual stimuli. The results, which accord with the notion that WM relies on long-term memory, indicate that monkeys perform serial DMS in audition remarkably poorly and that whatever success they had on this task depended largely, if not entirely, on the retention of stimulus traces in the passive form of short-term memory. PMID:22778411

Monkeys have a limited form of short-term memory in audition.

PubMed

Scott, Brian H; Mishkin, Mortimer; Yin, Pingbo

2012-07-24

A stimulus trace may be temporarily retained either actively [i.e., in working memory (WM)] or by the weaker mnemonic process we will call passive short-term memory, in which a given stimulus trace is highly susceptible to "overwriting" by a subsequent stimulus. It has been suggested that WM is the more robust process because it exploits long-term memory (i.e., a current stimulus activates a stored representation of that stimulus, which can then be actively maintained). Recent studies have suggested that monkeys may be unable to store acoustic signals in long-term memory, raising the possibility that they may therefore also lack auditory WM. To explore this possibility, we tested rhesus monkeys on a serial delayed match-to-sample (DMS) task using a small set of sounds presented with ~1-s interstimulus delays. Performance was accurate whenever a match or a nonmatch stimulus followed the sample directly, but it fell precipitously if a single nonmatch stimulus intervened between sample and match. The steep drop in accuracy was found to be due not to passive decay of the sample's trace, but to retroactive interference from the intervening nonmatch stimulus. This "overwriting" effect was far greater than that observed previously in serial DMS with visual stimuli. The results, which accord with the notion that WM relies on long-term memory, indicate that monkeys perform serial DMS in audition remarkably poorly and that whatever success they had on this task depended largely, if not entirely, on the retention of stimulus traces in the passive form of short-term memory.

Estimating bioaccessibility of trace elements in particles suspended in the Athabasca River using sequential extraction.

PubMed

Javed, Muhammad Babar; Shotyk, William

2018-05-10

Employing protocols developed for polar snow and ice, water samples were collected upstream, midstream and downstream of open pit bitumen mines and upgraders along the Lower Athabasca River (AR). The purpose was to: i) estimate the bioaccessibility of trace elements associated with particulate matter in the AR using sequential extraction, and ii) determine whether their forms have been measurably impacted by industrial activities. Of the trace metals known to be enriched in bitumen (V, Ni, Mo and Re), a substantial proportion of V (78-93%) and Ni (35-81%) was found in the residual fraction representing stable minerals. In contrast, Mo and Re were partitioned mainly into more reactive forms (water soluble, acid extractable, reducible and oxidisable). Comparing the non-residual fractions in upstream versus downstream sites, only water soluble Re was significantly (P = 0.005) greater downstream of industry. In respect to the potentially toxic chalcophile elements (Cu, Pb and Tl), no measurable change was observed in Cu and Pb distribution in upstream versus downstream sites. Only residual Tl was found at upstream and midstream sites, whereas a significant proportion of Tl was also present in the reducible fraction in downstream sites. Overall, a greater proportion of trace metals in the residual fraction at midstream sites appears to be due to inputs of atmospheric dust, clearly evident in microscopic images: energy dispersive spectroscopy and x-ray diffraction analyses showed that these particles were predominantly silicates, which are assumed to have limited bioaccessibility. Copyright © 2018 Elsevier Ltd. All rights reserved.