Two-tone nonlinear electrostatic waves in the quantum electron–hole plasma of semiconductors

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

Dubinov, A. E., E-mail: dubinov-ae@yandex.ru; Kitayev, I. N.

2017-01-15

Longitudinal electrostatic waves in the quantum electron–hole plasma of semiconductors are considered taking into account the degeneracy of electrons and holes and the exchange interaction. It is found in the framework of linear theory that the dispersion curve of longitudinal waves has two branches: plasmon and acoustic. An expression for the critical cutoff frequency for plasma oscillations and an expression for the speed of sound for acoustic vibrations are derived. It is shown that the plasma wave always exists in the form of a superposition of two components, characterized by different periods and wavelengths. Two nonlinear solutions are obtained withinmore » nonlinear theory: one in the form of a simple superposition of two tones and the other in the form of beats.« less

Dichromatic Langmuir waves in degenerate quantum plasma

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

Dubinov, A. E., E-mail: dubinov-ae@yandex.ru; Kitayev, I. N.

2015-06-15

Langmuir waves in fully degenerate quantum plasma are considered. It is shown that, in the linear approximation, Langmuir waves are always dichromatic. The low-frequency component of the waves corresponds to classical Langmuir waves, while the high-frequency component, to free-electron quantum oscillations. The nonlinear problem on the profile of dichromatic Langmuir waves is solved. Solutions in the form of a superposition of waves and in the form of beatings of its components are obtained.

Optimal simultaneous superpositioning of multiple structures with missing data

PubMed Central

Theobald, Douglas L.; Steindel, Phillip A.

2012-01-01

Motivation: Superpositioning is an essential technique in structural biology that facilitates the comparison and analysis of conformational differences among topologically similar structures. Performing a superposition requires a one-to-one correspondence, or alignment, of the point sets in the different structures. However, in practice, some points are usually ‘missing’ from several structures, for example, when the alignment contains gaps. Current superposition methods deal with missing data simply by superpositioning a subset of points that are shared among all the structures. This practice is inefficient, as it ignores important data, and it fails to satisfy the common least-squares criterion. In the extreme, disregarding missing positions prohibits the calculation of a superposition altogether. Results: Here, we present a general solution for determining an optimal superposition when some of the data are missing. We use the expectation–maximization algorithm, a classic statistical technique for dealing with incomplete data, to find both maximum-likelihood solutions and the optimal least-squares solution as a special case. Availability and implementation: The methods presented here are implemented in THESEUS 2.0, a program for superpositioning macromolecular structures. ANSI C source code and selected compiled binaries for various computing platforms are freely available under the GNU open source license from http://www.theseus3d.org. Contact: dtheobald@brandeis.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:22543369

On improvement of the series convergence in the problem of the vibrations of orhotropic rectangular prism

NASA Astrophysics Data System (ADS)

Lyashko, A. D.

2017-11-01

A new analytical presentation of the solution for steady-state oscillations of orthotopic rectangular prism is found. The corresponding infinite system of linear algebraic equations has been deduced by the superposition method. A countable set of precise eigenfrequencies and elementary eigenforms is found. The identities are found which make it possible to improve the convergence of all the infinite series in the solution of the problem. All the infinite series in presentation of solution are analytically summed up. Numerical calculations of stresses in the rectangular orthotropic prism with a uniform along the border and harmonic in time load on two opposite faces have been performed.

Comparison of modal superposition methods for the analytical solution to moving load problems.

DOT National Transportation Integrated Search

1994-01-01

The response of bridge structures to moving loads is investigated using modal superposition methods. Two distinct modal superposition methods are available: the modedisplacement method and the mode-acceleration method. While the mode-displacement met...

Efficient quantum transmission in multiple-source networks.

PubMed

Luo, Ming-Xing; Xu, Gang; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-04-02

A difficult problem in quantum network communications is how to efficiently transmit quantum information over large-scale networks with common channels. We propose a solution by developing a quantum encoding approach. Different quantum states are encoded into a coherent superposition state using quantum linear optics. The transmission congestion in the common channel may be avoided by transmitting the superposition state. For further decoding and continued transmission, special phase transformations are applied to incoming quantum states using phase shifters such that decoders can distinguish outgoing quantum states. These phase shifters may be precisely controlled using classical chaos synchronization via additional classical channels. Based on this design and the reduction of multiple-source network under the assumption of restricted maximum-flow, the optimal scheme is proposed for specially quantized multiple-source network. In comparison with previous schemes, our scheme can greatly increase the transmission efficiency.

Nonintegrable Schrodinger discrete breathers.

PubMed

Gómez-Gardeñes, J; Floría, L M; Peyrard, M; Bishop, A R

2004-12-01

In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrödinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable Ablowitz-Ladik lattice. These solutions are shown to be a superposition of a localized moving core and an excited extended state (background) to which the localized moving pulse is spatially asymptotic. The background is a linear combination of small amplitude nonlinear resonant plane waves and it plays an essential role in the energy balance governing the translational motion of the localized core. Perturbative collective variable theory predictions are critically analyzed in the light of the numerical results.

Nonclassical-light generation in a photonic-band-gap nonlinear planar waveguide

NASA Astrophysics Data System (ADS)

Peřina, Jan, Jr.; Sibilia, Concita; Tricca, Daniela; Bertolotti, Mario

2004-10-01

The optical parametric process occurring in a photonic-band-gap planar waveguide is studied from the point of view of nonclassical-light generation. The nonlinearly interacting optical fields are described by the generalized superposition of coherent signals and noise using the method of operator linear corrections to a classical strong solution. Scattered backward-propagating fields are taken into account. Squeezed light as well as light with sub-Poissonian statistics can be obtained in two-mode fields under the specified conditions.

Efficient Quantum Transmission in Multiple-Source Networks

PubMed Central

Luo, Ming-Xing; Xu, Gang; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-01-01

A difficult problem in quantum network communications is how to efficiently transmit quantum information over large-scale networks with common channels. We propose a solution by developing a quantum encoding approach. Different quantum states are encoded into a coherent superposition state using quantum linear optics. The transmission congestion in the common channel may be avoided by transmitting the superposition state. For further decoding and continued transmission, special phase transformations are applied to incoming quantum states using phase shifters such that decoders can distinguish outgoing quantum states. These phase shifters may be precisely controlled using classical chaos synchronization via additional classical channels. Based on this design and the reduction of multiple-source network under the assumption of restricted maximum-flow, the optimal scheme is proposed for specially quantized multiple-source network. In comparison with previous schemes, our scheme can greatly increase the transmission efficiency. PMID:24691590

Approximate analytical solutions in the analysis of elastic structures of complex geometry

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

A Simple Model for Nonlinear Confocal Ultrasonic Beams

NASA Astrophysics Data System (ADS)

Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen

2007-01-01

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

Parallel dynamics between non-Hermitian and Hermitian systems

NASA Astrophysics Data System (ADS)

Wang, P.; Lin, S.; Jin, L.; Song, Z.

2018-06-01

We reveals a connection between non-Hermitian and Hermitian systems by studying the connection between a family of non-Hermitian and Hermitian Hamiltonians based on exact solutions. In general, for a dynamic process in a non-Hermitian system H , there always exists a parallel dynamic process governed by the corresponding Hermitian conjugate system H†. We show that a linear superposition of the two parallel dynamics is exactly equivalent to the time evolution of a state under a Hermitian Hamiltonian H , and we present the relations between {H ,H ,H†} .

Modeling time-dependent corrosion fatigue crack propagation in 7000 series aluminum alloys

NASA Technical Reports Server (NTRS)

Mason, Mark E.; Gangloff, Richard P.

1994-01-01

Stress corrosion cracking and corrosion fatigue experiments were conducted with the susceptible S-L orientation of AA7075-T651, immersed in acidified and inhibited NaCl solution, to provide a basis for incorporating environmental effects into fatigue crack propagation life prediction codes such as NASA FLAGRO. This environment enhances da/dN by five to ten-fold compared to fatigue in moist air. Time-based crack growth rates from quasi-static load experiments are an order of magnitude too small for accurate linear superposition prediction of da/dN for loading frequencies above 0.001 Hz. Alternate methods of establishing da/dt, based on rising-load or ripple-load-enhanced crack tip strain rate, do not increase da/dt and do not improve linear superposition. Corrosion fatigue is characterized by two regimes of frequency dependence; da/dN is proportional to f(exp -1) below 0.001 Hz and to F(exp 0) to F(exp -0.1) for higher frequencies. Da/dN increases mildly both with increasing hold-time at K(sub max) and with increasing rise-time for a range of loading waveforms. The mild time-dependence is due to cycle-time-dependent corrosion fatigue growth. This behavior is identical for S-L nd L-T crack orientations. The frequency response of environmental fatigue in several 7000 series alloys is variable and depends on undefined compositional or microstructural variables. Speculative explanations are based on the effect of Mg on occluded crack chemistry and embritting hydrogen uptake, or on variable hydrogen diffusion in the crack tip process zone. Cracking in the 7075/NaCl system is adequately described for life prediction by linear superposition for prolonged load-cycle periods, and by a time-dependent upper bound relationship between da/dN and delta K for moderate loading times.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation. Possibilities to observe them are discussed in a cigar-shaped Bose-Einstein condensate with two hyperfine states. The results would enrich our knowledge on nonlinear excitations in many coupled nonlinear systems with transition coupling effects, such as multimode nonlinear fibers, coupled waveguides, and a multicomponent Bose-Einstein condensate system.

Fast inverse scattering solutions using the distorted Born iterative method and the multilevel fast multipole algorithm

PubMed Central

Hesford, Andrew J.; Chew, Weng C.

2010-01-01

The distorted Born iterative method (DBIM) computes iterative solutions to nonlinear inverse scattering problems through successive linear approximations. By decomposing the scattered field into a superposition of scattering by an inhomogeneous background and by a material perturbation, large or high-contrast variations in medium properties can be imaged through iterations that are each subject to the distorted Born approximation. However, the need to repeatedly compute forward solutions still imposes a very heavy computational burden. To ameliorate this problem, the multilevel fast multipole algorithm (MLFMA) has been applied as a forward solver within the DBIM. The MLFMA computes forward solutions in linear time for volumetric scatterers. The typically regular distribution and shape of scattering elements in the inverse scattering problem allow the method to take advantage of data redundancy and reduce the computational demands of the normally expensive MLFMA setup. Additional benefits are gained by employing Kaczmarz-like iterations, where partial measurements are used to accelerate convergence. Numerical results demonstrate both the efficiency of the forward solver and the successful application of the inverse method to imaging problems with dimensions in the neighborhood of ten wavelengths. PMID:20707438

Finite-Length Line Source Superposition Model (FLLSSM)

NASA Astrophysics Data System (ADS)

1980-03-01

A linearized thermal conduction model was developed to economically determine media temperatures in geologic repositories for nuclear wastes. Individual canisters containing either high level waste or spent fuel assemblies were represented as finite length line sources in a continuous media. The combined effects of multiple canisters in a representative storage pattern were established at selected points of interest by superposition of the temperature rises calculated for each canister. The methodology is outlined and the computer code FLLSSM which performs required numerical integrations and superposition operations is described.

Linear and nonlinear mechanical properties of a series of epoxy resins

NASA Technical Reports Server (NTRS)

Curliss, D. B.; Caruthers, J. M.

1987-01-01

The linear viscoelastic properties have been measured for a series of bisphenol-A-based epoxy resins cured with the diamine DDS. The linear viscoelastic master curves were constructed via time-temperature superposition of frequency dependent G-prime and G-double-prime isotherms. The G-double-prime master curves exhibited two sub-Tg transitions. Superposition of isotherms in the glass-to-rubber transition (i.e., alpha) and the beta transition at -60 C was achieved by simple horizontal shifts in the log frequency axis; however, in the region between alpha and beta, superposition could not be effected by simple horizontal shifts along the log frequency axis. The different temperature dependency of the alpha and beta relaxation mechanisms causes a complex response of G-double-prime in the so called alpha-prime region. A novel numerical procedure has been developed to extract the complete relaxation spectra and its temperature dependence from the G-prime and G-double-prime isothermal data in the alpha-prime region.

Linear solutions to metamaterial volume hologram design using a variational approach.

PubMed

Marks, Daniel L; Smith, David R

2018-04-01

Multiplex volume holograms are conventionally constructed by the repeated exposure of a photosensitive medium to a sequence of external fields, each field typically being the superposition of a reference wave that reconstructs the hologram and the other being a desired signal wave. Because there are no sources of radiation internal to the hologram, the pattern of material modulation is limited to the solutions to Helmholtz's equation in the medium. If the three-dimensional structure of the medium could be engineered at each point rather than limited to the patterns produced by standing waves, more versatile structures may result that can overcome the typical limitations to hologram dynamic range imposed by sequentially superimposing holograms. Metamaterial structures and other synthetic electromagnetic materials offer the possibility of achieving high medium contrast engineered at the subwavelength scale. By posing the multiplex volume holography problem as a linear medium design problem, we explore the potential improvements that such engineered synthetic media may provide over conventional multiplex volume holograms.

Evaluating the time and temperature dependent biaxial strength of Gore-Select ® series 57 proton exchange membrane using a pressure loaded blister test

NASA Astrophysics Data System (ADS)

Grohs, Jacob R.; Li, Yongqiang; Dillard, David A.; Case, Scott W.; Ellis, Michael W.; Lai, Yeh-Hung; Gittleman, Craig S.

Temperature and humidity fluctuations in operating fuel cells impose significant biaxial stresses in the constrained proton exchange membranes (PEMs) of a fuel cell stack. The strength of the PEM, and its ability to withstand cyclic environment-induced stresses, plays an important role in membrane integrity and consequently, fuel cell durability. In this study, a pressure loaded blister test is used to characterize the biaxial strength of Gore-Select ® series 57 over a range of times and temperatures. Hencky's classical solution for a pressurized circular membrane is used to estimate biaxial strength values from burst pressure measurements. A hereditary integral is employed to construct the linear viscoelastic analog to Hencky's linear elastic exact solution. Biaxial strength master curves are constructed using traditional time-temperature superposition principle techniques and the associated temperature shift factors show good agreement with shift factors obtained from constitutive (stress relaxation) and fracture (knife slit) tests of the material.

Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space

NASA Astrophysics Data System (ADS)

Volkoff, T. J.; Whaley, K. B.

2014-12-01

We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the branches of the superposition and another based on the ratio of the maximal quantum Fisher information of the superposition to that of its branches, i.e., the relative metrological usefulness of the superposition. A general formula for the effective sizes of these states according to the branch-distinguishability measure is obtained and applied to superposition states of N quantum harmonic oscillators composed of Gaussian branches. Considering optimal distinguishability of pure states on a time-evolution path leads naturally to a notion of distinguishability time that generalizes the well-known orthogonalization times of Mandelstam and Tamm and Margolus and Levitin. We further show that the distinguishability time provides a compact operational expression for the superposition size measure based on the relative quantum Fisher information. By restricting the maximization procedure in the definition of this measure to an appropriate algebra of observables, we show that the superposition size of, e.g., NOON states and hierarchical cat states, can scale linearly with the number of elementary particles comprising the superposition state, implying precision scaling inversely with the total number of photons when these states are employed as probes in quantum parameter estimation of a 1-local Hamiltonian in this algebra.

Aquifer response to stream-stage and recharge variations. I. Analytical step-response functions

USGS Publications Warehouse

Moench, A.F.; Barlow, P.M.

2000-01-01

Laplace transform step-response functions are presented for various homogeneous confined and leaky aquifer types and for anisotropic, homogeneous unconfined aquifers interacting with perennial streams. Flow is one-dimensional, perpendicular to the stream in the confined and leaky aquifers, and two-dimensional in a plane perpendicular to the stream in the water-table aquifers. The stream is assumed to penetrate the full thickness of the aquifer. The aquifers may be semi-infinite or finite in width and may or may not be bounded at the stream by a semipervious streambank. The solutions are presented in a unified manner so that mathematical relations among the various aquifer configurations are clearly demonstrated. The Laplace transform solutions are inverted numerically to obtain the real-time step-response functions for use in the convolution (or superposition) integral. To maintain linearity in the case of unconfined aquifers, fluctuations in the elevation of the water table are assumed to be small relative to the saturated thickness, and vertical flow into or out of the zone above the water table is assumed to occur instantaneously. Effects of hysteresis in the moisture distribution above the water table are therefore neglected. Graphical comparisons of the new solutions are made with known closed-form solutions.Laplace transform step-response functions are presented for various homogeneous confined and leaky aquifer types and for anisotropic, homogeneous unconfined aquifers interacting with perennial streams. Flow is one-dimensional, perpendicular to the stream in the confined and leaky aquifers, and two-dimensional in a plane perpendicular to the stream in the water-table aquifers. The stream is assumed to penetrate the full thickness of the aquifer. The aquifers may be semi-infinite or finite in width and may or may not be bounded at the stream by a semipervious streambank. The solutions are presented in a unified manner so that mathematical relations among the various aquifer configurations are clearly demonstrated. The Laplace transform solutions are inverted numerically to obtain the real-time step-response functions for use in the convolution (or superposition) integral. To maintain linearity in the case of unconfined aquifers, fluctuations in the elevation of the water table are assumed to be small relative to the saturated thickness, and vertical flow into or out of the zone above the water table is assumed to occur instantaneously. Effects of hysteresis in the moisture distribution above the water table are therefore neglected. Graphical comparisons of the new solutions are made with known closed-form solutions.

Electromagnetic pulses, localized and causal

NASA Astrophysics Data System (ADS)

Lekner, John

2018-01-01

We show that pulse solutions of the wave equation can be expressed as time Fourier superpositions of scalar monochromatic beam wave functions (solutions of the Helmholtz equation). This formulation is shown to be equivalent to Bateman's integral expression for solutions of the wave equation, for axially symmetric solutions. A closed-form one-parameter solution of the wave equation, containing no backward-propagating parts, is constructed from a beam which is the tight-focus limit of two families of beams. Application is made to transverse electric and transverse magnetic pulses, with evaluation of the energy, momentum and angular momentum for a pulse based on the general localized and causal form. Such pulses can be represented as superpositions of photons. Explicit total energy and total momentum values are given for the one-parameter closed-form pulse.

Analytical treatment of particle motion in circularly polarized slab-mode wave fields

NASA Astrophysics Data System (ADS)

Schreiner, Cedric; Vainio, Rami; Spanier, Felix

2018-02-01

Wave-particle interaction is a key process in particle diffusion in collisionless plasmas. We look into the interaction of single plasma waves with individual particles and discuss under which circumstances this is a chaotic process, leading to diffusion. We derive the equations of motion for a particle in the fields of a magnetostatic, circularly polarized, monochromatic wave and show that no chaotic particle motion can arise under such circumstances. A novel and exact analytic solution for the equations is presented. Additional plasma waves lead to a breakdown of the analytic solution and chaotic particle trajectories become possible. We demonstrate this effect by considering a linearly polarized, monochromatic wave, which can be seen as the superposition of two circularly polarized waves. Test particle simulations are provided to illustrate and expand our analytical considerations.

Pedagogical systematic derivation of Noether point symmetries in special relativistic field theories and extended gravity cosmology

NASA Astrophysics Data System (ADS)

Haas, Fernando

2016-11-01

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced.

On the formulation of the aerodynamic characteristics in aircraft dynamics

NASA Technical Reports Server (NTRS)

Tobak, M.; Schiff, L. B.

1976-01-01

The theory of functionals is used to reformulate the notions of aerodynamic indicial functions and superposition. Integral forms for the aerodynamic response to arbitrary motions are derived that are free of dependence on a linearity assumption. Simplifications of the integral forms lead to practicable nonlinear generalizations of the linear superpositions and stability derivative formulations. Applied to arbitrary nonplanar motions, the generalization yields a form for the aerodynamic response that can be compounded of the contributions from a limited number of well-defined characteristic motions, in principle reproducible in the wind tunnel. Further generalizations that would enable the consideration of random fluctuations and multivalued aerodynamic responses are indicated.

Analytical solutions to non-Fickian subsurface dispersion in uniform groundwater flow

USGS Publications Warehouse

Zou, S.; Xia, J.; Koussis, Antonis D.

1996-01-01

Analytical solutions are obtained by the Fourier transform technique for the one-, two-, and three-dimensional transport of a conservative solute injected instantaneously in a uniform groundwater flow. These solutions account for dispersive non-linearity caused by the heterogeneity of the hydraulic properties of aquifer systems and can be used as building blocks to construct solutions by convolution (principle of superposition) for source conditions other than slug injection. The dispersivity is assumed to vary parabolically with time and is thus constant for the entire system at any given time. Two approaches for estimating time-dependent dispersion parameters are developed for two-dimensional plumes. They both require minimal field tracer test data and, therefore, represent useful tools for assessing real-world aquifer contamination sites. The first approach requires mapped plume-area measurements at two specific times after the tracer injection. The second approach requires concentration-versus-time data from two sampling wells through which the plume passes. Detailed examples and comparisons with other procedures show that the methods presented herein are sufficiently accurate and easier to use than other available methods.

Application of the superposition principle to solar-cell analysis

NASA Technical Reports Server (NTRS)

Lindholm, F. A.; Fossum, J. G.; Burgess, E. L.

1979-01-01

The superposition principle of differential-equation theory - which applies if and only if the relevant boundary-value problems are linear - is used to derive the widely used shifting approximation that the current-voltage characteristic of an illuminated solar cell is the dark current-voltage characteristic shifted by the short-circuit photocurrent. Analytical methods are presented to treat cases where shifting is not strictly valid. Well-defined conditions necessary for superposition to apply are established. For high injection in the base region, the method of analysis accurately yields the dependence of the open-circuit voltage on the short-circuit current (or the illumination level).

Habemus superstratum! A constructive proof of the existence of superstrata

NASA Astrophysics Data System (ADS)

Bena, Iosif; Giusto, Stefano; Russo, Rodolfo; Shigemori, Masaki; Warner, Nicholas P.

2015-05-01

We construct the first example of a superstratum: a class of smooth horizonless supergravity solutions that are parameterized by arbitrary continuous functions of (at least) two variables and have the same charges as the supersymmetric D1-D5-P black hole. We work in Type IIB string theory on T 4 or K3 and our solutions involve a subset of fields that can be described by a six-dimensional supergravity with two tensor multiplets. The solutions can thus be constructed using a linear structure, and we give an explicit recipe to start from a superposition of modes specified by an arbitrary function of two variables and impose regularity to obtain the full horizonless solutions in closed form. We also give the precise CFT description of these solutions and show that they are not dual to descendants of chiral primaries. They are thus much more general than all the known solutions whose CFT dual is precisely understood. Hence our construction represents a substantial step toward the ultimate goal of constructing the fully generic superstratum that can account for a finite fraction of the entropy of the three-charge black hole in the regime of parameters where the classical black hole solution exists.

Efficient computational nonlinear dynamic analysis using modal modification response technique

NASA Astrophysics Data System (ADS)

Marinone, Timothy; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2012-08-01

Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by interconnecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases.

Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents

NASA Astrophysics Data System (ADS)

Kushch, Volodymyr I.; Sevostianov, Igor; Giraud, Albert

2017-11-01

An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.

Dirac electron in a chiral space-time crystal created by counterpropagating circularly polarized plane electromagnetic waves

NASA Astrophysics Data System (ADS)

Borzdov, G. N.

2017-10-01

The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero quasimomentum, the dispersion equation has two solutions which specify bispinor wave functions describing electron states with different energies and mean values of momentum and spin operators. The inversion of the quasimomentum results in two other linearly independent solutions. These four basic wave functions are uniquely defined by eight complex scalar functions (structural functions), which serve as convenient building blocks of the relations describing the electron properties. These properties are illustrated in graphical form over a wide range of quasimomenta. The superpositions of two basic wave functions describing different spin states and corresponding to (i) the same quasimomentum (unidirectional electron states with the spin precession) and (ii) the two equal-in-magnitude but oppositely directed quasimomenta (bidirectional electron states) are also treated.

The Influence of Finite-size Sources in Acousto-ultrasonics

NASA Technical Reports Server (NTRS)

Pavlakovic, Brian N.; Rose, Joseph L.

1994-01-01

This work explores the effects that the finite normal axisymmetric traction loading of an infinite isotropic plate has on wave propagation in acousto-ultrasonics (AU), in which guided waves are created using two normal incidence transducers. Although the work also addresses the effects of the transducer pressure distribution and pulse shape, this thesis concentrates on two main questions: how does the transducer's diameter control the phase velocity and frequency spectrum of the response, and how does the plate thickness relate to the plate's excitability? The mathematics of the time-harmonic solution and the physical principles and the practical considerations for AU wave generation are explained. Transient sources are modeled by the linear superposition of the time-harmonic solutions found using the Hankel transform and they are then compared to experimental data to provide insight into the relation between the size of the transducer and the preferred phase velocity.

Evaluation of Class II treatment by cephalometric regional superpositions versus conventional measurements.

PubMed

Efstratiadis, Stella; Baumrind, Sheldon; Shofer, Frances; Jacobsson-Hunt, Ulla; Laster, Larry; Ghafari, Joseph

2005-11-01

The aims of this study were (1) to evaluate cephalometric changes in subjects with Class II Division 1 malocclusion who were treated with headgear (HG) or Fränkel function regulator (FR) and (2) to compare findings from regional superpositions of cephalometric structures with those from conventional cephalometric measurements. Cephalographs were taken at baseline, after 1 year, and after 2 years of 65 children enrolled in a prospective randomized clinical trial. The spatial location of the landmarks derived from regional superpositions was evaluated in a coordinate system oriented on natural head position. The superpositions included the best anatomic fit of the anterior cranial base, maxillary base, and mandibular structures. Both the HG and the FR were effective in correcting the distoclusion, and they generated enhanced differential growth between the jaws. Differences between cranial and maxillary superpositions regarding mandibular displacement (Point B, pogonion, gnathion, menton) were noted: the HG had a more horizontal vector on maxillary superposition that was also greater (.0001 < P < .05) than the horizontal displacement observed with the FR. This discrepancy appeared to be related to (1) the clockwise (backward) rotation of the palatal and mandibular planes observed with the HG; the palatal plane's rotation, which was transferred through the occlusion to the mandibular plane, was factored out on maxillary superposition; and (2) the interaction between the inclination of the maxillary incisors and the forward movement of the mandible during growth. Findings from superpositions agreed with conventional angular and linear measurements regarding the basic conclusions for the primary effects of HG and FR. However, the results suggest that inferences of mandibular displacement are more reliable from maxillary than cranial superposition when evaluating occlusal changes during treatment.

Superposition of nonparaxial vectorial complex-source spherically focused beams: Axial Poynting singularity and reverse propagation

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2016-08-01

In this work, counterintuitive effects such as the generation of an axial (i.e., long the direction of wave motion) zero-energy flux density (i.e., axial Poynting singularity) and reverse (i.e., negative) propagation of nonparaxial quasi-Gaussian electromagnetic (EM) beams are examined. Generalized analytical expressions for the EM field's components of a coherent superposition of two high-order quasi-Gaussian vortex beams of opposite handedness and different amplitudes are derived based on the complex-source-point method, stemming from Maxwell's vector equations and the Lorenz gauge condition. The general solutions exhibiting unusual effects satisfy the Helmholtz and Maxwell's equations. The EM beam components are characterized by nonzero integer degree and order (n ,m ) , respectively, an arbitrary waist w0, a diffraction convergence length known as the Rayleigh range zR, and a weighting (real) factor 0 ≤α ≤1 that describes the transition of the beam from a purely vortex (α =0 ) to a nonvortex (α =1 ) type. An attractive feature for this superposition is the description of strongly focused (or strongly divergent) wave fields. Computations of the EM power density as well as the linear and angular momentum density fluxes illustrate the analysis with particular emphasis on the polarization states of the vector potentials forming the beams and the weight of the coherent beam superposition causing the transition from the vortex to the nonvortex type. Should some conditions determined by the polarization state of the vector potentials and the beam parameters be met, an axial zero-energy flux density is predicted in addition to a negative retrograde propagation effect. Moreover, rotation reversal of the angular momentum flux density with respect to the beam handedness is anticipated, suggesting the possible generation of negative (left-handed) torques. The results are particularly useful in applications involving the design of strongly focused optical laser tweezers, tractor beams, optical spanners, arbitrary scattering, radiation force, angular momentum, and torque in particle manipulation, and other related topics.

Regularized two-step brain activity reconstruction from spatiotemporal EEG data

NASA Astrophysics Data System (ADS)

Alecu, Teodor I.; Voloshynovskiy, Sviatoslav; Pun, Thierry

2004-10-01

We are aiming at using EEG source localization in the framework of a Brain Computer Interface project. We propose here a new reconstruction procedure, targeting source (or equivalently mental task) differentiation. EEG data can be thought of as a collection of time continuous streams from sparse locations. The measured electric potential on one electrode is the result of the superposition of synchronized synaptic activity from sources in all the brain volume. Consequently, the EEG inverse problem is a highly underdetermined (and ill-posed) problem. Moreover, each source contribution is linear with respect to its amplitude but non-linear with respect to its localization and orientation. In order to overcome these drawbacks we propose a novel two-step inversion procedure. The solution is based on a double scale division of the solution space. The first step uses a coarse discretization and has the sole purpose of globally identifying the active regions, via a sparse approximation algorithm. The second step is applied only on the retained regions and makes use of a fine discretization of the space, aiming at detailing the brain activity. The local configuration of sources is recovered using an iterative stochastic estimator with adaptive joint minimum energy and directional consistency constraints.

Habemus superstratum! A constructive proof of the existence of superstrata

DOE PAGES

Bena, Iosif; Giusto, Stefano; Russo, Rodolfo; ...

2015-05-21

Here, we construct the first example of a superstratum: a class of smooth horizonless supergravity solutions that are parameterized by arbitrary continuous functions of (at least) two variables and have the same charges as the supersymmetric D1-D5-P black hole. We work in Type IIB string theory on T 4 or K 3 and our solutions involve a subset of fields that can be described by a six-dimensional supergravity with two tensor multiplets. The solutions can thus be constructed using a linear structure, and we give an explicit recipe to start from a superposition of modes specified by an arbitrary functionmore » of two variables and impose regularity to obtain the full horizonless solutions in closed form. We also give the precise CFT description of these solutions and show that they are not dual to descendants of chiral primaries. They are thus much more general than all the known solutions whose CFT dual is precisely understood. Hence our construction represents a substantial step toward the ultimate goal of constructing the fully generic superstratum that can account for a finite fraction of the entropy of the three-charge black hole in the regime of parameters where the classical black hole solution exists.« less

Aerodynamic Analysis of the Truss-Braced Wing Aircraft Using Vortex-Lattice Superposition Approach

NASA Technical Reports Server (NTRS)

Ting, Eric Bi-Wen; Reynolds, Kevin Wayne; Nguyen, Nhan T.; Totah, Joseph J.

2014-01-01

The SUGAR Truss-BracedWing (TBW) aircraft concept is a Boeing-developed N+3 aircraft configuration funded by NASA ARMD FixedWing Project. This future generation transport aircraft concept is designed to be aerodynamically efficient by employing a high aspect ratio wing design. The aspect ratio of the TBW is on the order of 14 which is significantly greater than those of current generation transport aircraft. This paper presents a recent aerodynamic analysis of the TBW aircraft using a conceptual vortex-lattice aerodynamic tool VORLAX and an aerodynamic superposition approach. Based on the underlying linear potential flow theory, the principle of aerodynamic superposition is leveraged to deal with the complex aerodynamic configuration of the TBW. By decomposing the full configuration of the TBW into individual aerodynamic lifting components, the total aerodynamic characteristics of the full configuration can be estimated from the contributions of the individual components. The aerodynamic superposition approach shows excellent agreement with CFD results computed by FUN3D, USM3D, and STAR-CCM+.

Superposition-Based Analysis of First-Order Probabilistic Timed Automata

NASA Astrophysics Data System (ADS)

Fietzke, Arnaud; Hermanns, Holger; Weidenbach, Christoph

This paper discusses the analysis of first-order probabilistic timed automata (FPTA) by a combination of hierarchic first-order superposition-based theorem proving and probabilistic model checking. We develop the overall semantics of FPTAs and prove soundness and completeness of our method for reachability properties. Basically, we decompose FPTAs into their time plus first-order logic aspects on the one hand, and their probabilistic aspects on the other hand. Then we exploit the time plus first-order behavior by hierarchic superposition over linear arithmetic. The result of this analysis is the basis for the construction of a reachability equivalent (to the original FPTA) probabilistic timed automaton to which probabilistic model checking is finally applied. The hierarchic superposition calculus required for the analysis is sound and complete on the first-order formulas generated from FPTAs. It even works well in practice. We illustrate the potential behind it with a real-life DHCP protocol example, which we analyze by means of tool chain support.

Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

GPU-Based Point Cloud Superpositioning for Structural Comparisons of Protein Binding Sites.

PubMed

Leinweber, Matthias; Fober, Thomas; Freisleben, Bernd

2018-01-01

In this paper, we present a novel approach to solve the labeled point cloud superpositioning problem for performing structural comparisons of protein binding sites. The solution is based on a parallel evolution strategy that operates on large populations and runs on GPU hardware. The proposed evolution strategy reduces the likelihood of getting stuck in a local optimum of the multimodal real-valued optimization problem represented by labeled point cloud superpositioning. The performance of the GPU-based parallel evolution strategy is compared to a previously proposed CPU-based sequential approach for labeled point cloud superpositioning, indicating that the GPU-based parallel evolution strategy leads to qualitatively better results and significantly shorter runtimes, with speed improvements of up to a factor of 1,500 for large populations. Binary classification tests based on the ATP, NADH, and FAD protein subsets of CavBase, a database containing putative binding sites, show average classification rate improvements from about 92 percent (CPU) to 96 percent (GPU). Further experiments indicate that the proposed GPU-based labeled point cloud superpositioning approach can be superior to traditional protein comparison approaches based on sequence alignments.

Modeling Three-Dimensional Flow in Confined Aquifers by Superposition of Both Two- and Three-Dimensional Analytic Functions

NASA Astrophysics Data System (ADS)

Haitjema, Henk M.

1985-10-01

A technique is presented to incorporate three-dimensional flow in a Dupuit-Forchheimer model. The method is based on superposition of approximate analytic solutions to both two- and three-dimensional flow features in a confined aquifer of infinite extent. Three-dimensional solutions are used in the domain of interest, while farfield conditions are represented by two-dimensional solutions. Approximate three- dimensional solutions have been derived for a partially penetrating well and a shallow creek. Each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer. Because of this condition, the flow at some distance of a three-dimensional feature becomes nearly horizontal. Consequently, remotely from a three-dimensional feature, its three-dimensional solution is replaced by a corresponding two-dimensional one. The latter solution is trivial as compared to its three-dimensional counterpart, and its use greatly enhances the computational efficiency of the model. As an example, the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system.

Adsorption of Emerging Munitions Contaminants on Cellulose Surface: A Combined Theoretical and Experimental Investigation.

PubMed

Shukla, Manoj K; Poda, Aimee

2016-06-01

This manuscript reports results of an integrated theoretical and experimental investigation of adsorption of two emerging contaminants (DNAN and FOX-7) and legacy compound TNT on cellulose surface. Cellulose was modeled as trimeric form of the linear chain of 1 → 4 linked of β-D-glucopyranos in (4)C1 chair conformation. Geometries of modeled cellulose, munitions compounds and their complexes were optimized at the M06-2X functional level of Density Functional Theory using the 6-31G(d,p) basis set in gas phase and in water solution. The effect of water solution was modeled using the CPCM approach. Nature of potential energy surfaces was ascertained through harmonic vibrational frequency analysis. Interaction energies were corrected for basis set superposition error and the 6-311G(d,p) basis set was used. Molecular electrostatic potential mapping was performed to understand the reactivity of the investigated systems. It was predicted that adsorbates will be weakly adsorbed on the cellulose surface in water solution than in the gas phase.

Spatial Linear Instability of Confluent Wake/Boundary Layers

NASA Technical Reports Server (NTRS)

Liou, William W.; Liu, Feng-Jun; Rumsey, C. L. (Technical Monitor)

2001-01-01

The spatial linear instability of incompressible confluent wake/boundary layers is analyzed. The flow model adopted is a superposition of the Blasius boundary layer and a wake located above the boundary layer. The Orr-Sommerfeld equation is solved using a global numerical method for the resulting eigenvalue problem. The numerical procedure is validated by comparing the present solutions for the instability of the Blasius boundary layer and for the instability of a wake with published results. For the confluent wake/boundary layers, modes associated with the boundary layer and the wake, respectively, are identified. The boundary layer mode is found amplified as the wake approaches the wall. On the other hand, the modes associated with the wake, including a symmetric mode and an antisymmetric mode, are stabilized by the reduced distance between the wall and the wake. An unstable mode switching at low frequency is observed where the antisymmetric mode becomes more unstable than the symmetric mode when the wake velocity defect is high.

Helical localized wave solutions of the scalar wave equation.

PubMed

Overfelt, P L

2001-08-01

A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch.

Noise generated by convected gusts interacting with swept airfoil cascades

NASA Astrophysics Data System (ADS)

Envia, E.; Kerschen, E. J.

1986-07-01

An analysis is developed for the noise generated by the interaction of a rotor viscous wake with a cascade of swept stator vanes. The stator vanes span a channel formed by infinite parallel walls and containing a subsonic mean flow. High frequency interactions, for which the noise generation is concentrated at the vane leading edge, are considered. The analysis utilizes a superposition of the solution to the isolated stator vane problem, presented in an earlier paper, to develop an approximate solution to the cascade problem. The rotor wake model includes the features of wake circumferential lean and a linear spanwise variation of the magnitude of the wake deficit velocity. Calculations are presented which show that, for rotor wakes with moderate circumferential lean, stator sweep produces substantial reductions in noise level. The vane sweep must be oriented to enhance the phase lags along the vane leading edge produced by wake lean. The noise levels are found to be fairly insensitive to spanwise variations in the wake deficit.

Transient reaction of an elastic half-plane on a source of a concentrated boundary disturbance

NASA Astrophysics Data System (ADS)

Okonechnikov, A. S.; Tarlakovski, D. V.; Ul'yashina, A. N.; Fedotenkov, G. V.

2016-11-01

One of the key problems in studying the non-stationary processes of solid mechanics is obtaining of influence functions. These functions serve as solutions for the problems of effect of sudden concentrated loads on a body with linear elastic properties. Knowledge of the influence functions allows us to obtain the solutions for the problems with non-mixed boundary and initial conditions in the form of quadrature formulae with the help of superposition principle, as well as get the integral governing equations for the problems with mixed boundary and initial conditions. This paper offers explicit derivations for all nonstationary surface influence functions of an elastic half-plane in a plane strain condition. It is achieved with the help of combined inverse transform of a Fourier-Laplace integral transformation. The external disturbance is both dynamic and kinematic. The derived functions in xτ-domain are studied to find and describe singularities and are supplemented with graphs.

SUPERPOSITION OF POLYTROPES IN THE INNER HELIOSHEATH

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

Livadiotis, G., E-mail: glivadiotis@swri.edu

2016-03-15

This paper presents a possible generalization of the equation of state and Bernoulli's integral when a superposition of polytropic processes applies in space and astrophysical plasmas. The theory of polytropic thermodynamic processes for a fixed polytropic index is extended for a superposition of polytropic indices. In general, the superposition may be described by any distribution of polytropic indices, but emphasis is placed on a Gaussian distribution. The polytropic density–temperature relation has been used in numerous analyses of space plasma data. This linear relation on a log–log scale is now generalized to a concave-downward parabola that is able to describe themore » observations better. The model of the Gaussian superposition of polytropes is successfully applied in the proton plasma of the inner heliosheath. The estimated mean polytropic index is near zero, indicating the dominance of isobaric thermodynamic processes in the sheath, similar to other previously published analyses. By computing Bernoulli's integral and applying its conservation along the equator of the inner heliosheath, the magnetic field in the inner heliosheath is estimated, B ∼ 2.29 ± 0.16 μG. The constructed normalized histogram of the values of the magnetic field is similar to that derived from a different method that uses the concept of large-scale quantization, bringing incredible insights to this novel theory.« less

Superposition of Polytropes in the Inner Heliosheath

NASA Astrophysics Data System (ADS)

Livadiotis, G.

2016-03-01

This paper presents a possible generalization of the equation of state and Bernoulli's integral when a superposition of polytropic processes applies in space and astrophysical plasmas. The theory of polytropic thermodynamic processes for a fixed polytropic index is extended for a superposition of polytropic indices. In general, the superposition may be described by any distribution of polytropic indices, but emphasis is placed on a Gaussian distribution. The polytropic density-temperature relation has been used in numerous analyses of space plasma data. This linear relation on a log-log scale is now generalized to a concave-downward parabola that is able to describe the observations better. The model of the Gaussian superposition of polytropes is successfully applied in the proton plasma of the inner heliosheath. The estimated mean polytropic index is near zero, indicating the dominance of isobaric thermodynamic processes in the sheath, similar to other previously published analyses. By computing Bernoulli's integral and applying its conservation along the equator of the inner heliosheath, the magnetic field in the inner heliosheath is estimated, B ˜ 2.29 ± 0.16 μG. The constructed normalized histogram of the values of the magnetic field is similar to that derived from a different method that uses the concept of large-scale quantization, bringing incredible insights to this novel theory.

Linear stability analysis and nonlinear simulation of the channeling effect on viscous fingering instability in miscible displacement

NASA Astrophysics Data System (ADS)

Shahnazari, M. R.; Maleka Ashtiani, I.; Saberi, A.

2018-03-01

In this paper, the effect of channeling on viscous fingering instability of miscible displacement in porous media is studied. In fact, channeling is introduced as a solution to stabilize the viscous fingering instability. In this solution, narrow channels were placed next to the walls, and by considering an exponential function to model the channeling effect, a heterogeneous media is assumed. In linear stability analysis, the governing equations are transferred to Fourier space, and by introducing a novel numerical method, the transferred equations are analyzed. The growth rate based on the wave number diagram has been drawn up in three sections of the medium. It is found that the flow becomes more stable at the center and unstable along the walls when the permeability ratio is increased. Also when the permeability ratio is approximately equal to one, the channeling has no significant effect. In nonlinear simulations, by using stream function and vortices, new equations have been rewritten and it is shown that channeling has a profound effect on the growth of the fingers and mechanisms. In addition to the superposition of velocity vectors and concentration contours, the development of instability is investigated using the mixing length and sweep efficiency diagram. The results show that although channeling reduces instability, it increases the displacement process time.

Energy, momentum, and angular momentum of sound pulses.

PubMed

Lekner, John

2017-12-01

Pulse solutions of the wave equation can be expressed as superpositions of scalar monochromatic beam wavefunctions (solutions of the Helmholtz equation). This formulation leads to causal (unidirectional) propagation, in contrast to all currently known closed-form solutions of the wave equation. Application is made to the evaluation of the energy, momentum, and angular momentum of acoustic pulses, as integrals over the beam and pulse weight functions. Equivalence is established between integration over space of the energy, momentum, and angular momentum densities, and integration over the wavevector weight function. The inequality linking the total energy and the total momentum is made explicit in terms of the weight function formulation. It is shown that a general pulse can be viewed as a superposition of phonons, each with energy ℏck, z component of momentum ℏq, and z component of angular momentum ℏm. A closed-form solution of the wave equation is found, which is localized and causal, and its energy and momentum are evaluated explicitly.

Higher-order quantum entanglement

NASA Technical Reports Server (NTRS)

Zeilinger, Anton; Horne, Michael A.; Greenberger, Daniel M.

1992-01-01

In quantum mechanics, the general state describing two or more particles is a linear superposition of product states. Such a superposition is called entangled if it cannot be factored into just one product. When only two particles are entangled, the stage is set for Einstein-Podolsky-Rosen (EPR) discussions and Bell's proof that the EPR viewpoint contradicts quantum mechanics. If more than two particles are involved, new possibilities and phenomena arise. For example, the Greenberger, Horne, and Zeilinger (GHZ) disproof of EPR applies. Furthermore, as we point out, with three or more particles even entanglement itself can be an entangled property.

Steady-State Visual Evoked Potentials Can Be Explained by Temporal Superposition of Transient Event-Related Responses

PubMed Central

Capilla, Almudena; Pazo-Alvarez, Paula; Darriba, Alvaro; Campo, Pablo; Gross, Joachim

2011-01-01

Background One common criterion for classifying electrophysiological brain responses is based on the distinction between transient (i.e. event-related potentials, ERPs) and steady-state responses (SSRs). The generation of SSRs is usually attributed to the entrainment of a neural rhythm driven by the stimulus train. However, a more parsimonious account suggests that SSRs might result from the linear addition of the transient responses elicited by each stimulus. This study aimed to investigate this possibility. Methodology/Principal Findings We recorded brain potentials elicited by a checkerboard stimulus reversing at different rates. We modeled SSRs by sequentially shifting and linearly adding rate-specific ERPs. Our results show a strong resemblance between recorded and synthetic SSRs, supporting the superposition hypothesis. Furthermore, we did not find evidence of entrainment of a neural oscillation at the stimulation frequency. Conclusions/Significance This study provides evidence that visual SSRs can be explained as a superposition of transient ERPs. These findings have critical implications in our current understanding of brain oscillations. Contrary to the idea that neural networks can be tuned to a wide range of frequencies, our findings rather suggest that the oscillatory response of a given neural network is constrained within its natural frequency range. PMID:21267081

Oscillatory Dynamics of One-Dimensional Homogeneous Granular Chains

NASA Astrophysics Data System (ADS)

Starosvetsky, Yuli; Jayaprakash, K. R.; Hasan, Md. Arif; Vakakis, Alexander F.

The acoustics of the homogeneous granular chains has been studied extensively both numerically and experimentally in the references cited in the previous chapters. This chapter focuses on the oscillatory behavior of finite dimensional homogeneous granular chains. It is well known that normal vibration modes are the building blocks of the vibrations of linear systems due to the applicability of the principle of superposition. One the other hand, nonlinear theory is deprived of such a general superposition principle (although special cases of nonlinear superpositions do exist), but nonlinear normal modes ‒ NNMs still play an important role in the forced and resonance dynamics of these systems. In their basic definition [1], NNMs were defined as time-periodic nonlinear oscillations of discrete or continuous dynamical systems where all coordinates (degrees-of-freedom) oscillate in-unison with the same frequency; further extensions of this definition have been considered to account for NNMs of systems with internal resonances [2]...

Superposition: New Solutions from Known Solutions

ERIC Educational Resources Information Center

Roberts, Charles E.

2003-01-01

This note contains material to be presented to students in a first course in differential equations immediately after they have completed studying first-order differential equations and their applications. The purpose of presenting this material is four-fold: to review definitions studied previously; to provide a historical context which cites the…

CFD Extraction Tool for TecPlot From DPLR Solutions

NASA Technical Reports Server (NTRS)

Norman, David

2013-01-01

This invention is a TecPlot macro of a computer program in the TecPlot programming language that processes data from DPLR solutions in TecPlot format. DPLR (Data-Parallel Line Relaxation) is a NASA computational fluid dynamics (CFD) code, and TecPlot is a commercial CFD post-processing tool. The Tec- Plot data is in SI units (same as DPLR output). The invention converts the SI units into British units. The macro modifies the TecPlot data with unit conversions, and adds some extra calculations. After unit conversions, the macro cuts a slice, and adds vectors on the current plot for output format. The macro can also process surface solutions. Existing solutions use manual conversion and superposition. The conversion is complicated because it must be applied to a range of inter-related scalars and vectors to describe a 2D or 3D flow field. It processes the CFD solution to create superposition/comparison of scalars and vectors. The existing manual solution is cumbersome, open to errors, slow, and cannot be inserted into an automated process. This invention is quick and easy to use, and can be inserted into an automated data-processing algorithm.

Impact of chemical plant start-up emissions on ambient ozone concentration

NASA Astrophysics Data System (ADS)

Ge, Sijie; Wang, Sujing; Xu, Qiang; Ho, Thomas

2017-09-01

Flare emissions, especially start-up flare emissions, during chemical plant operations generate large amounts of ozone precursors that may cause highly localized and transient ground-level ozone increment. Such an adverse ozone impact could be aggravated by the synergies of multiple plant start-ups in an industrial zone. In this paper, a systematic study on ozone increment superposition due to chemical plant start-up emissions has been performed. It employs dynamic flaring profiles of two olefin plants' start-ups to investigate the superposition of the regional 1-hr ozone increment. It also summaries the superposition trend by manipulating the starting time (00:00-10:00) of plant start-up operations and the plant distance (4-32 km). The study indicates that the ozone increment induced by simultaneous start-up emissions from multiple chemical plants generally does not follow the linear superposition of the ozone increment induced by individual plant start-ups. Meanwhile, the trend of such nonlinear superposition related to the temporal (starting time and operating hours of plant start-ups) and spatial (plant distance) factors is also disclosed. This paper couples dynamic simulations of chemical plant start-up operations with air-quality modeling and statistical methods to examine the regional ozone impact. It could be helpful for technical decision support for cost-effective air-quality and industrial flare emission controls.

Linearity of holographic entanglement entropy

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

Almheiri, Ahmed; Dong, Xi; Swingle, Brian

Here, we consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certainmore » such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of entropy operators in general systems with a large number of degrees of freedom.« less

Linearity of holographic entanglement entropy

DOE PAGES

Almheiri, Ahmed; Dong, Xi; Swingle, Brian

2017-02-14

Here, we consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certainmore » such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of entropy operators in general systems with a large number of degrees of freedom.« less

Solution Methods for Certain Evolution Equations

NASA Astrophysics Data System (ADS)

Vega-Guzman, Jose Manuel

Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.

Projection operators for the Rossby and Poincare waves in a beta-plane approximation

NASA Astrophysics Data System (ADS)

Lebedkina, Anastasia; Ivan, Karpov; Sergej, Leble

2013-04-01

Study of the wave structure variations of atmospheric parameters is a due to a solving of number practical problems associated with the weather and the state of the environment requires knowledge of the spectral characteristics of atmospheric waves. Modern methods, for identification of wave disturbances in the atmosphere, based on the harmonic analysis of observations. The success of these application is determined by the presence of sets of experimental data obtained in the long-term (over the period of the wave) of the atmosphere on a large number of independent observation stations. Currently, the system of observation in the atmosphere, both terrestrial and satellite, unevenly covers the surface of the Earth and, despite the length of observation, doesn't solve the problem of identification of waves. Thus, the problem of identification wave disturbances conflicts fundamental difficulties, and solution needs in a new methods for the analysis of observations. The work complete a procedure to construct a projection operators for large-scale waves in the atmosphere. Advantage of this method is the ability to identify type of wave and its characteristics only on the base of a time series of observations. It means that the problem of waves identification can be solved on the basis of only one station observations. In the method assumed that the observed spatial and temporal structure of the atmosphere is determined by the superposition of different type waves. For each type of waves involved in this superposition, dispersion and polarization relations (between the components of the wave vector of the field) expect as known. Based on these assumptions, we can construct projection operators on the initial superposition state on the linear basis of vectors corresponding to the known type of atmospheric waves. The action of the design on the superposition state, which, in fact, is the result of observations, determine the amplitude and phase of the waves of a known type. The idea to use the polarization relations for the classification of waves originated in radio physics in the works of A. A. Novikov. In the theory of the electromagnetic field polarization relations is traditionally included in the analysis of wave phenomena. In the theory of acoustic-gravity waves, projection operators were introduced in a works of S. B. Leble. The object of study is a four-dimentional vector (components of the velocity, pressure and temperature). Based on these assumptions, we can construct the projection operators for superposition state on the linear basis, corresponding to the well-known type of waves. In this paper we consider procedure for construction of a projection operators for planetary Rossby and Poincare waves in the Earth's atmosphere in the approximation of the "beta-plane". In a result of work we constructed projection operators in this approximation for Poincare and Rossby waves. The tests for operators shown, that separation of the contribution of corresponding waves from source of the wave field is possible. Estimation accuracy of the operators and results of applying operators to the data TEC presented.

Wall function treatment for bubbly boundary layers at low void fractions.

PubMed

Soares, Daniel V; Bitencourt, Marcelo C; Loureiro, Juliana B R; Silva Freire, Atila P

2018-01-01

The present work investigates the role of different treatments of the lower boundary condition on the numerical prediction of bubbly flows. Two different wall function formulations are tested against experimental data obtained for bubbly boundary layers: (i) a new analytical solution derived through asymptotic techniques and (ii) the previous formulation of Troshko and Hassan (IJHMT, 44, 871-875, 2001a). A modified k-e model is used to close the averaged Navier-Stokes equations together with the hypothesis that turbulence can be modelled by a linear superposition of bubble and shear induced eddy viscosities. The work shows, in particular, how four corrections must the implemented in the standard single-phase k-e model to account for the effects of bubbles. The numerical implementation of the near wall functions is made through a finite elements code.

Rational Solutions to the ABS List: Transformation Approach

NASA Astrophysics Data System (ADS)

Zhang, Danda; Zhang, Da-Jun

2017-10-01

In the paper we derive rational solutions for the lattice potential modified Korteweg-de Vries equation, and Q2, Q1(δ), H3(δ), H2 and H1 in the Adler-Bobenko-Suris list. Bäcklund transformations between these lattice equations are used. All these rational solutions are related to a unified τ function in Casoratian form which obeys a bilinear superposition formula.

Maximum predictive power and the superposition principle

NASA Technical Reports Server (NTRS)

Summhammer, Johann

1994-01-01

In quantum physics the direct observables are probabilities of events. We ask how observed probabilities must be combined to achieve what we call maximum predictive power. According to this concept the accuracy of a prediction must only depend on the number of runs whose data serve as input for the prediction. We transform each probability to an associated variable whose uncertainty interval depends only on the amount of data and strictly decreases with it. We find that for a probability which is a function of two other probabilities maximum predictive power is achieved when linearly summing their associated variables and transforming back to a probability. This recovers the quantum mechanical superposition principle.

Bulk local states and crosscaps in holographic CFT

DOE PAGES

Nakayama, Yu; Ooguri, Hirosi

2016-10-17

In a weakly coupled gravity theory in the anti-de Sitter space, local states in the bulk are linear superpositions of Ishibashi states for a crosscap in the dual conformal field theory. The superposition structure can be constrained either by the microscopic causality in the bulk gravity or the bootstrap condition in the boundary conformal field theory. We show, contrary to some expectation, that these two conditions are not compatible to each other in the weak gravity regime. As a result, we also present an evidence to show that bulk local states in three dimensions are not organized by the Virasoromore » symmetry.« less

An efficient user-oriented method for calculating compressible flow in an about three-dimensional inlets. [panel method

NASA Technical Reports Server (NTRS)

Hess, J. L.; Mack, D. P.; Stockman, N. O.

1979-01-01

A panel method is used to calculate incompressible flow about arbitrary three-dimensional inlets with or without centerbodies for four fundamental flow conditions: unit onset flows parallel to each of the coordinate axes plus static operation. The computing time is scarcely longer than for a single solution. A linear superposition of these solutions quite rigorously gives incompressible flow about the inlet for any angle of attack, angle of yaw, and mass flow rate. Compressibility is accounted for by applying a well-proven correction to the incompressible flow. Since the computing times for the combination and the compressibility correction are small, flows at a large number of inlet operating conditions are obtained rather cheaply. Geometric input is aided by an automatic generating program. A number of graphical output features are provided to aid the user, including surface streamline tracing and automatic generation of curves of curves of constant pressure, Mach number, and flow inclination at selected inlet cross sections. The inlet method and use of the program are described. Illustrative results are presented.

Superposition of Translational and Rotational Motions under Self-Propulsion of Liquid Marbles Filled with Aqueous Solutions of Camphor.

PubMed

Bormashenko, Edward; Frenkel, Mark; Bormashenko, Yelena; Chaniel, Gilad; Valtsifer, Viktor; Binks, Bernard P

2017-11-21

Self-locomotion of liquid marbles, coated with lycopodium or fumed fluorosilica powder, filled with a saturated aqueous solution of camphor and placed on a water/vapor interface is reported. Self-propelled marbles demonstrated a complicated motion, representing a superposition of translational and rotational motions. Oscillations of the velocity of the center of mass and the angular velocity of marbles, occurring in the antiphase, were registered and explained qualitatively. Self-propulsion occurs because of the Marangoni solutocapillary flow inspired by the adsorption of camphor (evaporated from the liquid marble) by the water surface. Scaling laws describing translational and rotational motions are proposed and checked. The rotational motion of marbles arises from the asymmetry of the field of the Marangoni stresses because of the adsorption of camphor evaporated from marbles.

Linear viscoelasticity and thermorheological simplicity of n-hexadecane fluids under oscillatory shear via non-equilibrium molecular dynamics simulations.

PubMed

Tseng, Huan-Chang; Wu, Jiann-Shing; Chang, Rong-Yeu

2010-04-28

A small amplitude oscillatory shear flows with the classic characteristic of a phase shift when using non-equilibrium molecular dynamics simulations for n-hexadecane fluids. In a suitable range of strain amplitude, the fluid possesses significant linear viscoelastic behavior. Non-linear viscoelastic behavior of strain thinning, which means the dynamic modulus monotonously decreased with increasing strain amplitudes, was found at extreme strain amplitudes. Under isobaric conditions, different temperatures strongly affected the range of linear viscoelasticity and the slope of strain thinning. The fluid's phase states, containing solid-, liquid-, and gel-like states, can be distinguished through a criterion of the viscoelastic spectrum. As a result, a particular condition for the viscoelastic behavior of n-hexadecane molecules approaching that of the Rouse chain was obtained. Besides, more importantly, evidence of thermorheologically simple materials was presented in which the relaxation modulus obeys the time-temperature superposition principle. Therefore, using shift factors from the time-temperature superposition principle, the estimated Arrhenius flow activation energy was in good agreement with related experimental values. Furthermore, one relaxation modulus master curve well exhibited both transition and terminal zones. Especially regarding non-equilibrium thermodynamic states, variations in the density, with respect to frequencies, were revealed.

An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

NASA Astrophysics Data System (ADS)

Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

2005-12-01

We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs.

Why the soliton wavelet transform is useful for nonlinear dynamic phenomena

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1992-10-01

If signal analyses were perfect without noise and clutters, then any transform can be equally chosen to represent the signal without any loss of information. However, if the analysis using Fourier transform (FT) happens to be a nonlinear dynamic phenomenon, the effect of nonlinearity must be postponed until a later time when a complicated mode-mode coupling is attempted without the assurance of any convergence. Alternatively, there exists a new paradigm of linear transforms called wavelet transform (WT) developed for French oil explorations. Such a WT enjoys the linear superposition principle, the computational efficiency, and the signal/noise ratio enhancement for a nonsinusoidal and nonstationary signal. Our extensions to a dynamic WT and furthermore to an adaptive WT are possible due to the fact that there exists a large set of square-integrable functions that are special solutions of the nonlinear dynamic medium and could be adopted for the WT. In order to analyze nonlinear dynamics phenomena in ocean, we are naturally led to the construction of a soliton mother wavelet. This common sense of 'pay the nonlinear price now and enjoy the linearity later' is certainly useful to probe any nonlinear dynamics. Research directions in wavelets, such as adaptivity, and neural network implementations are indicated, e.g., tailoring an active sonar profile for explorations.

Probabilistic quantum cloning of a subset of linearly dependent states

NASA Astrophysics Data System (ADS)

Rui, Pinshu; Zhang, Wen; Liao, Yanlin; Zhang, Ziyun

2018-02-01

It is well known that a quantum state, secretly chosen from a certain set, can be probabilistically cloned with positive cloning efficiencies if and only if all the states in the set are linearly independent. In this paper, we focus on probabilistic quantum cloning of a subset of linearly dependent states. We show that a linearly-independent subset of linearly-dependent quantum states {| Ψ 1⟩,| Ψ 2⟩,…,| Ψ n ⟩} can be probabilistically cloned if and only if any state in the subset cannot be expressed as a linear superposition of the other states in the set {| Ψ 1⟩,| Ψ 2⟩,…,| Ψ n ⟩}. The optimal cloning efficiencies are also investigated.

Solving modal equations of motion with initial conditions using MSC/NASTRAN DMAP. Part 1: Implementing exact mode superposition

NASA Technical Reports Server (NTRS)

Abdallah, Ayman A.; Barnett, Alan R.; Ibrahim, Omar M.; Manella, Richard T.

1993-01-01

Within the MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) module TRD1, solving physical (coupled) or modal (uncoupled) transient equations of motion is performed using the Newmark-Beta or mode superposition algorithms, respectively. For equations of motion with initial conditions, only the Newmark-Beta integration routine has been available in MSC/NASTRAN solution sequences for solving physical systems and in custom DMAP sequences or alters for solving modal systems. In some cases, one difficulty with using the Newmark-Beta method is that the process of selecting suitable integration time steps for obtaining acceptable results is lengthy. In addition, when very small step sizes are required, a large amount of time can be spent integrating the equations of motion. For certain aerospace applications, a significant time savings can be realized when the equations of motion are solved using an exact integration routine instead of the Newmark-Beta numerical algorithm. In order to solve modal equations of motion with initial conditions and take advantage of efficiencies gained when using uncoupled solution algorithms (like that within TRD1), an exact mode superposition method using MSC/NASTRAN DMAP has been developed and successfully implemented as an enhancement to an existing coupled loads methodology at the NASA Lewis Research Center.

Control Surface Interaction Effects of the Active Aeroelastic Wing Wind Tunnel Model

NASA Technical Reports Server (NTRS)

Heeg, Jennifer

2006-01-01

This paper presents results from testing the Active Aeroelastic Wing wind tunnel model in NASA Langley s Transonic Dynamics Tunnel. The wind tunnel test provided an opportunity to study aeroelastic system behavior under combined control surface deflections, testing for control surface interaction effects. Control surface interactions were observed in both static control surface actuation testing and dynamic control surface oscillation testing. The primary method of evaluating interactions was examination of the goodness of the linear superposition assumptions. Responses produced by independently actuating single control surfaces were combined and compared with those produced by simultaneously actuating and oscillating multiple control surfaces. Adjustments to the data were required to isolate the control surface influences. Using dynamic data, the task increases, as both the amplitude and phase have to be considered in the data corrections. The goodness of static linear superposition was examined and analysis of variance was used to evaluate significant factors influencing that goodness. The dynamic data showed interaction effects in both the aerodynamic measurements and the structural measurements.

Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2017-12-01

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

Library-based illumination synthesis for critical CMOS patterning.

PubMed

Yu, Jue-Chin; Yu, Peichen; Chao, Hsueh-Yung

2013-07-01

In optical microlithography, the illumination source for critical complementary metal-oxide-semiconductor layers needs to be determined in the early stage of a technology node with very limited design information, leading to simple binary shapes. Recently, the availability of freeform sources permits us to increase pattern fidelity and relax mask complexities with minimal insertion risks to the current manufacturing flow. However, source optimization across many patterns is often treated as a design-of-experiments problem, which may not fully exploit the benefits of a freeform source. In this paper, a rigorous source-optimization algorithm is presented via linear superposition of optimal sources for pre-selected patterns. We show that analytical solutions are made possible by using Hopkins formulation and quadratic programming. The algorithm allows synthesized illumination to be linked with assorted pattern libraries, which has a direct impact on design rule studies for early planning and design automation for full wafer optimization.

Solitons interaction and integrability for a (2+1)-dimensional variable-coefficient Broer-Kaup system in water waves

NASA Astrophysics Data System (ADS)

Zhao, Xue-Hui; Tian, Bo; Guo, Yong-Jiang; Li, Hui-Min

2018-03-01

Under investigation in this paper is a (2+1)-dimensional variable-coefficient Broer-Kaup system in water waves. Via the symbolic computation, Bell polynomials and Hirota method, the Bäcklund transformation, Lax pair, bilinear forms, one- and two-soliton solutions are derived. Propagation and interaction for the solitons are illustrated: Amplitudes and shapes of the one soliton keep invariant during the propagation, which implies that the transport of the energy is stable for the (2+1)-dimensional water waves; and inelastic interactions between the two solitons are discussed. Elastic interactions between the two parabolic-, cubic- and periodic-type solitons are displayed, where the solitonic amplitudes and shapes remain unchanged except for certain phase shifts. However, inelastically, amplitudes of the two solitons have a linear superposition after each interaction which is called as a soliton resonance phenomenon.

Empirical modeling of environment-enhanced fatigue crack propagation in structural alloys for component life prediction

NASA Technical Reports Server (NTRS)

Richey, Edward, III

1995-01-01

This research aims to develop the methods and understanding needed to incorporate time and loading variable dependent environmental effects on fatigue crack propagation (FCP) into computerized fatigue life prediction codes such as NASA FLAGRO (NASGRO). In particular, the effect of loading frequency on FCP rates in alpha + beta titanium alloys exposed to an aqueous chloride solution is investigated. The approach couples empirical modeling of environmental FCP with corrosion fatigue experiments. Three different computer models have been developed and incorporated in the DOS executable program. UVAFAS. A multiple power law model is available, and can fit a set of fatigue data to a multiple power law equation. A model has also been developed which implements the Wei and Landes linear superposition model, as well as an interpolative model which can be utilized to interpolate trends in fatigue behavior based on changes in loading characteristics (stress ratio, frequency, and hold times).

Dyadic Green's function of a cluster of spheres.

PubMed

Moneda, Angela P; Chrissoulidis, Dimitrios P

2007-11-01

The electric dyadic Green's function (dGf) of a cluster of spheres is obtained by application of the superposition principle, dyadic algebra, and the indirect mode-matching method. The analysis results in a set of linear equations for the unknown, vector, wave amplitudes of the dGf; that set is solved by truncation and matrix inversion. The theory is exact in the sense that no simplifying assumptions are made in the analytical steps leading to the dGf, and it is general in the sense that any number, position, size and electrical properties can be considered for the spheres that cluster together. The point source can be anywhere, even within one of the spheres. Energy conservation, reciprocity, and other tests prove that this solution is correct. Numerical results are presented for an electric Hertz dipole radiating in the presence of an array of rexolite spheres, which manifests lensing and beam-forming capabilities.

Optimal Superpositioning of Flexible Molecule Ensembles

PubMed Central

Gapsys, Vytautas; de Groot, Bert L.

2013-01-01

Analysis of the internal dynamics of a biological molecule requires the successful removal of overall translation and rotation. Particularly for flexible or intrinsically disordered peptides, this is a challenging task due to the absence of a well-defined reference structure that could be used for superpositioning. In this work, we started the analysis with a widely known formulation of an objective for the problem of superimposing a set of multiple molecules as variance minimization over an ensemble. A negative effect of this superpositioning method is the introduction of ambiguous rotations, where different rotation matrices may be applied to structurally similar molecules. We developed two algorithms to resolve the suboptimal rotations. The first approach minimizes the variance together with the distance of a structure to a preceding molecule in the ensemble. The second algorithm seeks for minimal variance together with the distance to the nearest neighbors of each structure. The newly developed methods were applied to molecular-dynamics trajectories and normal-mode ensembles of the Aβ peptide, RS peptide, and lysozyme. These new (to our knowledge) superpositioning methods combine the benefits of variance and distance between nearest-neighbor(s) minimization, providing a solution for the analysis of intrinsic motions of flexible molecules and resolving ambiguous rotations. PMID:23332072

Might god toss coins?

NASA Astrophysics Data System (ADS)

Pearle, Philip

1982-03-01

In the problem of the gambler's ruin, a classic problem in probability theory, a number of gamblers play against each other until all but one of them is “wiped out.” It is shown that this problem is identical to a previously presented formulation of the reduction of the state vector, so that the state vectors in a linear superposition may be regarded as “playing” against each other until all but one of them is “wiped out.” This is a useful part of the description of an objectively real universe represented by a state vector that is a superposition of macroscopically distinguishable states dynamically created by the Hamiltonian and destroyed by the reduction mechanism.

Study of odor recorder using Mass Spectrometry

NASA Astrophysics Data System (ADS)

Miura, Tomohiro; Nakamoto, Takamichi; Moriizumi, Toyosaka

It is necessary to determine the recipe of a target odor with sufficient accuracy to realize an odor recorder for recording and reproducing it. We studied the recipe measurement method of a target odor using a mass spectrometry. It was confirmed that the linear superposition was valid when the binary mixture of the apple-flavor components such as isobutyric acid and ethyl valerate was measured. The superposition of a mass spectrum pattern may enable the recipe determination of a multi-component odor easily. In this research, we succeeded in the recipe determinations of orange flavor made up of 14 component odors when its typical recipe, the equalized, the citral-enhanced and the citronellol-enhanced ones were measured.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

PubMed

Goto, Hayato

2016-02-22

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Quantum cryptography using single-particle entanglement

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

Lee, Jae-Weon; Lee, Eok Kyun; Chung, Yong Wook

2003-07-01

A quantum cryptography scheme based on entanglement between a single-particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single-particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.

Preparation of Vibrationally Excited H2 in a Coherent Superposition of M-States Using Stark Induced Adiabatic Raman Passage (SARP)

NASA Astrophysics Data System (ADS)

Mukherjee, Nandini; Dong, Wenrui; Perreault, William; Zare, Richard

2017-04-01

We prepare a large ensemble of rovibrationally excited (v = 1, J = 2) H2 molecules in a coherent superposition of M-states using Stark-induced adiabatic Raman passage (SARP) with linearly polarized single mode pump (532 nm) and Stokes (699 nm) laser pulses of duration 6 ns and 4 ns. A biaxial superposition state, | ψ〉 = 1/ √2 [ | v = 1, J = 2, M = -2〉- | v = 1, J = 2, M = + 2〉], is prepared using SARP with a sequence of a pump laser pulse partially overlapping with a cross polarized Stokes laser pulse co-propagating along the quantization z-axis. The degree of phase coherence is measured by recording interference fringes in the ion signal produced using the O(2) line of 2 +1 resonance enhanced multiphoton ionization (REMPI) from the rovibrationally excited (v = 1, J = 2) level as a function of REMPI laser polarization angle. The ion signal is measured using a time-of-flight mass spectrometer. Nearly 60% population transfer from H2 (v = 0, J = 0) ground state to the superposition state in H2 (v = 1, J = 2) is measured from the depletion of Q(0) REMPI signal of the (v = 0, J = 0) ground state. The M-state superposition behaves much like a multi-slit interferometer where the number of slits, i.e. the number of M-states, and their separations, i.e. the relative phase, can be varied experimentally. This work has been supported by the U.S. Army Research Office.

Thermodynamics of a lattice gas with linear attractive potential

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

Pirjol, Dan; Schat, Carlos

We study the equilibrium thermodynamics of a one-dimensional lattice gas with interaction V(|i−j|)=−1/(μn) (ξ−1/n |i−j|) given by the superposition of a universal attractive interaction with strength −1/(μn) ξ<0, and a linear attractive potential 1/(μn{sup 2}) |i−j|. The interaction is rescaled with the lattice size n, such that the thermodynamical limit n → ∞ is well-behaved. The thermodynamical properties of the system can be found exactly, both for a finite size lattice and in the thermodynamical limit n → ∞. The lattice gas can be mapped to a system of non-interacting bosons which are placed on known energy levels. The exactmore » solution shows that the system has a liquid-gas phase transition for ξ > 0. In the large temperature limit T ≫ T{sub 0}(ρ) = ρ{sup 2}/(4μ) with ρ the density, the system becomes spatially homogeneous, and the equation of state is given to a good approximation by a lattice version of the van der Waals equation, with critical temperature T{sub c}{sup (vdW)}=1/(12μ) (3ξ−1)« less

Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

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

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com; Wang, Jie, E-mail: wangjie@iun.edu

2015-07-15

We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system.

Exact solutions for layered thermocapillary convection of a viscous incompressible fluid with specified stresses on the bottom

NASA Astrophysics Data System (ADS)

Prosviryakov, E. Yu.; Spevak, L. F.

2017-12-01

A new exact solution of the Oberbeck-Boussinesq system is found. The Marangoni thermocapillary convection in an infinite fluid layer is described. It is demonstrated that the specification of tangential stresses at both boundaries of the layered velocity field is nonstationary. Velocities describe a superposition of unidirectional flows with an intermediate time interval when there are counterflows.

Exact periodic solutions of the sixth-order generalized Boussinesq equation

NASA Astrophysics Data System (ADS)

Kamenov, O. Y.

2009-09-01

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): utt = uxx + 3(u2)xx + uxxxx + αuxxxxxx, α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

Quantum Brownian motion with inhomogeneous damping and diffusion

NASA Astrophysics Data System (ADS)

Massignan, Pietro; Lampo, Aniello; Wehr, Jan; Lewenstein, Maciej

2015-03-01

We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear function of the position of the particle. Physically, this corresponds to a configuration in which damping and diffusion are spatially inhomogeneous. We derive systematically the quantum master equation for the Brownian particle in the Born-Markov approximation and we discuss the appearance of additional terms, for various polynomials forms of the coupling. We discuss the cases of linear and quadratic coupling in great detail and we derive, using Wigner function techniques, the stationary solutions of the master equation for a Brownian particle in a harmonic trapping potential. We predict quite generally Gaussian stationary states, and we compute the aspect ratio and the spread of the distributions. In particular, we find that these solutions may be squeezed (superlocalized) with respect to the position of the Brownian particle. We analyze various restrictions to the validity of our theory posed by non-Markovian effects and by the Heisenberg principle. We further study the dynamical stability of the system, by applying a Gaussian approximation to the time-dependent Wigner function, and we compute the decoherence rates of coherent quantum superpositions in position space. Finally, we propose a possible experimental realization of the physics discussed here, by considering an impurity particle embedded in a degenerate quantum gas.

Experiments testing macroscopic quantum superpositions must be slow

PubMed Central

Mari, Andrea; De Palma, Giacomo; Giovannetti, Vittorio

2016-01-01

We consider a thought experiment where the preparation of a macroscopically massive or charged particle in a quantum superposition and the associated dynamics of a distant test particle apparently allow for superluminal communication. We give a solution to the paradox which is based on the following fundamental principle: any local experiment, discriminating a coherent superposition from an incoherent statistical mixture, necessarily requires a minimum time proportional to the mass (or charge) of the system. For a charged particle, we consider two examples of such experiments, and show that they are both consistent with the previous limitation. In the first, the measurement requires to accelerate the charge, that can entangle with the emitted photons. In the second, the limitation can be ascribed to the quantum vacuum fluctuations of the electromagnetic field. On the other hand, when applied to massive particles our result provides an indirect evidence for the existence of gravitational vacuum fluctuations and for the possibility of entangling a particle with quantum gravitational radiation. PMID:26959656

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.

VIBRA: An interactive computer program for steady-state vibration response analysis of linear damped structures

NASA Technical Reports Server (NTRS)

Bowman, L. M.

1984-01-01

An interactive steady state frequency response computer program with graphics is documented. Single or multiple forces may be applied to the structure using a modal superposition approach to calculate response. The method can be reapplied to linear, proportionally damped structures in which the damping may be viscous or structural. The theoretical approach and program organization are described. Example problems, user instructions, and a sample interactive session are given to demonstate the program's capability in solving a variety of problems.

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1987-01-01

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

Implementation and validation of collapsed cone superposition for radiopharmaceutical dosimetry of photon emitters

NASA Astrophysics Data System (ADS)

Sanchez-Garcia, Manuel; Gardin, Isabelle; Lebtahi, Rachida; Dieudonné, Arnaud

2015-10-01

Two collapsed cone (CC) superposition algorithms have been implemented for radiopharmaceutical dosimetry of photon emitters. The straight CC (SCC) superposition method uses a water energy deposition kernel (EDKw) for each electron, positron and photon components, while the primary and scatter CC (PSCC) superposition method uses different EDKw for primary and once-scattered photons. PSCC was implemented only for photons originating from the nucleus, precluding its application to positron emitters. EDKw are linearly scaled by radiological distance, taking into account tissue density heterogeneities. The implementation was tested on 100, 300 and 600 keV mono-energetic photons and 18F, 99mTc, 131I and 177Lu. The kernels were generated using the Monte Carlo codes MCNP and EGSnrc. The validation was performed on 6 phantoms representing interfaces between soft-tissues, lung and bone. The figures of merit were γ (3%, 3 mm) and γ (5%, 5 mm) criterions corresponding to the computation comparison on 80 absorbed doses (AD) points per phantom between Monte Carlo simulations and CC algorithms. PSCC gave better results than SCC for the lowest photon energy (100 keV). For the 3 isotopes computed with PSCC, the percentage of AD points satisfying the γ (5%, 5 mm) criterion was always over 99%. A still good but worse result was found with SCC, since at least 97% of AD-values verified the γ (5%, 5 mm) criterion, except a value of 57% for the 99mTc with the lung/bone interface. The CC superposition method for radiopharmaceutical dosimetry is a good alternative to Monte Carlo simulations while reducing computation complexity.

Implementation and validation of collapsed cone superposition for radiopharmaceutical dosimetry of photon emitters.

PubMed

Sanchez-Garcia, Manuel; Gardin, Isabelle; Lebtahi, Rachida; Dieudonné, Arnaud

2015-10-21

Two collapsed cone (CC) superposition algorithms have been implemented for radiopharmaceutical dosimetry of photon emitters. The straight CC (SCC) superposition method uses a water energy deposition kernel (EDKw) for each electron, positron and photon components, while the primary and scatter CC (PSCC) superposition method uses different EDKw for primary and once-scattered photons. PSCC was implemented only for photons originating from the nucleus, precluding its application to positron emitters. EDKw are linearly scaled by radiological distance, taking into account tissue density heterogeneities. The implementation was tested on 100, 300 and 600 keV mono-energetic photons and (18)F, (99m)Tc, (131)I and (177)Lu. The kernels were generated using the Monte Carlo codes MCNP and EGSnrc. The validation was performed on 6 phantoms representing interfaces between soft-tissues, lung and bone. The figures of merit were γ (3%, 3 mm) and γ (5%, 5 mm) criterions corresponding to the computation comparison on 80 absorbed doses (AD) points per phantom between Monte Carlo simulations and CC algorithms. PSCC gave better results than SCC for the lowest photon energy (100 keV). For the 3 isotopes computed with PSCC, the percentage of AD points satisfying the γ (5%, 5 mm) criterion was always over 99%. A still good but worse result was found with SCC, since at least 97% of AD-values verified the γ (5%, 5 mm) criterion, except a value of 57% for the (99m)Tc with the lung/bone interface. The CC superposition method for radiopharmaceutical dosimetry is a good alternative to Monte Carlo simulations while reducing computation complexity.

Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2017-12-01

An exact solution of the Helmholtz equation u xx + u yy + u zz + k 2 u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.

An Inexpensive Mechanical Model for Projectile Motion

ERIC Educational Resources Information Center

Kagan, David

2011-01-01

As experienced physicists, we see the beauty and simplicity of projectile motion. It is merely the superposition of uniform linear motion along the direction of the initial velocity vector and the downward motion due to the constant acceleration of gravity. We see the kinematic equations as just the mathematical machinery to perform the…

Photorefractive Nonlinear Optics

DTIC Science & Technology

1991-01-15

conjugate interferometer for the measurement of thin film thickness, refractive index and absorption coefficients. Also, we have investigated...conjugate interferometer for the measurement of thin film thickness, refractive index and absorption coefficients. Also, we have investigated...interaction by considering the refractive index grating as a linear superposition of the gratings from each of the frequency components of the

Nonlinear viscoelastic characterization of polymer materials using a dynamic-mechanical methodology

NASA Technical Reports Server (NTRS)

Strganac, Thomas W.; Payne, Debbie Flowers; Biskup, Bruce A.; Letton, Alan

1995-01-01

Polymer materials retrieved from LDEF exhibit nonlinear constitutive behavior; thus the authors present a method to characterize nonlinear viscoelastic behavior using measurements from dynamic (oscillatory) mechanical tests. Frequency-derived measurements are transformed into time-domain properties providing the capability to predict long term material performance without a lengthy experimentation program. Results are presented for thin-film high-performance polymer materials used in the fabrication of high-altitude scientific balloons. Predictions based upon a linear test and analysis approach are shown to deteriorate for moderate to high stress levels expected for extended applications. Tests verify that nonlinear viscoelastic response is induced by large stresses. Hence, an approach is developed in which the stress-dependent behavior is examined in a manner analogous to modeling temperature-dependent behavior with time-temperature correspondence and superposition principles. The development leads to time-stress correspondence and superposition of measurements obtained through dynamic mechanical tests. Predictions of material behavior using measurements based upon linear and nonlinear approaches are compared with experimental results obtained from traditional creep tests. Excellent agreement is shown for the nonlinear model.

Heralded creation of photonic qudits from parametric down-conversion using linear optics

NASA Astrophysics Data System (ADS)

Yoshikawa, Jun-ichi; Bergmann, Marcel; van Loock, Peter; Fuwa, Maria; Okada, Masanori; Takase, Kan; Toyama, Takeshi; Makino, Kenzo; Takeda, Shuntaro; Furusawa, Akira

2018-05-01

We propose an experimental scheme to generate, in a heralded fashion, arbitrary quantum superpositions of two-mode optical states with a fixed total photon number n based on weakly squeezed two-mode squeezed state resources (obtained via weak parametric down-conversion), linear optics, and photon detection. Arbitrary d -level (qudit) states can be created this way where d =n +1 . Furthermore, we experimentally demonstrate our scheme for n =2 . The resulting qutrit states are characterized via optical homodyne tomography. We also discuss possible extensions to more than two modes concluding that, in general, our approach ceases to work in this case. For illustration and with regards to possible applications, we explicitly calculate a few examples such as NOON states and logical qubit states for quantum error correction. In particular, our approach enables one to construct bosonic qubit error-correction codes against amplitude damping (photon loss) with a typical suppression of √{n }-1 losses and spanned by two logical codewords that each correspond to an n -photon superposition for two bosonic modes.

Plasmon excitations with a semi-integer angular momentum.

PubMed

Mendonça, J T; Serbeto, A; Vieira, J

2018-05-18

We provide an explicit model for a spin-1/2 quasi-particle, based on the superposition of plasmon excitations in a quantum plasmas with intrinsic orbital angular momentum. Such quasi-particle solutions can show remarkable similarities with single electrons moving in vacuum: they have spin-1/2, a finite rest mass, and a quantum dispersion. We also show that these quasi-particle solutions satisfy a criterium of energy minimum.

Flattened halos in a nontopological soliton model of dark matter

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

Mielke, Eckehard W.; Peralta, Humberto H.

2004-12-15

Soliton type solutions of a scalar model with a {phi}{sup 6} self-interaction are analyzed for their density profiles as toy model of dark matter halos. We construct exact solutions with nontrivial ellipticity due to angular momentum and propose a 'nonlinear superposition' of round and flattened halos in order to improve the scaling relations and the correspondence of the predicted rotation curves to the empirical Burkert fit.

Exploiting Elementary Landscapes for TSP, Vehicle Routing and Scheduling

DTIC Science & Technology

2015-09-03

Traveling Salesman Problem (TSP) and Graph Coloring are elementary. Problems such as MAX-kSAT are a superposition of k elementary landscapes. This...search space. Problems such as the Traveling Salesman Problem (TSP), Graph Coloring, the Frequency Assignment Problem , as well as Min-Cut and Max-Cut...echoing our earlier esults on the Traveling Salesman Problem . Using two locally optimal solutions as “parent” solutions, we have developed a

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.

Linear transformer driver for pulse generation with fifth harmonic

DOEpatents

Mazarakis, Michael G.; Kim, Alexander A.; Sinebryukhov, Vadim A.; Volkov, Sergey N.; Kondratiev, Sergey S.; Alexeenko, Vitaly M.; Bayol, Frederic; Demol, Gauthier; Stygar, William A.; Leckbee, Joshua; Oliver, Bryan V.; Kiefer, Mark L.

2017-03-21

A linear transformer driver includes at least one ferrite ring positioned to accept a load. The linear transformer driver also includes a first, second, and third power delivery module. The first power delivery module sends a first energy in the form of a first pulse to the load. The second power delivery module sends a second energy in the form of a second pulse to the load. The third power delivery module sends a third energy in the form of a third pulse to the load. The linear transformer driver is configured to form a flat-top pulse by the superposition of the first, second, and third pulses. The first, second, and third pulses have different frequencies.

Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

USGS Publications Warehouse

Granato, Gregory E.; Smith, Kirk P.

1999-01-01

Discrete or composite samples of highway runoff may not adequately represent in-storm water-quality fluctuations because continuous records of water stage, specific conductance, pH, and temperature of the runoff indicate that these properties fluctuate substantially during a storm. Continuous records of water-quality properties can be used to maximize the information obtained about the stormwater runoff system being studied and can provide the context needed to interpret analyses of water samples. Concentrations of the road-salt constituents calcium, sodium, and chloride in highway runoff were estimated from theoretical and empirical relations between specific conductance and the concentrations of these ions. These relations were examined using the analysis of 233 highwayrunoff samples collected from August 1988 through March 1995 at four highway-drainage monitoring stations along State Route 25 in southeastern Massachusetts. Theoretically, the specific conductance of a water sample is the sum of the individual conductances attributed to each ionic species in solution-the product of the concentrations of each ion in milliequivalents per liter (meq/L) multiplied by the equivalent ionic conductance at infinite dilution-thereby establishing the principle of superposition. Superposition provides an estimate of actual specific conductance that is within measurement error throughout the conductance range of many natural waters, with errors of less than ?5 percent below 1,000 microsiemens per centimeter (?S/cm) and ?10 percent between 1,000 and 4,000 ?S/cm if all major ionic constituents are accounted for. A semi-empirical method (adjusted superposition) was used to adjust for concentration effects-superposition-method prediction errors at high and low concentrations-and to relate measured specific conductance to that calculated using superposition. The adjusted superposition method, which was developed to interpret the State Route 25 highway-runoff records, accounts for contributions of constituents other than calcium, sodium, and chloride in dilute waters. The adjusted superposition method also accounts for the attenuation of each constituent's contribution to conductance as ionic strength increases. Use of the adjusted superposition method generally reduced predictive error to within measurement error throughout the range of specific conductance (from 37 to 51,500 ?S/cm) in the highway runoff samples. The effects of pH, temperature, and organic constituents on the relation between concentrations of dissolved constituents and measured specific conductance were examined but these properties did not substantially affect interpretation of the Route 25 data set. Predictive abilities of the adjusted superposition method were similar to results obtained by standard regression techniques, but the adjusted superposition method has several advantages. Adjusted superposition can be applied using available published data about the constituents in precipitation, highway runoff, and the deicing chemicals applied to a highway. This semi-empirical method can be used as a predictive and diagnostic tool before a substantial number of samples are collected, but the power of the regression method is based upon a large number of water-quality analyses that may be affected by a bias in the data.

Electric current locator

DOEpatents

King, Paul E [Corvallis, OR; Woodside, Charles Rigel [Corvallis, OR

2012-02-07

The disclosure herein provides an apparatus for location of a quantity of current vectors in an electrical device, where the current vector has a known direction and a known relative magnitude to an input current supplied to the electrical device. Mathematical constants used in Biot-Savart superposition equations are determined for the electrical device, the orientation of the apparatus, and relative magnitude of the current vector and the input current, and the apparatus utilizes magnetic field sensors oriented to a sensing plane to provide current vector location based on the solution of the Biot-Savart superposition equations. Description of required orientations between the apparatus and the electrical device are disclosed and various methods of determining the mathematical constants are presented.

WHAEM: PROGRAM DOCUMENTATION FOR THE WELLHEAD ANALYTIC ELEMENT MODEL

EPA Science Inventory

The Wellhead Analytic Element Model (WhAEM) demonstrates a new technique for the definition of time-of-travel capture zones in relatively simple geohydrologic settings. he WhAEM package includes an analytic element model that uses superposition of (many) analytic solutions to gen...

DEMONSTRATION OF THE ANALYTIC ELEMENT METHOD FOR WELLHEAD PROTECTION

EPA Science Inventory

A new computer program has been developed to determine time-of-travel capture zones in relatively simple geohydrological settings. The WhAEM package contains an analytic element model that uses superposition of (many) closed form analytical solutions to generate a ground-water fl...

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

PubMed Central

Goto, Hayato

2016-01-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997

DEMONSTRATION OF THE ANALYTIC ELEMENT METHOD FOR WELLHEAD PROJECTION - PROJECT SUMMARY

EPA Science Inventory

A new computer program has been developed to determine time-of-travel capture zones in relatively simple geohydrological settings. The WhAEM package contains an analytic element model that uses superposition of (many) closed form analytical solutions to generate a ground-water fl...

The Relativistic Rocket

ERIC Educational Resources Information Center

Antippa, Adel F.

2009-01-01

We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful…

Born-Infeld corrections to Coulombian interactions.

PubMed

Ferraro, Rafael; Lipchak, María Evangelina

2008-04-01

Two-dimensional Born-Infeld electrostatic fields behaving as the superposition of two pointlike charges in the linearized (Maxwellian) limit are investigated by means of a nonholomorphic mapping of the complex plane. The changes in the Coulombian interaction between two charges in Born-Infeld theory are computed. Remarkably, the force between equal charges goes to zero as they approach each other.

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

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

Dodonov, V.V., E-mail: vdodonov@fis.unb.br; Valverde, C.; Universidade Paulista, BR 153, km 7, 74845-090 Goiânia, GO

2016-08-15

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-Hermitianmore » 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.« less

Modeling Microscale Electro-thermally Induced Vortex Flows

NASA Astrophysics Data System (ADS)

Paul, Rajorshi; Tang, Tian; Kumar, Aloke

2017-11-01

In presence of a high frequency alternating electric field and a laser induced heat source, vortex flows are generated inside micro-channels. Such electro-thermally influenced micro-vortices can be used for manipulating nano-particles, programming colloidal assemblies, trapping biological cells as well as for fabricating designed bacterial biofilms. In this study, a theoretical model is developed for microscale electro-thermally induced vortex flows with multiple heat sources. Semi-analytical solutions are obtained, using Hankel transformation and linear superposition, for the temperature, pressure and velocity fields. The effect of material properties such as electrical and thermal conductivities, as well as experimental parameters such as the frequency and strength of the alternating electric field, and the intensity and heating profile of the laser source, are systematically investigated. Resolution for a pair of laser sources is determined by analyzing the strength of the micro-vortices under the influence of two heating sources. Results from this work will provide useful insights into the design of efficient optical tweezers and Rapid Electrokinetic Patterning techniques.

Structure of the BBGKY hierarchy near phase transition

NASA Astrophysics Data System (ADS)

Ramanathan, G. V.; Jedrzejek, C.

1980-06-01

A nonperturbative method, as opposed to diagrammatic expansions, is used to study critical phenomena in a fluid with a small hard core and a weak, long-ranged attractive potential. Using the natural small parameter related to the inverse of the range of the attractive potential, spatially uniformly valid asymptotic estimates are made for the magnitudes of all correlations (which are defined as the excess from the generalized superposition approximation) in a region near phase transition in arbitrary number of dimensions. It is shown that if the dimension of the space is larger than four, the correlation hierarchy truncates at the three-body level. The pair correlation satisfies a linear equation. The solution is precisely of Ornstein-Zernike form. For dimensions smaller than four, the hierarchy is still an infinite chain, but considerably simpler than the BBGKY hierarchy. In this case, at the critical point, the correlations are shown to satisfy a scaling law which is the same as that for S4 spin systems.

Refined Zigzag Theory for Homogeneous, Laminated Composite, and Sandwich Plates: A Homogeneous Limit Methodology for Zigzag Function Selection

NASA Technical Reports Server (NTRS)

Tessler, Alexander; DiSciuva, Marco; Gherlone, marco

2010-01-01

The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is presented from a multi-scale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse kinematic field is that of first-order shear-deformation theory, whereas the fine kinematic field has a piecewise-linear zigzag distribution through the thickness. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct sets of zigzag functions. By examining elastostatic solutions for highly heterogeneous sandwich plates, the best-performing zigzag functions are identified. The RZT predictive capabilities to model homogeneous and highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy ; and a wide range of applicability. The present theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient CO-continuous finite elements, and is thus appropriate for the analysis and design of high-performance load-bearing aerospace structures.

Laser phase control of high-order harmonic generation at large internuclear distance: the H+ -H2+ system.

PubMed

Bandrauk, André D; Barmaki, Samira; Kamta, Gerard Lagmago

2007-01-05

Exact (Born-Oppenheimer) 3-D numerical solutions of the time-dependent Schrödinger equation are obtained for the one electron linear H+-H2+ atom-molecule system at large internuclear distance R in interaction with two-cycles intense (I>10(14) W cm(-2)) 800 nm laser pulses. High-order harmonic generation (HHG) spectra are obtained with an energy cutoff larger than the atomic maximum of I(p)+3U(p), where I(p) is the ionization potential and U(p) is the ponderomotive energy. At large R, this extended cutoff is shown to be related to the nature of electron transfer, whose direction is shown to depend critically on the carrier-envelope phase (CEP) of the ultrashort pulse. Constructive and destructive interferences in the HHG spectrum resulting from coherent superpositions of electronic states in the H+-H2+ system are interpreted in terms of multiple electron trajectories extracted from a time profile analysis.

Axisymmetric capillary-gravity waves at the interface of two viscous, immiscible fluids - Initial value problem

NASA Astrophysics Data System (ADS)

Farsoiya, Palas Kumar; Dasgupta, Ratul

2017-11-01

When the interface between two radially unbounded, viscous fluids lying vertically in a stable configuration (denser fluid below) at rest, is perturbed, radially propagating capillary-gravity waves are formed which damp out with time. We study this process analytically using a recently developed linearised theory. For small amplitude initial perturbations, the analytical solution to the initial value problem, represented as a linear superposition of Bessel modes at time t = 0 , is found to agree very well with results obtained from direct numerical simulations of the Navier-Stokes equations, for a range of initial conditions. Our study extends the earlier work by John W. Miles who studied this initial value problem analytically, taking into account, a single viscous fluid only. Implications of this study for the mechanistic understanding of droplet impact into a deep pool, will be discussed. Some preliminary, qualitative comparison with experiments will also be presented. We thank SERB Dept. Science & Technology, Govt. of India, Grant No. EMR/2016/000830 for financial support.

Effect of environmental torques on short-term attitude prediction for a rolling-wheel spacecraft in a sun-synchronous orbit

NASA Technical Reports Server (NTRS)

Hodge, W. F.

1972-01-01

A numerical evaluation and an analysis of the effects of environmental disturbance torques on the attitude of a hexagonal cylinder rolling wheel spacecraft were performed. The resulting perturbations caused by five such torques were found to be very small and exhibited linearity such that linearized equations of motion yielded accurate results over short periods and the separate perturbations contributed by each torque were additive in the sense of superposition. Linearity of the torque perturbations was not affected by moderate system design changes and persisted for torque-to-angular momentum ratios up to 100 times the nominal expected value. As these conditions include many possible applications, similar linear behavior might be anticipated for other rolling-wheel spacecraft.

WHAEM: PROGRAM DOCUMENTATION FOR THE WELLHEAD ANALYTIC ELEMENT MODEL (EPA/600/SR-94/210)

EPA Science Inventory

A new computer program has been developed to determine time-of-travel capture zones in relatively simple geohydrological settings. The WhAEM package contains an analytic element model that uses superposition of (many) closed form analytical solutions to generate a groundwater flo...

A constrained robust least squares approach for contaminant release history identification

NASA Astrophysics Data System (ADS)

Sun, Alexander Y.; Painter, Scott L.; Wittmeyer, Gordon W.

2006-04-01

Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one- and two-dimensional test problems. When the system is ill-conditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.

Stability of matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Ali, Sk. Golam; Roy, S. K.; Talukdar, B.

2010-08-01

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.

Green's function and Bloch theory for the analysis of the dynamic response of a periodically supported beam to a moving load

NASA Astrophysics Data System (ADS)

Lassoued, R.; Lecheheb, M.; Bonnet, G.

2012-08-01

This paper describes an analytical method for the wave field induced by a moving load on a periodically supported beam. The Green's function for an Euler beam without support is evaluated by using the direct integration. Afterwards, it introduces the supports into the model established by using the superposition principle which states that the response from all the sleeper points and from the external point force add up linearly to give a total response. The periodicity of the supports is described by Bloch's theorem. The homogeneous system thus obtained represents a linear differential equation which governs rail response. It is initially solved in the homogeneous case, and it admits a no null solution if its determinant is null, this permits the establishment the dispersion equation to Bloch waves and wave bands. The Bloch waves and dispersion curves contain all the physics of the dynamic problem and the wave field induced by a dynamic load applied to the system is finally obtained by decomposition into Bloch waves, similarly to the usual decomposition into dynamic modes on a finite structure. The method is applied to obtain the field induced by a load moving at constant velocity on a thin beam supported by periodic elastic supports.

Multiple pure tone noise prediction

NASA Astrophysics Data System (ADS)

Han, Fei; Sharma, Anupam; Paliath, Umesh; Shieh, Chingwei

2014-12-01

This paper presents a fully numerical method for predicting multiple pure tones, also known as “Buzzsaw” noise. It consists of three steps that account for noise source generation, nonlinear acoustic propagation with hard as well as lined walls inside the nacelle, and linear acoustic propagation outside the engine. Noise generation is modeled by steady, part-annulus computational fluid dynamics (CFD) simulations. A linear superposition algorithm is used to construct full-annulus shock/pressure pattern just upstream of the fan from part-annulus CFD results. Nonlinear wave propagation is carried out inside the duct using a pseudo-two-dimensional solution of Burgers' equation. Scattering from nacelle lip as well as radiation to farfield is performed using the commercial solver ACTRAN/TM. The proposed prediction process is verified by comparing against full-annulus CFD simulations as well as against static engine test data for a typical high bypass ratio aircraft engine with hardwall as well as lined inlets. Comparisons are drawn against nacelle unsteady pressure transducer measurements at two axial locations as well as against near- and far-field microphone array measurements outside the duct. This is the first fully numerical approach (no experimental or empirical input is required) to predict multiple pure tone noise generation, in-duct propagation and far-field radiation. It uses measured blade coordinates to calculate MPT noise.

Electronic structure and magnetic ordering in manganese hydride

NASA Astrophysics Data System (ADS)

Magnitskaya, M. V.; Kulikov, N. I.

1991-03-01

The self-consistent electron energy bands of antiferromagnetic (AFM) and non-magnetic manganese hydride are calculated using the linear muffintin orbital method (LMTO). The calculated values of equilibrium volume and of magnetic moment on the manganese site are in good agreement with experiment. The Fermi surface of paramagnetic MnH contains two nesting parts, and their superposition gives rise to AFM gap.

Relative Water Uptake as a Criterion for the Design of Trickle Irrigation Systems

NASA Astrophysics Data System (ADS)

Communar, G.; Friedman, S. P.

2008-12-01

Previously derived analytical solutions to the 2- and 3-dimensional water flow problems describing trickle irrigation are not being widely used in practice because those formulations either ignore root water uptake or refer to it as a known input. In this lecture we are going to describe a new modeling approach and demonstrate its applicability for designing the geometry of trickle irrigation systems, namely the spacing between the emitters and drip lines. The major difference between our and previous modeling approaches is that we refer to the root water uptake as to the unknown solution of the problem and not as to a known input. We postulate that the solution to the steady-state water flow problem with a root sink that is acting under constant, maximum suction defines un upper bound to the relative water uptake (water use efficiency) in actual transient situations and propose to use it as a design criterion. Following previous derivations of analytical solutions we assume that the soil hydraulic conductivity increases exponentially with its matric head, which allows the linearization of the Richards equation, formulated in terms of the Kirchhoff matric flux potential. Since the transformed problem is linear, the relative water uptake for any given configuration of point or line sources and sinks can be calculated by superposition of the Green's functions of all relevant water sources and sinks. In addition to evaluating the relative water uptake, we also derived analytical expressions for the steam functions. The stream lines separating the water uptake zone from the percolating water provide insight to the dependence of the shape and extent of the actual rooting zone on the source- sink geometry and soil properties. A minimal number of just 3 system parameters: Gardner's (1958) alfa as a soil type quantifier and the depth and diameter of the pre-assumed active root zone are sufficient to characterize the interplay between capillary and gravitational effects on water flow and the competition between the processes of root water uptake and percolation. For accounting also for evaporation from the soil surface, when significant, another parameter is required, adopting the solution of Lomen and Warrick (1978).

Qudit-teleportation for photons with linear optics.

PubMed

Goyal, Sandeep K; Boukama-Dzoussi, Patricia E; Ghosh, Sibasish; Roux, Filippus S; Konrad, Thomas

2014-04-01

Quantum Teleportation, the transfer of the state of one quantum system to another without direct interaction between both systems, is an important way to transmit information encoded in quantum states and to generate quantum correlations (entanglement) between remote quantum systems. So far, for photons, only superpositions of two distinguishable states (one "qubit") could be teleported. Here we show how to teleport a "qudit", i.e. a superposition of an arbitrary number d of distinguishable states present in the orbital angular momentum of a single photon using d beam splitters and d additional entangled photons. The same entanglement resource might also be employed to collectively teleport the state of d/2 photons at the cost of one additional entangled photon per qubit. This is superior to existing schemes for photonic qubits, which require an additional pair of entangled photons per qubit.

Qudit-Teleportation for photons with linear optics

NASA Astrophysics Data System (ADS)

Goyal, Sandeep K.; Boukama-Dzoussi, Patricia E.; Ghosh, Sibasish; Roux, Filippus S.; Konrad, Thomas

2014-04-01

Quantum Teleportation, the transfer of the state of one quantum system to another without direct interaction between both systems, is an important way to transmit information encoded in quantum states and to generate quantum correlations (entanglement) between remote quantum systems. So far, for photons, only superpositions of two distinguishable states (one ``qubit'') could be teleported. Here we show how to teleport a ``qudit'', i.e. a superposition of an arbitrary number d of distinguishable states present in the orbital angular momentum of a single photon using d beam splitters and d additional entangled photons. The same entanglement resource might also be employed to collectively teleport the state of d/2 photons at the cost of one additional entangled photon per qubit. This is superior to existing schemes for photonic qubits, which require an additional pair of entangled photons per qubit.

Qudit-Teleportation for photons with linear optics

PubMed Central

Goyal, Sandeep K.; Boukama-Dzoussi, Patricia E.; Ghosh, Sibasish; Roux, Filippus S.; Konrad, Thomas

2014-01-01

Quantum Teleportation, the transfer of the state of one quantum system to another without direct interaction between both systems, is an important way to transmit information encoded in quantum states and to generate quantum correlations (entanglement) between remote quantum systems. So far, for photons, only superpositions of two distinguishable states (one “qubit”) could be teleported. Here we show how to teleport a “qudit”, i.e. a superposition of an arbitrary number d of distinguishable states present in the orbital angular momentum of a single photon using d beam splitters and d additional entangled photons. The same entanglement resource might also be employed to collectively teleport the state of d/2 photons at the cost of one additional entangled photon per qubit. This is superior to existing schemes for photonic qubits, which require an additional pair of entangled photons per qubit. PMID:24686274

Viscoelastic Properties of Human Tracheal Tissues.

PubMed

Safshekan, Farzaneh; Tafazzoli-Shadpour, Mohammad; Abdouss, Majid; Shadmehr, Mohammad B

2017-01-01

The physiological performance of trachea is highly dependent on its mechanical behavior, and therefore, the mechanical properties of its components. Mechanical characterization of trachea is key to succeed in new treatments such as tissue engineering, which requires the utilization of scaffolds which are mechanically compatible with the native human trachea. In this study, after isolating human trachea samples from brain-dead cases and proper storage, we assessed the viscoelastic properties of tracheal cartilage, smooth muscle, and connective tissue based on stress relaxation tests (at 5% and 10% strains for cartilage and 20%, 30%, and 40% for smooth muscle and connective tissue). After investigation of viscoelastic linearity, constitutive models including Prony series for linear viscoelasticity and quasi-linear viscoelastic, modified superposition, and Schapery models for nonlinear viscoelasticity were fitted to the experimental data to find the best model for each tissue. We also investigated the effect of age on the viscoelastic behavior of tracheal tissues. Based on the results, all three tissues exhibited a (nonsignificant) decrease in relaxation rate with increasing the strain, indicating viscoelastic nonlinearity which was most evident for cartilage and with the least effect for connective tissue. The three-term Prony model was selected for describing the linear viscoelasticity. Among different models, the modified superposition model was best able to capture the relaxation behavior of the three tracheal components. We observed a general (but not significant) stiffening of tracheal cartilage and connective tissue with aging. No change in the stress relaxation percentage with aging was observed. The results of this study may be useful in the design and fabrication of tracheal tissue engineering scaffolds.

Eshelby's problem of a spherical inclusion eccentrically embedded in a finite spherical body

PubMed Central

He, Q.-C.

2017-01-01

Resorting to the superposition principle, the solution of Eshelby's problem of a spherical inclusion located eccentrically inside a finite spherical domain is obtained in two steps: (i) the solution to the problem of a spherical inclusion in an infinite space; (ii) the solution to the auxiliary problem of the corresponding finite spherical domain subjected to appropriate boundary conditions. Moreover, a set of functions called the sectional and harmonic deviators are proposed and developed to work out the auxiliary solution in a series form, including the displacement and Eshelby tensor fields. The analytical solutions are explicitly obtained and illustrated when the geometric and physical parameters and the boundary condition are specified. PMID:28293141

Discrete shear-transformation-zone plasticity modeling of notched bars

NASA Astrophysics Data System (ADS)

Kondori, Babak; Amine Benzerga, A.; Needleman, Alan

2018-02-01

Plane strain tension analyses of un-notched and notched bars are carried out using discrete shear transformation zone plasticity. In this framework, the carriers of plastic deformation are shear transformation zones (STZs) which are modeled as Eshelby inclusions. Superposition is used to represent a boundary value problem solution in terms of discretely modeled Eshelby inclusions, given analytically for an infinite elastic medium, and an image solution that enforces the prescribed boundary conditions. The image problem is a standard linear elastic boundary value problem that is solved by the finite element method. Potential STZ activation sites are randomly distributed in the bars and constitutive relations are specified for their evolution. Results are presented for un-notched bars, for bars with blunt notches and for bars with sharp notches. The computed stress-strain curves are serrated with the magnitude of the associated stress-drops depending on bar size, notch acuity and STZ evolution. Cooperative deformation bands (shear bands) emerge upon straining and, in some cases, high stress levels occur within the bands. Effects of specimen geometry and size on the stress-strain curves are explored. Depending on STZ kinetics, notch strengthening, notch insensitivity or notch weakening are obtained. The analyses provide a rationale for some conflicting findings regarding notch effects on the mechanical response of metallic glasses.

Improved scatter correction using adaptive scatter kernel superposition

NASA Astrophysics Data System (ADS)

Sun, M.; Star-Lack, J. M.

2010-11-01

Accurate scatter correction is required to produce high-quality reconstructions of x-ray cone-beam computed tomography (CBCT) scans. This paper describes new scatter kernel superposition (SKS) algorithms for deconvolving scatter from projection data. The algorithms are designed to improve upon the conventional approach whose accuracy is limited by the use of symmetric kernels that characterize the scatter properties of uniform slabs. To model scatter transport in more realistic objects, nonstationary kernels, whose shapes adapt to local thickness variations in the projection data, are proposed. Two methods are introduced: (1) adaptive scatter kernel superposition (ASKS) requiring spatial domain convolutions and (2) fast adaptive scatter kernel superposition (fASKS) where, through a linearity approximation, convolution is efficiently performed in Fourier space. The conventional SKS algorithm, ASKS, and fASKS, were tested with Monte Carlo simulations and with phantom data acquired on a table-top CBCT system matching the Varian On-Board Imager (OBI). All three models accounted for scatter point-spread broadening due to object thickening, object edge effects, detector scatter properties and an anti-scatter grid. Hounsfield unit (HU) errors in reconstructions of a large pelvis phantom with a measured maximum scatter-to-primary ratio over 200% were reduced from -90 ± 58 HU (mean ± standard deviation) with no scatter correction to 53 ± 82 HU with SKS, to 19 ± 25 HU with fASKS and to 13 ± 21 HU with ASKS. HU accuracies and measured contrast were similarly improved in reconstructions of a body-sized elliptical Catphan phantom. The results show that the adaptive SKS methods offer significant advantages over the conventional scatter deconvolution technique.

Hyperspherical nuclear motion of H3 + and D3 + in the electronic triplet state, a 3Sigmau +.

PubMed

Ferreira, Tiago Mendes; Alijah, Alexander; Varandas, António J C

2008-02-07

The potential energy surface of H(3) (+) in the lowest electronic triplet state, a (3)Sigma(u) (+), shows three equivalent minima at linear nuclear configurations. The vibrational levels of H(3) (+) and D(3) (+) on this surface can therefore be described as superimposed linear molecule states. Owing to such a superposition, each vibrational state characterized by quantum numbers of an isolated linear molecule obtains a one- and a two-dimensional component. The energy splittings between the two components have now been rationalized within a hyperspherical picture. It is shown that nuclear motion along the hyperangle phi mainly accounts for the splittings and provides upper bounds. This hyperspherical motion can be considered an extension of the antisymmetric stretching motion of the individual linear molecule.

Contact stresses in gear teeth: A new method of analysis

NASA Technical Reports Server (NTRS)

Somprakit, Paisan; Huston, Ronald L.; Oswald, Fred B.

1991-01-01

A new, innovative procedure called point load superposition for determining the contact stresses in mating gear teeth. It is believed that this procedure will greatly extend both the range of applicability and the accuracy of gear contact stress analysis. Point load superposition is based upon fundamental solutions from the theory of elasticity. It is an iterative numerical procedure which has distinct advantages over the classical Hertz method, the finite element method, and over existing applications with the boundary element method. Specifically, friction and sliding effects, which are either excluded from or difficult to study with the classical methods, are routinely handled with the new procedure. Presented here are the basic theory and the algorithms. Several examples are given. Results are consistent with those of the classical theories. Applications to spur gears are discussed.

MAGNETO-ACOUSTIC WAVES IN A GRAVITATIONALLY STRATIFIED MAGNETIZED PLASMA: EIGEN-SOLUTIONS AND THEIR APPLICATIONS TO THE SOLAR ATMOSPHERE

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

Mather, J. F.; Erdélyi, R., E-mail: robertus@sheffield.ac.uk

2016-05-10

Magneto-acoustic gravity (MAG) waves have been studied intensively in the context of astrophysical plasmas. There are three popular choices of analytic modeling using a Cartesian coordinate system: a magnetic field parallel, perpendicular, or at an angle to the gravitational field. Here, we study a gravitationally stratified plasma embedded in a parallel, so called vertical, magnetic field. We find a governing equation for the auxiliary quantity Θ = p {sub 1}/ ρ {sub 0}, and find solutions in terms of hypergeometric functions. With the convenient relationship between Θ and the vertical velocity component, v {sub z}, we derive the solution formore » v{sub z}. We show that the four linearly independent functions for v{sub z} can also be cast as single hypergeometric functions, rather than the Frobenius series derived by Leroy and Schwartz. We are then able to analyze a case of approximation for a one-layer solution, taking the small wavelength limit. Motivated by solar atmospheric applications, we finally commence study of the eigenmodes of perturbations for a two-layer model using our solutions, solving the dispersion relation numerically. We show that, for a transition between a photospheric and chromospheric plasma embedded in a vertical magnetic field, modes exist that are between the observationally widely investigated three and five minute oscillation periods, interpreted as solar global oscillations in the lower solar atmosphere . It is also shown that, when the density contrast between the layers is large (e.g., applied to photosphere/chromosphere-corona), the global eigenmodes are practically a superposition of the same as in each of the separate one-layer systems.« less

Numerical solution of the exterior oblique derivative BVP using the direct BEM formulation

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Špir, Róbert; Mikula, Karol

2016-04-01

The fixed gravimetric boundary value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. A direct formulation of the boundary element method (BEM) for the Laplace equation leads to a boundary integral equation (BIE) where a harmonic function is represented as a superposition of the single-layer and double-layer potential. Such a potential representation is applied to obtain a numerical solution of FGBVP. The oblique derivative problem is treated by a decomposition of the gradient of the unknown disturbing potential into its normal and tangential components. Our numerical scheme uses the collocation with linear basis functions. It involves a triangulated discretization of the Earth's surface as our computational domain considering its complicated topography. To achieve high-resolution numerical solutions, parallel implementations using the MPI subroutines as well as an iterative elimination of far zones' contributions are performed. Numerical experiments present a reconstruction of a harmonic function above the Earth's topography given by the spherical harmonic approach, namely by the EGM2008 geopotential model up to degree 2160. The SRTM30 global topography model is used to approximate the Earth's surface by the triangulated discretization. The obtained BEM solution with the resolution 0.05 deg (12,960,002 nodes) is compared with EGM2008. The standard deviation of residuals 5.6 cm indicates a good agreement. The largest residuals are obviously in high mountainous regions. They are negative reaching up to -0.7 m in Himalayas and about -0.3 m in Andes and Rocky Mountains. A local refinement in the area of Slovakia confirms an improvement of the numerical solution in this mountainous region despite of the fact that the Earth's topography is here considered in more details.

Estimating radiated flux density from wildland fires using the raw output of limited bandpass detectors

Treesearch

Robert L. Kremens; Matthew B. Dickinson

2015-01-01

We have simulated the radiant emission spectra from wildland fires such as would be observed at a scale encompassing the pre-frontal fuel bed, the flaming front and the zone of post-frontal combustion and cooling. For these simulations, we developed a 'mixed-pixel' model where the fire infrared spectrum is estimated as the linear superposition of spectra of...

Cluster-type entangled coherent states: Generation and application

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

An, Nguyen Ba; Kim, Jaewan; Korea Institute for Advanced Study, 207-43 Cheongryangni 2-dong, Dongdaemun-gu, Seoul 130-722

2009-10-15

We consider a type of (M+N)-mode entangled coherent states and propose a simple deterministic scheme to generate these states that can fly freely in space. We then exploit such free-flying states to teleport certain kinds of superpositions of multimode coherent states. We also address the issue of manipulating size and type of entangled coherent states by means of linear optics elements only.

Cluster-type entangled coherent states: Generation and application

NASA Astrophysics Data System (ADS)

An, Nguyen Ba; Kim, Jaewan

2009-10-01

We consider a type of (M+N) -mode entangled coherent states and propose a simple deterministic scheme to generate these states that can fly freely in space. We then exploit such free-flying states to teleport certain kinds of superpositions of multimode coherent states. We also address the issue of manipulating size and type of entangled coherent states by means of linear optics elements only.

Atomic Schroedinger cat-like states

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

Enriquez-Flores, Marco; Rosas-Ortiz, Oscar; Departamento de Fisica, Cinvestav, A.P. 14-740, Mexico D.F. 07000

2010-10-11

After a short overview of the basic mathematical structure of quantum mechanics we analyze the Schroedinger's antinomic example of a living and dead cat mixed in equal parts. Superpositions of Glauber kets are shown to approximate such macroscopic states. Then, two-level atomic states are used to construct mesoscopic kittens as appropriate linear combinations of angular momentum eigenkets for j = 1/2. Some general comments close the present contribution.

Evaluation of the vibration-rotation-tunneling dynamics at the basis set superposition error corrected global minimum geometry of the ammonia dimer

NASA Astrophysics Data System (ADS)

Muguet, Francis F.; Robinson, G. Wilse; Bassez-Muguet, M. Palmyre

1995-03-01

With the help of a new scheme to correct for the basis set superposition error (BSSE), we find that an eclipsed nonlinear geometry becomes energetically favored over the eclipsed linear hydrogen-bonded geometry. From a normal mode analysis of the potential energy surface (PES) in the vicinity of the nonlinear geometry, we suggest that several dynamical interchange pathways must be taken into account. The minimal molecular symmetry group to be considered should be the double group of G36, but still larger multiple groups may be required. An interpretation of experimental vibration-rotation-tunneling (VRT) data in terms of the G144 group, which implies monomer inversions, may not be the only alternative. It appears that group theoretical considerations alone are insufficient for understanding the complex VRT dynamics of the ammonia dimer.

Linear and nonlinear response in sheared soft spheres

NASA Astrophysics Data System (ADS)

Tighe, Brian

2013-11-01

Packings of soft spheres provide an idealized model of foams, emulsions, and grains, while also serving as the canonical example of a system undergoing a jamming transition. Packings' mechanical response has now been studied exhaustively in the context of ``strict linear response,'' i.e. by linearizing about a stable static packing and solving the resulting equations of motion. Both because the system is close to a critical point and because the soft sphere pair potential is non-analytic at the point of contact, it is reasonable to ask under what circumstances strict linear response provides a good approximation to the actual response. We simulate sheared soft sphere packings close to jamming and identify two distinct strain scales: (i) the scale on which strict linear response fails, coinciding with a topological change in the packing's contact network; and (ii) the scale on which linear superposition of the averaged stress-strain curve breaks down. This latter scale provides a ``weak linear response'' criterion and is likely to be more experimentally relevant.

Chiral resolution of spin angular momentum in linearly polarized and unpolarized light

PubMed Central

Hernández, R. J.; Mazzulla, A.; Provenzano, C.; Pagliusi, P.; Cipparrone, G.

2015-01-01

Linearly polarized (LP) and unpolarized (UP) light are racemic entities since they can be described as superposition of opposite circularly polarized (CP) components of equal amplitude. As a consequence they do not carry spin angular momentum. Chiral resolution of a racemate, i.e. separation of their chiral components, is usually performed via asymmetric interaction with a chiral entity. In this paper we provide an experimental evidence of the chiral resolution of linearly polarized and unpolarized Gaussian beams through the transfer of spin angular momentum to chiral microparticles. Due to the interplay between linear and angular momentum exchange, basic manipulation tasks, as trapping, spinning or orbiting of micro-objects, can be performed by light with zero helicity. The results might broaden the perspectives for development of miniaturized and cost-effective devices. PMID:26585284

Constitutive Modeling, Nonlinear Behavior, and the Stress-Optic Law

DTIC Science & Technology

2011-01-01

estimates of D̂ from dynamic mechanical measurements. Some results are shown in Figure 58 for a filled EPDM rubber [116]. There is rough agreement with...elastomers and filler-reinforced rubber . 5.1 Linearity and the superposition principle The problem of analyzing viscoelastic mechanical behavior is greatly...deformation such as shear. For crosslinked rubber the strain can be defined in terms of the strain function suggested by the statistical theories of

Magnetic Barkhausen Noise Measurements Using Tetrapole Probe Designs

NASA Astrophysics Data System (ADS)

McNairnay, Paul

A magnetic Barkhausen noise (MBN) testing system was developed for Defence Research and Development Canada (DRDC) to perform MBN measurements on the Royal Canadian Navy's Victoria class submarine hulls that can be correlated with material properties, including residual stress. The DRDC system was based on the design of a MBN system developed by Steven White at Queen's University, which was capable of performing rapid angular dependent measurements through the implementation of a flux controlled tetrapole probe. In tetrapole probe designs, the magnetic excitation field is rotated in the surface plane of the sample under the assumption of linear superposition of two orthogonal magnetic fields. During the course of this work, however, the validity of flux superposition in ferromagnetic materials, for the purpose of measuring MBN, was brought into question. Consequently, a study of MBN anisotropy using tetrapole probes was performed. Results indicate that MBN anisotropy measured under flux superposition does not simulate MBN anisotropy data obtained through manual rotation of a single dipole excitation field. It is inferred that MBN anisotropy data obtained with tetrapole probes is the result of the magnetic domain structure's response to an orthogonal magnetization condition and not necessarily to any bulk superposition magnetization in the sample. A qualitative model for the domain configuration under two orthogonal magnetic fields is proposed to describe the results. An empirically derived fitting equation, that describes tetrapole MBN anisotropy data, is presented. The equation describes results in terms of two largely independent orthogonal fields, and includes interaction terms arising due to competing orthogonally magnetized domain structures and interactions with the sample's magnetic easy axis. The equation is used to fit results obtained from a number of samples and tetrapole orientations and in each case correctly identifies the samples' magnetic easy axis.

Control of Exciton Valley Coherence in Transition Metal Dichalcogenide Monolayers

NASA Astrophysics Data System (ADS)

Wang, Gang

Current research on Transition Metal Dichalcogenide (TMD) Monolayers is stimulated by their strong light-matter interaction and the possibility to use the valley index in addition to spin as an information carrier. The direct gap interband transitions in TMD monolayers are governed by chiral optical selection rules. Determined by laser helicity, optical transitions in either the K+ or K- valley in momentum space are induced. Very recently the optical generation of valley polarization and valley coherence (coherent superposition of valley states) have been reported. In this work we go a step further by discussing the coherent manipulation of valley states. Linearly polarized laser excitation prepares a coherent superposition of valley states. We demonstrate the control of the exciton valley coherence in monolayer WSe2 by tuning the applied magnetic field perpendicular to the monolayer plane. The induced valley Zeeman splitting between K+ and K- results in a change of the oscillation frequency of the superposition of the valley states, which corresponds to a rotation of the exciton valley pseudo-spin. We show rotation of this coherent superposition of valley states by angles as large as 30 degrees in applied fields up to 9T and discuss valley coherence in other TMD monolayer materials. This exciton valley coherence control on ps time scale could be an important step towards complete control of qubits based on the valley degree of freedom. In collaboration with X. Marie, T. Amand, C. Robert, F. Cadiz, P. Renucci, B. Urbaszek (Université de Toulouse, INSA-CNRS-UPS, LPCNO, France), B. L. Liu (Institute of Physics, Chinese Academy of Sciences, China) and we acknowledge ERC Grant No. 306719.

Mode separation in frequency-wavenumber domain through compressed sensing of far-field Lamb waves

NASA Astrophysics Data System (ADS)

Gao, Fei; Zeng, Liang; Lin, Jing; Luo, Zhi

2017-07-01

This method based on Lamb waves shows great potential for long-range damage detection. Mode superposition resulting from multi-modal and dispersive characteristics makes signal interpretation and damage feature extraction difficult. Mode separation in the frequency-wavenumber (f-k) domain using a 1D sparse sensing array is a promising solution. However, due to the lack of prior knowledge about damage location, this method based on 1D linear measurement, for the mode extraction of arbitrary reflections caused by defects that are not in line with the sensor array, is restricted. In this paper, an improved compressed sensing method under the far-field assumption is established, which is beneficial to the reconstruction of reflections in the f-k domain. Hence, multiple components consisting of structure and damage features could be recovered via a limited number of measurements. Subsequently, a mode sweeping process based on theoretical dispersion curves has been designed for mode characterization and direction of arrival estimation. Moreover, 2D f-k filtering and inverse transforms are applied to the reconstructed f-k distribution in order to extract the purified mode of interest. As a result, overlapping waveforms can be separated and the direction of defects can be estimated. A uniform linear sensor array consisting of 16 laser excitations is finally employed for experimental investigations and the results demonstrate the efficiency of the proposed method.

Derivation of regularized Grad's moment system from kinetic equations: modes, ghosts and non-Markov fluxes

NASA Astrophysics Data System (ADS)

Karlin, Ilya

2018-04-01

Derivation of the dynamic correction to Grad's moment system from kinetic equations (regularized Grad's 13 moment system, or R13) is revisited. The R13 distribution function is found as a superposition of eight modes. Three primary modes, known from the previous derivation (Karlin et al. 1998 Phys. Rev. E 57, 1668-1672. (doi:10.1103/PhysRevE.57.1668)), are extended into the nonlinear parameter domain. Three essentially nonlinear modes are identified, and two ghost modes which do not contribute to the R13 fluxes are revealed. The eight-mode structure of the R13 distribution function implies partition of R13 fluxes into two types of contributions: dissipative fluxes (both linear and nonlinear) and nonlinear streamline convective fluxes. Physical interpretation of the latter non-dissipative and non-local in time effect is discussed. A non-perturbative R13-type solution is demonstrated for a simple Lorentz scattering kinetic model. The results of this study clarify the intrinsic structure of the R13 system. This article is part of the theme issue `Hilbert's sixth problem'.

Sensitivity of resistive and Hall measurements to local inhomogeneities: Finite-field, intensity, and area corrections

NASA Astrophysics Data System (ADS)

Koon, Daniel W.; Wang, Fei; Petersen, Dirch Hjorth; Hansen, Ole

2014-10-01

We derive exact, analytic expressions for the sensitivity of sheet resistance and Hall sheet resistance measurements to local inhomogeneities for the cases of nonzero magnetic fields, strong perturbations, and perturbations over a finite area, extending our earlier results on weak perturbations. We express these sensitivities for conductance tensor components and for other charge transport quantities. Both resistive and Hall sensitivities, for a van der Pauw specimen in a finite magnetic field, are a superposition of the zero-field sensitivities to both sheet resistance and Hall sheet resistance. Strong perturbations produce a nonlinear correction term that depends on the strength of the inhomogeneity. Solution of the specific case of a finite-sized circular inhomogeneity coaxial with a circular specimen suggests a first-order correction for the general case. Our results are confirmed by computer simulations on both a linear four-point probe array on a large circular disc and a van der Pauw square geometry. Furthermore, the results also agree well with Náhlík et al. published experimental results for physical holes in a circular copper foil disc.

Experimentally validated quantitative linear model for the device physics of elastomeric microfluidic valves

NASA Astrophysics Data System (ADS)

Kartalov, Emil P.; Scherer, Axel; Quake, Stephen R.; Taylor, Clive R.; Anderson, W. French

2007-03-01

A systematic experimental study and theoretical modeling of the device physics of polydimethylsiloxane "pushdown" microfluidic valves are presented. The phase space is charted by 1587 dimension combinations and encompasses 45-295μm lateral dimensions, 16-39μm membrane thickness, and 1-28psi closing pressure. Three linear models are developed and tested against the empirical data, and then combined into a fourth-power-polynomial superposition. The experimentally validated final model offers a useful quantitative prediction for a valve's properties as a function of its dimensions. Typical valves (80-150μm width) are shown to behave like thin springs.

A note on singularities of the 3-D Euler equation

NASA Technical Reports Server (NTRS)

Tanveer, S.

1994-01-01

In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

A New Look at Two Old Problems in Electrostatics, or Much Ado with Hemispheres

ERIC Educational Resources Information Center

DasGupta, Ananda

2007-01-01

In this paper, we take a look at two electrostatics problems concerning hemispheres. The first problem concerns the direction of the electric field on the flat cap of a uniformly charged hemisphere. We show that the symmetry and principle of superposition coupled with Gauss's law gives a delightfully simple solution and then go on to examine how…

Toroidal halos in a nontopological soliton model of dark matter

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

Mielke, Eckehard W.; Perez, Jose A. Velez

2007-02-15

Soliton type solutions of an axionlike scalar model with self-interaction are analyzed further as a toy model of dark matter halos. For a 'nonlinear superposition' of round and flattened configurations we found ringlike substructures in the density profile similarly as has been inferred for our Galaxy from the observed excess of the diffuse component of cosmic gamma rays.

Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions.

PubMed

Kedziora, David J; Ankiewicz, Adrian; Akhmediev, Nail

2013-07-01

We present a systematic classification for higher-order rogue-wave solutions of the nonlinear Schrödinger equation, constructed as the nonlinear superposition of first-order breathers via the recursive Darboux transformation scheme. This hierarchy is subdivided into structures that exhibit varying degrees of radial symmetry, all arising from independent degrees of freedom associated with physical translations of component breathers. We reveal the general rules required to produce these fundamental patterns. Consequently, we are able to extrapolate the general shape for rogue-wave solutions beyond order 6, at which point accuracy limitations due to current standards of numerical generation become non-negligible. Furthermore, we indicate how a large set of irregular rogue-wave solutions can be produced by hybridizing these fundamental structures.

An integrated theoretical and experimental investigation of insensitive munition compounds adsorption on cellulose, cellulose triacetate, chitin and chitosan surfaces.

PubMed

Gurtowski, Luke A; Griggs, Chris S; Gude, Veera G; Shukla, Manoj K

2018-02-01

This manuscript reports results of combined computational chemistry and batch adsorption investigation of insensitive munition compounds, 2,4-dinitroanisole (DNAN), triaminotrinitrobenzene (TATB), 1,1-diamino-2,2-dinitroethene (FOX-7) and nitroguanidine (NQ), and traditional munition compound 2,4,6-trinitrotoluene (TNT) on the surfaces of cellulose, cellulose triacetate, chitin and chitosan biopolymers. Cellulose, cellulose triacetate, chitin and chitosan were modeled as trimeric form of the linear chain of 4 C 1 chair conformation of β-d-glucopyranos, its triacetate form, β-N-acetylglucosamine and D-glucosamine, respectively, in the 1➔4 linkage. Geometries were optimized at the M062X functional level of the density functional theory (DFT) using the 6-31G(d,p) basis set in the gas phase and in the bulk water solution using the conductor-like polarizable continuum model (CPCM) approach. The nature of potential energy surfaces of the optimized geometries were ascertained through the harmonic vibrational frequency analysis. The basis set superposition error (BSSE) corrected interaction energies were obtained using the 6-311G(d,p) basis set at the same theoretical level. The computed BSSE in the gas phase was used to correct interaction energy in the bulk water solution. Computed and experimental results regarding the ability of considered surfaces in adsorbing the insensitive munitions compounds are discussed. Copyright © 2017. Published by Elsevier B.V.

Relationships between nonlinear normal modes and response to random inputs

NASA Astrophysics Data System (ADS)

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2017-02-01

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.

A straightforward characterization of non-modal effects from the evolution of linear dynamical systems

NASA Astrophysics Data System (ADS)

Arratia, Cristobal

2014-11-01

A simple construction will be shown, which reveals a general property satisfied by the evolution in time of a state vector composed by a superposition of orthogonal eigenmodes of a linear dynamical system. This property results from the conservation of the inner product between such state vectors evolving forward and backwards in time, and it can be simply evaluated from the state vector and its first and second time derivatives. This provides an efficient way to characterize, instantaneously along any specific phase-space trajectory of the linear system, the relevance of the non-normality of the linearized Navier-Stokes operator on the energy (or any other norm) gain or decay of small perturbations. Examples of this characterization applied to stationary or time dependent base flows will be shown. CONICYT, Concurso de Apoyo al Retorno de Investigadores del Extranjero, folio 821320055.

The nonlinearity of passive extraocular muscles

PubMed Central

Quaia, Christian; Ying, Howard S.; Optican, Lance M.

2011-01-01

Passive extraocular muscles (EOMs), like most biological tissues, are hyper-elastic, i.e., their stiffness increases as they are stretched. It has always been assumed, and in a few occasions argued, that this is their only nonlinearity and that it can be ignored in central gaze. However, using novel measurement techniques in anesthetized paralyzed monkeys, we have recently demonstrated that EOMs are characterized by another prominent nonlinearity: the forces induced by sequences of stretches do not sum. Thus, superposition, a central tenet of linear and quasi-linear models, does not hold in passive EOMs. Here, we outline the implications of this finding, especially in light of the common assumption that it is easier for the brain to control a linear than a nonlinear plant. We argue against this common belief: the specific nonlinearity of passive EOMs may actually make it easier for the brain to control the plant than if muscles were linear. PMID:21950971

Estimating Tsunami Runup with Fault Plane Parameters

NASA Astrophysics Data System (ADS)

Sepulveda, I.; Liu, P. L. F.

2016-12-01

The forecasting of tsunami runup has often been done by solving numerical models. The execution times, however, make them unsuitable for the purpose of warning. We offer an alternative method that provides analytical relationship between the runup height, the fault plane parameters and the characteristic of coastal bathymetry. The method uses the model of Okada (1985) to estimate the coseismic deformation and the corresponding sea surface displacement (η(x,0)). Once the tsunami waves are generated, Carrier & Greenspan (1958) solution (C&G) is adopted to yield analytical expressions for the shoreline elevation and velocity. Two types of problems are investigated. In the first, the bathymetry is modeled as a constant slope that is connected to a constant depth region, where a seismic event occurs. This is a boundary value problem (BVP). In the second, the bathymetry is further simplified as a constant slope, on which a seismic event occurs. This is an initial value problem (IVP). Both problems are depicted in Figure 1. We derive runup solutions in terms of the fault parameters. The earthquake is associated with vertical coseismic seafloor displacements by using Okada's elastic model. In addition to the simplifications considered in Okada's model, we further assume (1) a strike parallel to the shoreline, (2) a very long rupture area and (3) a fast earthquake so surface elevation mimics the seafloor displacements. Then the tsunami origin is modeled in terms of the fault depth (d), fault width (W), fault slip (s) and dip angle (δ). We describe the solution for the BVP. Madsen & Schaeffer (2010) utilized C&G to derive solutions for the shoreline elevation of sinusoidal waves imposed in the offshore boundary. A linear superposition of this solution represents any arbitrary incident wave. Furthermore, we can prescribe the boundary condition at the toe of sloping beach by adopting the linear shallow wave equations in the constant depth area. By means of a dimensional analysis, the runup R is determined by Eq.1. Kanoglu (2004) derived a non-dimensional expression for long wave runup originated over a sloping beach. In our work we determine an analytical expression for a sinusoidal initial condition. Following the same procedure as the BVP, the expression for the runup R in the IVP is given by Eq.2. The curves F1 and F2 are plotted in Figure 2.

Estimation of Rotary Stability Derivatives at Subsonic and Transonic Speeds

NASA Technical Reports Server (NTRS)

Tobak, Murray; Lessing, Henry C.

1961-01-01

The first part of this paper pertains to the estimation of subsonic rotary stability derivatives of wings. The unsteady potential flow problem is solved by a superposition of steady flow solutions. Numerical results for the damping coefficients of triangular wings are presented as functions of aspect ratio and Mach number, and are compared with experimental results over the Mach number range 0 to 1. In the second part, experimental results are used. to point out a close correlation between the nonlinear variations with angle of attack of the static pitching-moment curve slope and the damping-in-pitch coefficient. The underlying basis for the correlation is found as a result of an analysis in which the indicial function concept and. the principle of super-position are adapted to apply to the nonlinear problem. The form of the result suggests a method of estimating nonlinear damping coefficients from results of static wind-tunnel measurements.

Nature and mechanisms of elastic deformations for a rock mass with several workings. [Deviations from superposition of individual effects

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

Yagunov, A.S.; Seryakov, V.M.

1985-07-01

This paper presents results of a study which indicates that as a result of the solution for a nonuniform rock mass by the FEM it is established that, first, from the direction of the hanging wall of workings and at the surface, the nature of elastic deformation of the rock is equivalent to that observed under natural conditions, and from the direction of the lying wall of workings and close to their ends there is short-lived rotational creation of elastic displacements, extinguished as plastic deformation develops. Second, the superposition principle, taken as the basis for algebraic summation of displacements andmore » deformations due to individual workings, is not entirely observed in their joint effect on the rock mass in the elastic stage, and with plastic and shear deformation of rocks (partial or complete), depending on their bedding conditions.« less

Multiparticle Solutions in 2+1 Gravity and Time Machines

NASA Astrophysics Data System (ADS)

Steif, Alan R.

Multiparticle solutions for sources moving at the speed of light and corresponding to superpositions of single-particle plane-wave solutions are constructed in 2+1 gravity. It is shown that the two-particle spacetimes admit closed timelike curves provided the center-of-momentum energy exceeds a certain critical value. This occurs, however, at the cost of unphysical boundary conditions which are analogous to those affecting Gott’s time machine. As the energy exceeds the critical value, the closed timelike curves first occur at spatial infinity, then migrate inward as the energy is further increased. The total mass of the system also becomes imaginary for particle energies greater than the critical value.

A new method for constructing analytic elements for groundwater flow.

NASA Astrophysics Data System (ADS)

Strack, O. D.

2007-12-01

The analytic element method is based upon the superposition of analytic functions that are defined throughout the infinite domain, and can be used to meet a variety of boundary conditions. Analytic elements have been use successfully for a number of problems, mainly dealing with the Poisson equation (see, e.g., Theory and Applications of the Analytic Element Method, Reviews of Geophysics, 41,2/1005 2003 by O.D.L. Strack). The majority of these analytic elements consists of functions that exhibit jumps along lines or curves. Such linear analytic elements have been developed also for other partial differential equations, e.g., the modified Helmholz equation and the heat equation, and were constructed by integrating elementary solutions, the point sink and the point doublet, along a line. This approach is limiting for two reasons. First, the existence is required of the elementary solutions, and, second, the integration tends to limit the range of solutions that can be obtained. We present a procedure for generating analytic elements that requires merely the existence of a harmonic function with the desired properties; such functions exist in abundance. The procedure to be presented is used to generalize this harmonic function in such a way that the resulting expression satisfies the applicable differential equation. The approach will be applied, along with numerical examples, for the modified Helmholz equation and for the heat equation, while it is noted that the method is in no way restricted to these equations. The procedure is carried out entirely in terms of complex variables, using Wirtinger calculus.

Physicochemical controls on absorbed water film thickness in unsaturated geological media

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

Tokunaga, T.

2011-06-14

Adsorbed water films commonly coat mineral surfaces in unsaturated soils and rocks, reducing flow and transport rates. Therefore, it is important to understand how adsorbed film thickness depends on matric potential, surface chemistry, and solution chemistry. Here, the problem of adsorbed water film thickness is examined through combining capillary scaling with the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Novel aspects of this analysis include determining capillary influences on film thicknesses, and incorporating solution chemistry-dependent electrostatic potential at air-water interfaces. Capillary analysis of monodisperse packings of spherical grains provided estimated ranges of matric potentials where adsorbed films are stable, and showed that pendular ringsmore » within drained porous media retain most of the 'residual' water except under very low matric potentials. Within drained pores, capillary contributions to thinning of adsorbed films on spherical grains are shown to be small, such that DLVO calculations for flat surfaces are suitable approximations. Hamaker constants of common soil minerals were obtained to determine ranges of the dispersion component to matric potential-dependent film thickness. The pressure component associated with electrical double layer forces was estimated using the compression and linear superposition approximations. The pH-dependent electrical double layer pressure component is the dominant contribution to film thicknesses at intermediate values of matric potential, especially in lower ionic strength solutions (< 10 mol m{sup -3}) on surfaces with higher magnitude electrostatic potentials (more negative than - 50 mV). Adsorbed water films are predicted to usually range in thickness from 1 to 20 nm in drained pores and fractures of unsaturated environments.« less

Physicochemical controls on adsorbed water film thickness in unsaturated geological media

NASA Astrophysics Data System (ADS)

Tokunaga, Tetsu K.

2011-08-01

Adsorbed water films commonly coat mineral surfaces in unsaturated soils and rocks, reducing flow and transport rates. Therefore, it is important to understand how adsorbed film thickness depends on matric potential, surface chemistry, and solution chemistry. Here the problem of adsorbed water film thickness is examined by combining capillary scaling with the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Novel aspects of this analysis include determining capillary influences on film thicknesses and incorporating solution chemistry-dependent electrostatic potential at air-water interfaces. Capillary analysis of monodisperse packings of spherical grains provided estimated ranges of matric potentials where adsorbed films are stable and showed that pendular rings within drained porous media retain most of the "residual" water except under very low matric potentials. Within drained pores, capillary contributions to thinning of adsorbed films on spherical grains are shown to be small, such that DLVO calculations for flat surfaces are suitable approximations. Hamaker constants of common soil minerals were obtained to determine ranges of the dispersion component to matric potential-dependent film thickness. The pressure component associated with electrical double-layer forces was estimated using the compression and linear superposition approximations. The pH-dependent electrical double-layer pressure component is the dominant contribution to film thicknesses at intermediate values of matric potential, especially in lower ionic strength solutions (<10 mol m-3) on surfaces with higher-magnitude electrostatic potentials (more negative than ≈-50 mV). Adsorbed water films are predicted to usually range in thickness from ≈1 to 20 nm in drained pores and fractures of unsaturated environments.

A Survey of Quantum Programming Languages: History, Methods, and Tools

DTIC Science & Technology

2008-01-01

and entanglement , to achieve computational solutions to certain problems in less time (fewer computational cycles) than is possible using classical...superposition of quantum bits, entanglement , destructive measurement, and the no-cloning theorem. These differences must be thoroughly understood and even...computers using well-known languages such as C, C++, Java, and rapid prototyping languages such as Maple, Mathematica, and Matlab . A good on-line

Certification of windshear performance with RTCA class D radomes

NASA Technical Reports Server (NTRS)

Mathews, Bruce D.; Miller, Fran; Rittenhouse, Kirk; Barnett, Lee; Rowe, William

1994-01-01

Superposition testing of detection range performance forms a digital signal for input into a simulation of signal and data processing equipment and algorithms to be employed in a sensor system for advanced warning of hazardous windshear. For suitable pulse-Doppler radar, recording of the digital data at the input to the digital signal processor furnishes a realistic operational scenario and environmentally responsive clutter signal including all sidelobe clutter, ground moving target indications (GMTI), and large signal spurious due to mainbeam clutter and/or RFI respective of the urban airport clutter and aircraft scenarios (approach and landing antenna pointing). For linear radar system processes, a signal at the same point in the process from a hazard phenomena may be calculated from models of the scattering phenomena, for example, as represented in fine 3 dimensional reflectivity and velocity grid structures. Superposition testing furnishes a competing signal environment for detection and warning time performance confirmation of phenomena uncontrollable in a natural environment.

Cavity-QED interactions of two correlated atoms

NASA Astrophysics Data System (ADS)

Esfandiarpour, Saeideh; Safari, Hassan; Bennett, Robert; Yoshi Buhmann, Stefan

2018-05-01

We consider the resonant van der Waals (vdW) interaction between two correlated identical two-level atoms (at least one of which being excited) within the framework of macroscopic cavity quantum electrodynamics in linear, dispersing and absorbing media. The interaction of both atoms with the body-assisted electromagnetic field of the cavity is assumed to be strong. Our time-independent evaluation is based on an extended Jaynes–Cummings model. For a system prepared in a superposition of its dressed states, we derive the general form of the vdW forces, using a Lorentzian single-mode approximation. We demonstrate the applicability of this approach by considering the case of a planar cavity and showing the position dependence of Rabi oscillations. We also show that in the limiting case of weak coupling, our results reproduce the perturbative ones for the case where the field is initially in vacuum state while the atomic state is in a superposition of two correlated states sharing one excitation.

Molecular Based Temperature and Strain Rate Dependent Yield Criterion for Anisotropic Elastomeric Thin Films

NASA Technical Reports Server (NTRS)

Bosi, F.; Pellegrino, S.

2017-01-01

A molecular formulation of the onset of plasticity is proposed to assess temperature and strain rate effects in anisotropic semi-crystalline rubbery films. The presented plane stress criterion is based on the strain rate-temperature superposition principle and the cooperative theory of yielding, where some parameters are assumed to be material constants, while others are considered to depend on specific modes of deformation. An orthotropic yield function is developed for a linear low density polyethylene thin film. Uniaxial and biaxial inflation experiments were carried out to determine the yield stress of the membrane via a strain recovery method. It is shown that the 3% offset method predicts the uniaxial elastoplastic transition with good accuracy. Both the tensile yield points along the two principal directions of the film and the biaxial yield stresses are found to obey the superposition principle. The proposed yield criterion is compared against experimental measurements, showing excellent agreement over a wide range of deformation rates and temperatures.

Modified superposition: A simple time series approach to closed-loop manual controller identification

NASA Technical Reports Server (NTRS)

Biezad, D. J.; Schmidt, D. K.; Leban, F.; Mashiko, S.

1986-01-01

Single-channel pilot manual control output in closed-tracking tasks is modeled in terms of linear discrete transfer functions which are parsimonious and guaranteed stable. The transfer functions are found by applying a modified super-position time series generation technique. A Levinson-Durbin algorithm is used to determine the filter which prewhitens the input and a projective (least squares) fit of pulse response estimates is used to guarantee identified model stability. Results from two case studies are compared to previous findings, where the source of data are relatively short data records, approximately 25 seconds long. Time delay effects and pilot seasonalities are discussed and analyzed. It is concluded that single-channel time series controller modeling is feasible on short records, and that it is important for the analyst to determine a criterion for best time domain fit which allows association of model parameter values, such as pure time delay, with actual physical and physiological constraints. The purpose of the modeling is thus paramount.

Multivariate Time Series Decomposition into Oscillation Components.

PubMed

Matsuda, Takeru; Komaki, Fumiyasu

2017-08-01

Many time series are considered to be a superposition of several oscillation components. We have proposed a method for decomposing univariate time series into oscillation components and estimating their phases (Matsuda & Komaki, 2017 ). In this study, we extend that method to multivariate time series. We assume that several oscillators underlie the given multivariate time series and that each variable corresponds to a superposition of the projections of the oscillators. Thus, the oscillators superpose on each variable with amplitude and phase modulation. Based on this idea, we develop gaussian linear state-space models and use them to decompose the given multivariate time series. The model parameters are estimated from data using the empirical Bayes method, and the number of oscillators is determined using the Akaike information criterion. Therefore, the proposed method extracts underlying oscillators in a data-driven manner and enables investigation of phase dynamics in a given multivariate time series. Numerical results show the effectiveness of the proposed method. From monthly mean north-south sunspot number data, the proposed method reveals an interesting phase relationship.

Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

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

Onate, C.A., E-mail: oaclems14@physicist.net; Onyeaju, M.C.; Ikot, A.N.

2016-12-15

The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.

The Dirac equation in Schwarzschild black hole coupled to a stationary electromagnetic field

NASA Astrophysics Data System (ADS)

Al-Badawi, A.; Owaidat, M. Q.

2017-08-01

We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzschild solution to an external, stationary electromagnetic field. The set of equations representing the uncharged Dirac particle in the Newman-Penrose formalism is decoupled into a radial and an angular parts. We obtain exact analytical solutions of the angular equations. We manage to obtain the radial wave equations with effective potentials. Finally, we study the potentials by plotting them as a function of radial distance and examine the effect of the twisting parameter and the frequencies on the potentials.

Linear Depolarization of Lidar Returns by Aged Smoke Particles

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Liu, Li

2016-01-01

We use the numerically exact (superposition) T-matrix method to analyze recent measurements of the backscattering linear depolarization ratio (LDR) for a plume of aged smoke at lidar wavelengths ranging from 355 to 1064 nm. We show that the unique spectral dependence of the measured LDRs can be modeled, but only by assuming expressly nonspherical morphologies of smoke particles containing substantial amounts of nonabsorbing (or weakly absorbing) refractory materials such as sulfates. Our results demonstrate that spectral backscattering LDR measurements can be indicative of the presence of morphologically complex smoke particles, but additional (e.g., passive polarimetric or bistatic lidar) measurements may be required for a definitive characterization of the particle morphology and composition.

Polarized ensembles of random pure states

NASA Astrophysics Data System (ADS)

Deelan Cunden, Fabio; Facchi, Paolo; Florio, Giuseppe

2013-08-01

A new family of polarized ensembles of random pure states is presented. These ensembles are obtained by linear superposition of two random pure states with suitable distributions, and are quite manageable. We will use the obtained results for two purposes: on the one hand we will be able to derive an efficient strategy for sampling states from isopurity manifolds. On the other, we will characterize the deviation of a pure quantum state from separability under the influence of noise.

Stochastic models for atomic clocks

NASA Technical Reports Server (NTRS)

Barnes, J. A.; Jones, R. H.; Tryon, P. V.; Allan, D. W.

1983-01-01

For the atomic clocks used in the National Bureau of Standards Time Scales, an adequate model is the superposition of white FM, random walk FM, and linear frequency drift for times longer than about one minute. The model was tested on several clocks using maximum likelihood techniques for parameter estimation and the residuals were acceptably random. Conventional diagnostics indicate that additional model elements contribute no significant improvement to the model even at the expense of the added model complexity.

Decoherence in quantum systems in a static gravitational field

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Khorrami, Mohammad; Loran, Farhang

2016-09-01

A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that there are two time scales for such an evolution (decoherence). Both time scales are inversely proportional to the red shift difference between the two points. These time scales correspond to decoherences which are linear and quadratic, respectively, in time.

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

NASA Astrophysics Data System (ADS)

Sazonov, S. V.; Ustinov, N. V.

2017-02-01

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky-Vakhnenko equation. Different types of solutions of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.

Nonlinear spike-and-slab sparse coding for interpretable image encoding.

PubMed

Shelton, Jacquelyn A; Sheikh, Abdul-Saboor; Bornschein, Jörg; Sterne, Philip; Lücke, Jörg

2015-01-01

Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) and modelling varying pixel intensities. Traditionally, images are modelled as a sparse linear superposition of dictionary elements, where the probabilistic view of this problem is that the coefficients follow a Laplace or Cauchy prior distribution. We propose a novel model that instead uses a spike-and-slab prior and nonlinear combination of components. With the prior, our model can easily represent exact zeros for e.g. the absence of an image component, such as an edge, and a distribution over non-zero pixel intensities. With the nonlinearity (the nonlinear max combination rule), the idea is to target occlusions; dictionary elements correspond to image components that can occlude each other. There are major consequences of the model assumptions made by both (non)linear approaches, thus the main goal of this paper is to isolate and highlight differences between them. Parameter optimization is analytically and computationally intractable in our model, thus as a main contribution we design an exact Gibbs sampler for efficient inference which we can apply to higher dimensional data using latent variable preselection. Results on natural and artificial occlusion-rich data with controlled forms of sparse structure show that our model can extract a sparse set of edge-like components that closely match the generating process, which we refer to as interpretable components. Furthermore, the sparseness of the solution closely follows the ground-truth number of components/edges in the images. The linear model did not learn such edge-like components with any level of sparsity. This suggests that our model can adaptively well-approximate and characterize the meaningful generation process.

Nonlinear Spike-And-Slab Sparse Coding for Interpretable Image Encoding

PubMed Central

Shelton, Jacquelyn A.; Sheikh, Abdul-Saboor; Bornschein, Jörg; Sterne, Philip; Lücke, Jörg

2015-01-01

Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) and modelling varying pixel intensities. Traditionally, images are modelled as a sparse linear superposition of dictionary elements, where the probabilistic view of this problem is that the coefficients follow a Laplace or Cauchy prior distribution. We propose a novel model that instead uses a spike-and-slab prior and nonlinear combination of components. With the prior, our model can easily represent exact zeros for e.g. the absence of an image component, such as an edge, and a distribution over non-zero pixel intensities. With the nonlinearity (the nonlinear max combination rule), the idea is to target occlusions; dictionary elements correspond to image components that can occlude each other. There are major consequences of the model assumptions made by both (non)linear approaches, thus the main goal of this paper is to isolate and highlight differences between them. Parameter optimization is analytically and computationally intractable in our model, thus as a main contribution we design an exact Gibbs sampler for efficient inference which we can apply to higher dimensional data using latent variable preselection. Results on natural and artificial occlusion-rich data with controlled forms of sparse structure show that our model can extract a sparse set of edge-like components that closely match the generating process, which we refer to as interpretable components. Furthermore, the sparseness of the solution closely follows the ground-truth number of components/edges in the images. The linear model did not learn such edge-like components with any level of sparsity. This suggests that our model can adaptively well-approximate and characterize the meaningful generation process. PMID:25954947

High-order Two-way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering

NASA Technical Reports Server (NTRS)

Fibich, Gadi; Tsynkov, Semyon

2000-01-01

When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.

Relationship between the Arctic oscillation and surface air temperature in multi-decadal time-scale

NASA Astrophysics Data System (ADS)

Tanaka, Hiroshi L.; Tamura, Mina

2016-09-01

In this study, a simple energy balance model (EBM) was integrated in time, considering a hypothetical long-term variability in ice-albedo feedback mimicking the observed multi-decadal temperature variability. A natural variability was superimposed on a linear warming trend due to the increasing radiative forcing of CO2. The result demonstrates that the superposition of the natural variability and the background linear trend can offset with each other to show the warming hiatus for some period. It is also stressed that the rapid warming during 1970-2000 can be explained by the superposition of the natural variability and the background linear trend at least within the simple model. The key process of the fluctuating planetary albedo in multi-decadal time scale is investigated using the JRA-55 reanalysis data. It is found that the planetary albedo increased for 1958-1970, decreased for 1970-2000, and increased for 2000-2012, as expected by the simple EBM experiments. The multi-decadal variability in the planetary albedo is compared with the time series of the AO mode and Barents Sea mode of surface air temperature. It is shown that the recent AO negative pattern showing warm Arctic and cold mid-latitudes is in good agreement with planetary albedo change indicating negative anomaly in high latitudes and positive anomaly in mid-latitudes. Moreover, the Barents Sea mode with the warm Barents Sea and cold mid-latitudes shows long-term variability similar to planetary albedo change. Although further studies are needed, the natural variabilities of both the AO mode and Barents Sea mode indicate some possible link to the planetary albedo as suggested by the simple EBM to cause the warming hiatus in recent years.

Relationships between nonlinear normal modes and response to random inputs

DOE PAGES

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2016-07-25

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). Here, this work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing.more » Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.« less

Approximate analytical solutions in the analysis of thin elastic plates

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green's function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points.

A triangular thin shell finite element: Nonlinear analysis. [structural analysis

NASA Technical Reports Server (NTRS)

Thomas, G. R.; Gallagher, R. H.

1975-01-01

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Structural Technology Evaluation and Analysis Program (STEAP) Delivery Order 0042: Development of the Equivalent Overload Model, Demonstration of the Failure of Superposition, and Relaxation/Redistribution Measurement

DTIC Science & Technology

2011-09-01

with the bilinear plasticity relation. We used the bilinear relation, which allowed a full range of hardening from isotropic to kinematic to be...43 Table 12. Verification of the Weight Function Method for Single Corner Crack at a Hole in an Infinite ...determine the “Young’s Modulus,” or the slope of the linear region of the curve, the experimental data is curve fit with

Real-time dose computation: GPU-accelerated source modeling and superposition/convolution

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

Jacques, Robert; Wong, John; Taylor, Russell

Purpose: To accelerate dose calculation to interactive rates using highly parallel graphics processing units (GPUs). Methods: The authors have extended their prior work in GPU-accelerated superposition/convolution with a modern dual-source model and have enhanced performance. The primary source algorithm supports both focused leaf ends and asymmetric rounded leaf ends. The extra-focal algorithm uses a discretized, isotropic area source and models multileaf collimator leaf height effects. The spectral and attenuation effects of static beam modifiers were integrated into each source's spectral function. The authors introduce the concepts of arc superposition and delta superposition. Arc superposition utilizes separate angular sampling for themore » total energy released per unit mass (TERMA) and superposition computations to increase accuracy and performance. Delta superposition allows single beamlet changes to be computed efficiently. The authors extended their concept of multi-resolution superposition to include kernel tilting. Multi-resolution superposition approximates solid angle ray-tracing, improving performance and scalability with a minor loss in accuracy. Superposition/convolution was implemented using the inverse cumulative-cumulative kernel and exact radiological path ray-tracing. The accuracy analyses were performed using multiple kernel ray samplings, both with and without kernel tilting and multi-resolution superposition. Results: Source model performance was <9 ms (data dependent) for a high resolution (400{sup 2}) field using an NVIDIA (Santa Clara, CA) GeForce GTX 280. Computation of the physically correct multispectral TERMA attenuation was improved by a material centric approach, which increased performance by over 80%. Superposition performance was improved by {approx}24% to 0.058 and 0.94 s for 64{sup 3} and 128{sup 3} water phantoms; a speed-up of 101-144x over the highly optimized Pinnacle{sup 3} (Philips, Madison, WI) implementation. Pinnacle{sup 3} times were 8.3 and 94 s, respectively, on an AMD (Sunnyvale, CA) Opteron 254 (two cores, 2.8 GHz). Conclusions: The authors have completed a comprehensive, GPU-accelerated dose engine in order to provide a substantial performance gain over CPU based implementations. Real-time dose computation is feasible with the accuracy levels of the superposition/convolution algorithm.« less

Groundwater flow to a horizontal or slanted well in an unconfined aquifer

NASA Astrophysics Data System (ADS)

Zhan, Hongbin; Zlotnik, Vitaly A.

2002-07-01

New semianalytical solutions for evaluation of the drawdown near horizontal and slanted wells with finite length screens in unconfined aquifers are presented. These fully three-dimensional solutions consider instantaneous drainage or delayed yield and aquifer anisotropy. As a basis, solution for the drawdown created by a point source in a uniform anisotropic unconfined aquifer is derived in Laplace domain. Using superposition, the point source solution is extended to the cases of the horizontal and slanted wells. The previous solutions for vertical wells can be described as a special case of the new solutions. Numerical Laplace inversion allows effective evaluation of the drawdown in real time. Examples illustrate the effects of well geometry and the aquifer parameters on drawdown. Results can be used to generate type curves from observations in piezometers and partially or fully penetrating observation wells. The proposed solutions and software are useful for the parameter identification, design of remediation systems, drainage, and mine dewatering.

Communication: Two measures of isochronal superposition

NASA Astrophysics Data System (ADS)

Roed, Lisa Anita; Gundermann, Ditte; Dyre, Jeppe C.; Niss, Kristine

2013-09-01

A liquid obeys isochronal superposition if its dynamics is invariant along the isochrones in the thermodynamic phase diagram (the curves of constant relaxation time). This paper introduces two quantitative measures of isochronal superposition. The measures are used to test the following six liquids for isochronal superposition: 1,2,6 hexanetriol, glycerol, polyphenyl ether, diethyl phthalate, tetramethyl tetraphenyl trisiloxane, and dibutyl phthalate. The latter four van der Waals liquids obey isochronal superposition to a higher degree than the two hydrogen-bonded liquids. This is a prediction of the isomorph theory, and it confirms findings by other groups.

Communication: Two measures of isochronal superposition.

PubMed

Roed, Lisa Anita; Gundermann, Ditte; Dyre, Jeppe C; Niss, Kristine

2013-09-14

A liquid obeys isochronal superposition if its dynamics is invariant along the isochrones in the thermodynamic phase diagram (the curves of constant relaxation time). This paper introduces two quantitative measures of isochronal superposition. The measures are used to test the following six liquids for isochronal superposition: 1,2,6 hexanetriol, glycerol, polyphenyl ether, diethyl phthalate, tetramethyl tetraphenyl trisiloxane, and dibutyl phthalate. The latter four van der Waals liquids obey isochronal superposition to a higher degree than the two hydrogen-bonded liquids. This is a prediction of the isomorph theory, and it confirms findings by other groups.

THESEUS: maximum likelihood superpositioning and analysis of macromolecular structures

PubMed Central

Theobald, Douglas L.; Wuttke, Deborah S.

2008-01-01

Summary THESEUS is a command line program for performing maximum likelihood (ML) superpositions and analysis of macromolecular structures. While conventional superpositioning methods use ordinary least-squares (LS) as the optimization criterion, ML superpositions provide substantially improved accuracy by down-weighting variable structural regions and by correcting for correlations among atoms. ML superpositioning is robust and insensitive to the specific atoms included in the analysis, and thus it does not require subjective pruning of selected variable atomic coordinates. Output includes both likelihood-based and frequentist statistics for accurate evaluation of the adequacy of a superposition and for reliable analysis of structural similarities and differences. THESEUS performs principal components analysis for analyzing the complex correlations found among atoms within a structural ensemble. PMID:16777907

Evaluation of a neutron spectrum from Bonner spheres measurements using a Bayesian parameter estimation combined with the traditional unfolding methods

NASA Astrophysics Data System (ADS)

Mazrou, H.; Bezoubiri, F.

2018-07-01

In this work, a new program developed under MATLAB environment and supported by the Bayesian software WinBUGS has been combined to the traditional unfolding codes namely MAXED and GRAVEL, to evaluate a neutron spectrum from the Bonner spheres measured counts obtained around a shielded 241AmBe based-neutron irradiator located at a Secondary Standards Dosimetry Laboratory (SSDL) at CRNA. In the first step, the results obtained by the standalone Bayesian program, using a parametric neutron spectrum model based on a linear superposition of three components namely: a thermal-Maxwellian distribution, an epithermal (1/E behavior) and a kind of a Watt fission and Evaporation models to represent the fast component, were compared to those issued from MAXED and GRAVEL assuming a Monte Carlo default spectrum. Through the selection of new upper limits for some free parameters, taking into account the physical characteristics of the irradiation source, of both considered models, good agreement was obtained for investigated integral quantities i.e. fluence rate and ambient dose equivalent rate compared to MAXED and GRAVEL results. The difference was generally below 4% for investigated parameters suggesting, thereby, the reliability of the proposed models. In the second step, the Bayesian results obtained from the previous calculations were used, as initial guess spectra, for the traditional unfolding codes, MAXED and GRAVEL to derive the solution spectra. Here again the results were in very good agreement, confirming the stability of the Bayesian solution.

Entanglement of Multi-qudit States Constructed by Linearly Independent Coherent States: Balanced Case

NASA Astrophysics Data System (ADS)

Najarbashi, G.; Mirzaei, S.

2016-03-01

Multi-mode entangled coherent states are important resources for linear optics quantum computation and teleportation. Here we introduce the generalized balanced N-mode coherent states which recast in the multi-qudit case. The necessary and sufficient condition for bi-separability of such balanced N-mode coherent states is found. We particularly focus on pure and mixed multi-qubit and multi-qutrit like states and examine the degree of bipartite as well as tripartite entanglement using the concurrence measure. Unlike the N-qubit case, it is shown that there are qutrit states violating monogamy inequality. Using parity, displacement operator and beam splitters, we will propose a scheme for generating balanced N-mode entangled coherent states for even number of terms in superposition.

Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics

NASA Technical Reports Server (NTRS)

Roe, P. L.

1984-01-01

A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries.

Linear parameter varying identification of ankle joint intrinsic stiffness during imposed walking movements.

PubMed

Sobhani Tehrani, Ehsan; Jalaleddini, Kian; Kearney, Robert E

2013-01-01

This paper describes a novel model structure and identification method for the time-varying, intrinsic stiffness of human ankle joint during imposed walking (IW) movements. The model structure is based on the superposition of a large signal, linear, time-invariant (LTI) model and a small signal linear-parameter varying (LPV) model. The methodology is based on a two-step algorithm; the LTI model is first estimated using data from an unperturbed IW trial. Then, the LPV model is identified using data from a perturbed IW trial with the output predictions of the LTI model removed from the measured torque. Experimental results demonstrate that the method accurately tracks the continuous-time variation of normal ankle intrinsic stiffness when the joint position changes during the IW movement. Intrinsic stiffness gain decreases from full plantarflexion to near the mid-point of plantarflexion and then increases substantially as the ankle is dosriflexed.

Effects of entanglement in an ideal optical amplifier

NASA Astrophysics Data System (ADS)

Franson, J. D.; Brewster, R. A.

2018-04-01

In an ideal linear amplifier, the output signal is linearly related to the input signal with an additive noise that is independent of the input. The decoherence of a quantum-mechanical state as a result of optical amplification is usually assumed to be due to the addition of quantum noise. Here we show that entanglement between the input signal and the amplifying medium can produce an exponentially-large amount of decoherence in an ideal optical amplifier even when the gain is arbitrarily close to unity and the added noise is negligible. These effects occur for macroscopic superposition states, where even a small amount of gain can leave a significant amount of which-path information in the environment. Our results show that the usual input/output relation of a linear amplifier does not provide a complete description of the output state when post-selection is used.

Coherent Optical Transients and Spectral Line Narrowing Phenomena in Four Wave Mixing Spectroscopies: Theoretical and Experimental Studies.

NASA Astrophysics Data System (ADS)

Dugan, Mark Allen

1990-08-01

The theoretical basis for new signal transients and spectral features generated in field correlated four wave mixing (4WM) spectroscopies is developed. Special attention is given to those signal responses that are sensitive to phase/amplitude correlation among the input driving fields and not simply their intensity correlation. Thus, the cases of incoherent broadband excitation and of coherent short pulsed excitation will be discussed and compared. Applications to the coherent Raman spectroscopies, both electronically nonresonant and fully resonant, are analyzed. Novel interferometric oscillatory behavior is exposed in terms of field-matter detuning beats and matter-matter bi-level and tri-level quantum beats. In addition new detuning resonances are found that have sub-material linewidths and lock onto the mode frequency of the driven chromophore. These spectral features are a member of a class of bichromophore resonant lineshapes arising from nonlinear mixing with correlated driving fields. The origin of such bichromophore resonances can be based on a coupling between two field-matter superposition states driven by correlated fields on separate chromophores. Analytic results are presented and modelled to anticipate the experimental results presented in a following chapter. The onset of resolvable homogeneous electronic memory is reported in room temperature solutions of dye molecules. A narrowing of the homogeneous linewidths with increasing concentration of these dye solutions is observed in sub-picosecond photon echo experiments. This effect is attributed to aggregation which results in a delocalization of the electronic states over several molecules. Ultra -fast spectral diffusion in these dye aggregates is observed in stimulated photon echo measurements. Aggregate bands, seen in the linear absorption spectrum only at high concentrations, can be probed in more dilute solutions with nonlinear four wave mixing.

Strain accumulation in bituminous binders under repeated creep-recovery loading predicted from small-amplitude oscillatory shear (SAOS) experiments

NASA Astrophysics Data System (ADS)

Laukkanen, Olli-Ville; Winter, H. Henning

2017-11-01

The creep-recovery (CR) test starts out with a period of shearing at constant stress (creep) and is followed by a period of zero-shear stress where some of the accumulated shear strain gets reversed. Linear viscoelasticity (LVE) allows one to predict the strain response to repeated creep-recovery (RCR) loading from measured small-amplitude oscillatory shear (SAOS) data. Only the relaxation and retardation time spectra of a material need to be known and these can be determined from SAOS data. In an application of the Boltzmann superposition principle (BSP), the strain response to RCR loading can be obtained as a linear superposition of the strain response to many single creep-recovery tests. SAOS and RCR data were collected for several unmodified and modified bituminous binders, and the measured and predicted RCR responses were compared. Generally good agreement was found between the measured and predicted strain accumulation under RCR loading. However, in the case of modified binders, the strain accumulation was slightly overestimated (≤20% relative error) due to the insufficient SAOS information at long relaxation times. Our analysis also demonstrates that the evolution in the strain response under RCR loading, caused by incomplete recovery, can be reasonably well predicted by the presented methodology. It was also shown that the outlined modeling framework can be used, as a first approximation, to estimate the rutting resistance of bituminous binders by predicting the values of the Multiple Stress Creep Recovery (MSCR) test parameters.

PSF mapping-based correction of eddy-current-induced distortions in diffusion-weighted echo-planar imaging.

PubMed

In, Myung-Ho; Posnansky, Oleg; Speck, Oliver

2016-05-01

To accurately correct diffusion-encoding direction-dependent eddy-current-induced geometric distortions in diffusion-weighted echo-planar imaging (DW-EPI) and to minimize the calibration time at 7 Tesla (T). A point spread function (PSF) mapping based eddy-current calibration method is newly presented to determine eddy-current-induced geometric distortions even including nonlinear eddy-current effects within the readout acquisition window. To evaluate the temporal stability of eddy-current maps, calibration was performed four times within 3 months. Furthermore, spatial variations of measured eddy-current maps versus their linear superposition were investigated to enable correction in DW-EPIs with arbitrary diffusion directions without direct calibration. For comparison, an image-based eddy-current correction method was additionally applied. Finally, this method was combined with a PSF-based susceptibility-induced distortion correction approach proposed previously to correct both susceptibility and eddy-current-induced distortions in DW-EPIs. Very fast eddy-current calibration in a three-dimensional volume is possible with the proposed method. The measured eddy-current maps are very stable over time and very similar maps can be obtained by linear superposition of principal-axes eddy-current maps. High resolution in vivo brain results demonstrate that the proposed method allows more efficient eddy-current correction than the image-based method. The combination of both PSF-based approaches allows distortion-free images, which permit reliable analysis in diffusion tensor imaging applications at 7T. © 2015 Wiley Periodicals, Inc.

Application of low-order potential solutions to higher-order vertical traction boundary problems in an elastic half-space

PubMed Central

Taylor, Adam G.

2018-01-01

New solutions of potential functions for the bilinear vertical traction boundary condition are derived and presented. The discretization and interpolation of higher-order tractions and the superposition of the bilinear solutions provide a method of forming approximate and continuous solutions for the equilibrium state of a homogeneous and isotropic elastic half-space subjected to arbitrary normal surface tractions. Past experimental measurements of contact pressure distributions in granular media are reviewed in conjunction with the application of the proposed solution method to analysis of elastic settlement in shallow foundations. A numerical example is presented for an empirical ‘saddle-shaped’ traction distribution at the contact interface between a rigid square footing and a supporting soil medium. Non-dimensional soil resistance is computed as the reciprocal of normalized surface displacements under this empirical traction boundary condition, and the resulting internal stresses are compared to classical solutions to uniform traction boundary conditions. PMID:29892456

Homogeneous partial differential equations for superpositions of indeterminate functions of several variables

NASA Astrophysics Data System (ADS)

Asai, Kazuto

2009-02-01

We determine essentially all partial differential equations satisfied by superpositions of tree type and of a further special type. These equations represent necessary and sufficient conditions for an analytic function to be locally expressible as an analytic superposition of the type indicated. The representability of a real analytic function by a superposition of this type is independent of whether that superposition involves real-analytic functions or C^{\\rho}-functions, where the constant \\rho is determined by the structure of the superposition. We also prove that the function u defined by u^n=xu^a+yu^b+zu^c+1 is generally non-representable in any real (resp. complex) domain as f\\bigl(g(x,y),h(y,z)\\bigr) with twice differentiable f and differentiable g, h (resp. analytic f, g, h).

Linearized inversion of multiple scattering seismic energy

NASA Astrophysics Data System (ADS)

Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad

2014-05-01

Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. So, imaging seismic data with the single-scattering assumption does not locate multiple bounces events in their actual subsurface positions. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single scattering energy such as nearly vertical faults. Standard migration of these multiples provides subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. The resultant image obtained by the adjoint operator is a smoothed depiction of the true subsurface reflectivity model and is heavily masked by migration artifacts and the source wavelet fingerprint that needs to be properly deconvolved. Hence, we proposed a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. The proposed algorithm uses the least-square image based on single-scattering assumption as a constraint to invert for the part of the image that is illuminated by internal scattering energy. Then, we posed the problem of imaging double-scattering energy as a least-square minimization problem that requires solving the normal equation of the following form: GTGv = GTd, (1) where G is a linearized forward modeling operator that predicts double-scattered seismic data. Also, GT is a linearized adjoint operator that image double-scattered seismic data. Gradient-based optimization algorithms solve this linear system. Hence, we used a quasi-Newton optimization technique to find the least-square minimizer. In this approach, an estimate of the Hessian matrix that contains curvature information is modified at every iteration by a low-rank update based on gradient changes at every step. At each iteration, the data residual is imaged using GT to determine the model update. Application of the linearized inversion to synthetic data to image a vertical fault plane demonstrate the effectiveness of this methodology to properly delineate the vertical fault plane and give better amplitude information than the standard migrated image using the adjoint operator that takes into account internal multiples. Thus, least-square imaging of multiple scattering enhances the spatial resolution of the events illuminated by internal scattering energy. It also deconvolves the source signature and helps remove the fingerprint of the acquisition geometry. The final image is obtained by the superposition of the least-square solution based on single scattering assumption and the least-square solution based on double scattering assumption.

Development of a mechanics-based model of brain deformations during intracerebral hemorrhage evacuation

NASA Astrophysics Data System (ADS)

Narasimhan, Saramati; Weis, Jared A.; Godage, Isuru S.; Webster, Robert; Weaver, Kyle; Miga, Michael I.

2017-03-01

Intracerebral hemorrhages (ICHs) occur in 24 out of 100,000 people annually and have high morbidity and mortality rates. The standard treatment is conservative. We hypothesize that a patient-specific, mechanical model coupled with a robotic steerable needle, used to aspirate a hematoma, would result in a minimally invasive approach to ICH management that will improve outcomes. As a preliminary study, three realizations of a tissue aspiration framework are explored within the context of a biphasic finite element model based on Biot's consolidation theory. Short-term transient effects were neglected in favor of steady state formulation. The Galerkin Method of Weighted Residuals was used to solve coupled partial differential equations using linear basis functions, and assumptions of plane strain and homogeneous isotropic properties. All aspiration models began with the application of aspiration pressure sink(s), calculated pressures and displacements, and the use of von Mises stresses within a tissue failure criterion. With respect to aspiration strategies, one model employs an element-deletion strategy followed by aspiration redeployment on the remaining grid, while the other approaches use principles of superposition on a fixed grid. While the element-deletion approach had some intuitive appeal, without incorporating a dynamic grid strategy, it evolved into a less realistic result. The superposition strategy overcame this, but would require empirical investigations to determine the optimum distribution of aspiration sinks to match material removal. While each modeling framework demonstrated some promise, the superposition method's ease of computation, ability to incorporate the surgical plan, and better similarity to existing empirical observational data, makes it favorable.

Location of acoustic radiators and inversion for energy density using radio-frequency sources and thunder recordings

NASA Astrophysics Data System (ADS)

Anderson, J.; Johnson, J. B.; Arechiga, R. O.; Edens, H. E.; Thomas, R. J.

2011-12-01

We use radio frequency (VHF) pulse locations mapped with the New Mexico Tech Lightning Mapping Array (LMA) to study the distribution of thunder sources in lightning channels. A least squares inversion is used to fit channel acoustic energy radiation with broadband (0.01 to 500 Hz) acoustic recordings using microphones deployed local (< 10 km) to the lightning. We model the thunder (acoustic) source as a superposition of line segments connecting the LMA VHF pulses. An optimum branching algorithm is used to reconstruct conductive channels delineated by VHF sources, which we discretize as a superposition of finely-spaced (0.25 m) acoustic point sources. We consider total radiated thunder as a weighted superposition of acoustic waves from individual channels, each with a constant current along its length that is presumed to be proportional to acoustic energy density radiated per unit length. Merged channels are considered as a linear sum of current-carrying branches and radiate proportionally greater acoustic energy. Synthetic energy time series for a given microphone location are calculated for each independent channel. We then use a non-negative least squares inversion to solve for channel energy densities to match the energy time series determined from broadband acoustic recordings across a 4-station microphone network. Events analyzed by this method have so far included 300-1000 VHF sources, and correlations as high as 0.5 between synthetic and recorded thunder energy were obtained, despite the presence of wind noise and 10-30 m uncertainty in VHF source locations.

THESEUS: maximum likelihood superpositioning and analysis of macromolecular structures.

PubMed

Theobald, Douglas L; Wuttke, Deborah S

2006-09-01

THESEUS is a command line program for performing maximum likelihood (ML) superpositions and analysis of macromolecular structures. While conventional superpositioning methods use ordinary least-squares (LS) as the optimization criterion, ML superpositions provide substantially improved accuracy by down-weighting variable structural regions and by correcting for correlations among atoms. ML superpositioning is robust and insensitive to the specific atoms included in the analysis, and thus it does not require subjective pruning of selected variable atomic coordinates. Output includes both likelihood-based and frequentist statistics for accurate evaluation of the adequacy of a superposition and for reliable analysis of structural similarities and differences. THESEUS performs principal components analysis for analyzing the complex correlations found among atoms within a structural ensemble. ANSI C source code and selected binaries for various computing platforms are available under the GNU open source license from http://monkshood.colorado.edu/theseus/ or http://www.theseus3d.org.

Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime.

PubMed

Liu, Xiang; Chandrasekhar, S; Winzer, P J; Chraplyvy, A R; Tkach, R W; Zhu, B; Taunay, T F; Fishteyn, M; DiGiovanni, D J

2012-08-13

Coherent superposition of light waves has long been used in various fields of science, and recent advances in digital coherent detection and space-division multiplexing have enabled the coherent superposition of information-carrying optical signals to achieve better communication fidelity on amplified-spontaneous-noise limited communication links. However, fiber nonlinearity introduces highly correlated distortions on identical signals and diminishes the benefit of coherent superposition in nonlinear transmission regime. Here we experimentally demonstrate that through coordinated scrambling of signal constellations at the transmitter, together with appropriate unscrambling at the receiver, the full benefit of coherent superposition is retained in the nonlinear transmission regime of a space-diversity fiber link based on an innovatively engineered multi-core fiber. This scrambled coherent superposition may provide the flexibility of trading communication capacity for performance in future optical fiber networks, and may open new possibilities in high-performance and secure optical communications.

Scaling and Multiscaling in Financial Time Series

DTIC Science & Technology

2005-01-07

stable process (Mandelbrot, Fama , 1963) The return process X(t) satisfies: dX(t) = µ dt + σ dLα(t) where Lα(t) is an α-stable Levy process. The returns r...year Future JY/USD 7.104 0.02 6 months Nikkei 225 7.104 0.030 1.5 year Future Nikkei 7.104 0.02 6 months Japanese Yen 7.104 0.022 1.0 year French index...the horizon) - Optimal portfolios are stable by linear superposition. → CAPM : Relates the mean return of some asset to its covariance with the

An Introduction to Magnetospheric Physics by Means of Simple Models

NASA Technical Reports Server (NTRS)

Stern, D. P.

1981-01-01

The large scale structure and behavior of the Earth's magnetosphere is discussed. The model is suitable for inclusion in courses on space physics, plasmas, astrophysics or the Earth's environment, as well as for self-study. Nine quantitative problems, dealing with properties of linear superpositions of a dipole and a constant field are presented. Topics covered include: open and closed models of the magnetosphere; field line motion; the role of magnetic merging (reconnection); magnetospheric convection; and the origin of the magnetopause, polar cusps, and high latitude lobes.

Aerodynamic mathematical modeling - basic concepts

NASA Technical Reports Server (NTRS)

Tobak, M.; Schiff, L. B.

1981-01-01

The mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers is reviewed. Bryan's original formulation, linear aerodynamic indicial functions, and superposition are considered. These concepts are extended into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well defined characteristic motions, reproducible in principle either in wind tunnel experiments or flow field computations. A further generalization leads to a form accommodating the discontinuous and double valued behavior characteristics of hysteresis in the steady state aerodynamic response.

Basic corrections to predictions of solar cell performance required by nonlinearities

NASA Technical Reports Server (NTRS)

Lindholm, F. A.; Fossum, J. G.; Burgess, E. L.

1976-01-01

The superposition principle is used to derive the approximation that the current-voltage characteristic of an illuminated solar cell is the dark current-voltage characteristic shifted by the short-circuit photocurrent. The derivation requires the linearity of the boundary value problems that underlie the electrical characteristics. The shifting approximation is invalid if considerable photocurrent and considerable dark current both occur within the junction space-charge region; it is invalid also if sizable series resistance is present or if high-injection concentrations of holes and electrons exist within the quasi-neutral regions.

Terahertz emission driven by two-color laser pulses at various frequency ratios

NASA Astrophysics Data System (ADS)

Wang, W.-M.; Sheng, Z.-M.; Li, Y.-T.; Zhang, Y.; Zhang, J.

2017-08-01

We present a simulation study of terahertz radiation from a gas driven by two-color laser pulses in a broad range of frequency ratios ω1/ω0 . Our particle-in-cell simulation results show that there are three series with ω1/ω0=2 n , n +1 /2 , n ±1 /3 (n is a positive integer) for high-efficiency and stable radiation generation. The radiation strength basically decreases with the increasing ω1 and scales linearly with the laser wavelength. These rules are broken when ω1/ω0<1 and much stronger radiation may be generated at any ω1/ω0 . These results can be explained with a model based on gas ionization by two linear-superposition laser fields, rather than a multiwave mixing model.

The origin of non-classical effects in a one-dimensional superposition of coherent states

NASA Technical Reports Server (NTRS)

Buzek, V.; Knight, P. L.; Barranco, A. Vidiella

1992-01-01

We investigate the nature of the quantum fluctuations in a light field created by the superposition of coherent fields. We give a physical explanation (in terms of Wigner functions and phase-space interference) why the 1-D superposition of coherent states in the direction of the x-quadrature leads to the squeezing of fluctuations in the y-direction, and show that such a superposition can generate the squeezed vacuum and squeezed coherent states.

On type B cyclogenesis in a quasi-geostrophic model

NASA Astrophysics Data System (ADS)

Grotjahn, Richard

2005-01-01

A quasi-geostrophic (QG) model is used to approximate some aspects of 'type B' cyclogenesis as described in an observational paper that appeared several decades earlier in this journal. Though often cited, that earlier work has some ambiguity that has propagated into subsequent analyses. The novel aspects examined here include allowing advective nonlinearity to distort and amplify structures that are quasi-coherent and nearly stable in a linear form of the model; also, separate upper and lower structures are localized in space. Cases are studied separately where the upper trough tracks across different low-level features: an enhanced baroclinic zone (stronger horizontal temperature gradient) or a region of augmented temperature. Growth by superposition of lower and upper features is excluded by experimental design. The dynamics are evaluated with the vertical motion equation, the QG vorticity equation, the QG perturbation energy equation, and 'potential-vorticity thinking'. Results are compared against 'control' cases having no additional low-level features. Nonlinearity is examined relative to a corresponding linear calculation and is generally positive. The results are perhaps richer than the seminal article might imply, because growth is enhanced not only when properties of the lower feature reinforce growth but also when the lower feature opposes decay of the upper feature. For example, growth is enhanced where low-level warm advection introduces rising warm air to oppose the rising cold air ahead of the upper trough. Such growth is magnified when adjacent warm and cold anomalies have a strong baroclinic zone between them. The enhanced growth triggers an upstream tilt in the solution whose properties further accelerate the growth.

Radiometry rocks

NASA Astrophysics Data System (ADS)

Harvey, James E.

2012-10-01

Professor Bill Wolfe was an exceptional mentor for his graduate students, and he made a major contribution to the field of optical engineering by teaching the (largely ignored) principles of radiometry for over forty years. This paper describes an extension of Bill's work on surface scatter behavior and the application of the BRDF to practical optical engineering problems. Most currently-available image analysis codes require the BRDF data as input in order to calculate the image degradation from residual optical fabrication errors. This BRDF data is difficult to measure and rarely available for short EUV wavelengths of interest. Due to a smooth-surface approximation, the classical Rayleigh-Rice surface scatter theory cannot be used to calculate BRDFs from surface metrology data for even slightly rough surfaces. The classical Beckmann-Kirchhoff theory has a paraxial limitation and only provides a closed-form solution for Gaussian surfaces. Recognizing that surface scatter is a diffraction process, and by utilizing sound radiometric principles, we first developed a linear systems theory of non-paraxial scalar diffraction in which diffracted radiance is shift-invariant in direction cosine space. Since random rough surfaces are merely a superposition of sinusoidal phase gratings, it was a straightforward extension of this non-paraxial scalar diffraction theory to develop a unified surface scatter theory that is valid for moderately rough surfaces at arbitrary incident and scattered angles. Finally, the above two steps are combined to yield a linear systems approach to modeling image quality for systems suffering from a variety of image degradation mechanisms. A comparison of image quality predictions with experimental results taken from on-orbit Solar X-ray Imager (SXI) data is presented.

Application of linear logic to simulation

NASA Astrophysics Data System (ADS)

Clarke, Thomas L.

1998-08-01

Linear logic, since its introduction by Girard in 1987 has proven expressive and powerful. Linear logic has provided natural encodings of Turing machines, Petri nets and other computational models. Linear logic is also capable of naturally modeling resource dependent aspects of reasoning. The distinguishing characteristic of linear logic is that it accounts for resources; two instances of the same variable are considered differently from a single instance. Linear logic thus must obey a form of the linear superposition principle. A proportion can be reasoned with only once, unless a special operator is applied. Informally, linear logic distinguishes two kinds of conjunction, two kinds of disjunction, and also introduces a modal storage operator that explicitly indicates propositions that can be reused. This paper discuses the application of linear logic to simulation. A wide variety of logics have been developed; in addition to classical logic, there are fuzzy logics, affine logics, quantum logics, etc. All of these have found application in simulations of one sort or another. The special characteristics of linear logic and its benefits for simulation will be discussed. Of particular interest is a connection that can be made between linear logic and simulated dynamics by using the concept of Lie algebras and Lie groups. Lie groups provide the connection between the exponential modal storage operators of linear logic and the eigen functions of dynamic differential operators. Particularly suggestive are possible relations between complexity result for linear logic and non-computability results for dynamical systems.

Exact solutions for sound radiation from a moving monopole above an impedance plane.

PubMed

Ochmann, Martin

2013-04-01

The acoustic field of a monopole source moving with constant velocity at constant height above an infinite locally reacting plane can be expressed in analytical form by combining the Lorentz transformation with the method of superimposing complex or real point sources. For a plane with masslike response, the solution in Lorentz space consists of a superposition of monopoles only and therefore, does not differ in principle from the solution for the corresponding stationary boundary value problem. However, by considering a frequency independent surface impedance, e.g., with pure absorbing behavior, the half-space Green's function is now comprised of not only a line of monopoles but also of dipoles. For certain field points at a special line g, this solution can be written explicitly by using an exponential integral. For arbitrary field points, the method of stationary phase leads to an asymptotic solution for the reflection coefficient which agrees with prior results from the literature.

Time-dependent corrosion fatique crack propagation in 7000 series aluminum alloys. M.S. Thesis

NASA Technical Reports Server (NTRS)

Mason, Mark E.

1995-01-01

The goal of this research is to characterize environmentally assisted subcritical crack growth for the susceptible short-longitudinal orientation of aluminum alloy 7075-T651, immersed in acidified and inhibited NaCl solution. This work is necessary in order to provide a basis for incorporating environmental effects into fatigue crack propagation life prediction codes such as NASA-FLAGRO (NASGRO). This effort concentrates on determining relevant inputs to a superposition model in order to more accurately model environmental fatigue crack propagation.

Virtual source for a Mathieu-Gauss beam

NASA Astrophysics Data System (ADS)

Dan, Li; Zhijun, Ren; Suyu, Deng

2017-05-01

We introduce a group of virtual sources for generating 2nth-order even Mathieu-Gauss beams based on the beam superposition. Integral and differential representations are derived for a 2nth-order even Mathieu-Gauss wave and the solution yields a corresponding 2nth-order even paraxial Mathieu-Gauss beam in an appropriate limit. The first three orders of nonparaxial corrections for the on-axis field of the 2nth-order even paraxial Mathieu-Gauss beam are obtained using the integral representation.

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

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

Sazonov, S. V., E-mail: sazonov.sergey@gmail.com; Ustinov, N. V., E-mail: n-ustinov@mail.ru

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky–Vakhnenko equation. Different types of solutionsmore » of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.« less

Flux-Based Deadbeat Control of Induction-Motor Torque

NASA Technical Reports Server (NTRS)

Kenny, Barbara H.; Lorenz, Robert D.

2003-01-01

An improved method and prior methods of deadbeat direct torque control involve the use of pulse-width modulation (PWM) of applied voltages. The prior methods are based on the use of stator flux and stator current as state variables, leading to mathematical solutions of control equations in forms that do not lend themselves to clear visualization of solution spaces. In contrast, the use of rotor and stator fluxes as the state variables in the present improved method lends itself to graphical representations that aid in understanding possible solutions under various operating conditions. In addition, the present improved method incorporates the superposition of high-frequency carrier signals for use in a motor-self-sensing technique for estimating the rotor shaft angle at any speed (including low or even zero speed) without need for additional shaft-angle-measuring sensors.

Investigation on the Accuracy of Superposition Predictions of Film Cooling Effectiveness

NASA Astrophysics Data System (ADS)

Meng, Tong; Zhu, Hui-ren; Liu, Cun-liang; Wei, Jian-sheng

2018-05-01

Film cooling effectiveness on flat plates with double rows of holes has been studied experimentally and numerically in this paper. This configuration is widely used to simulate the multi-row film cooling on turbine vane. Film cooling effectiveness of double rows of holes and each single row was used to study the accuracy of superposition predictions. Method of stable infrared measurement technique was used to measure the surface temperature on the flat plate. This paper analyzed the factors that affect the film cooling effectiveness including hole shape, hole arrangement, row-to-row spacing and blowing ratio. Numerical simulations were performed to analyze the flow structure and film cooling mechanisms between each film cooling row. Results show that the blowing ratio within the range of 0.5 to 2 has a significant influence on the accuracy of superposition predictions. At low blowing ratios, results obtained by superposition method agree well with the experimental data. While at high blowing ratios, the accuracy of superposition prediction decreases. Another significant factor is hole arrangement. Results obtained by superposition prediction are nearly the same as experimental values of staggered arrangement structures. For in-line configurations, the superposition values of film cooling effectiveness are much higher than experimental data. For different hole shapes, the accuracy of superposition predictions on converging-expanding holes is better than cylinder holes and compound angle holes. For two different hole spacing structures in this paper, predictions show good agreement with the experiment results.

Quantum superposition at the half-metre scale.

PubMed

Kovachy, T; Asenbaum, P; Overstreet, C; Donnelly, C A; Dickerson, S M; Sugarbaker, A; Hogan, J M; Kasevich, M A

2015-12-24

The quantum superposition principle allows massive particles to be delocalized over distant positions. Though quantum mechanics has proved adept at describing the microscopic world, quantum superposition runs counter to intuitive conceptions of reality and locality when extended to the macroscopic scale, as exemplified by the thought experiment of Schrödinger's cat. Matter-wave interferometers, which split and recombine wave packets in order to observe interference, provide a way to probe the superposition principle on macroscopic scales and explore the transition to classical physics. In such experiments, large wave-packet separation is impeded by the need for long interaction times and large momentum beam splitters, which cause susceptibility to dephasing and decoherence. Here we use light-pulse atom interferometry to realize quantum interference with wave packets separated by up to 54 centimetres on a timescale of 1 second. These results push quantum superposition into a new macroscopic regime, demonstrating that quantum superposition remains possible at the distances and timescales of everyday life. The sub-nanokelvin temperatures of the atoms and a compensation of transverse optical forces enable a large separation while maintaining an interference contrast of 28 per cent. In addition to testing the superposition principle in a new regime, large quantum superposition states are vital to exploring gravity with atom interferometers in greater detail. We anticipate that these states could be used to increase sensitivity in tests of the equivalence principle, measure the gravitational Aharonov-Bohm effect, and eventually detect gravitational waves and phase shifts associated with general relativity.

Immittance Data Validation by Kramers‐Kronig Relations – Derivation and Implications

PubMed Central

2017-01-01

Abstract Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers‐Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two‐sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non‐linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences. PMID:29577007

Thermalization as an invisibility cloak for fragile quantum superpositions

NASA Astrophysics Data System (ADS)

Hahn, Walter; Fine, Boris V.

2017-07-01

We propose a method for protecting fragile quantum superpositions in many-particle systems from dephasing by external classical noise. We call superpositions "fragile" if dephasing occurs particularly fast, because the noise couples very differently to the superposed states. The method consists of letting a quantum superposition evolve under the internal thermalization dynamics of the system, followed by a time-reversal manipulation known as Loschmidt echo. The thermalization dynamics makes the superposed states almost indistinguishable during most of the above procedure. We validate the method by applying it to a cluster of spins ½.

Design and simulation of a superposition compound eye system based on hybrid diffractive-refractive lenses.

PubMed

Zhang, Shuqing; Zhou, Luyang; Xue, Changxi; Wang, Lei

2017-09-10

Compound eyes offer a promising field of miniaturized imaging systems. In one application of a compound eye, superposition of compound eye systems forms a composite image by superposing the images produced by different channels. The geometric configuration of superposition compound eye systems is achieved by three micro-lens arrays with different pitches and focal lengths. High resolution is indispensable for the practicability of superposition compound eye systems. In this paper, hybrid diffractive-refractive lenses are introduced into the design of a compound eye system for this purpose. With the help of ZEMAX, two superposition compound eye systems with and without hybrid diffractive-refractive lenses were separately designed. Then, we demonstrate the effectiveness of using a hybrid diffractive-refractive lens to improve the image quality.

FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

NASA Astrophysics Data System (ADS)

Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

2004-12-01

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

Transverse low frequency wave in a two fluid solar wind. M.S. Thesis

NASA Technical Reports Server (NTRS)

Solodyna, G. V.

1973-01-01

Investigation is made of the properties of low frequency transverse waves in a two-fluid solar wind having a radial magnetic field and radial streaming velocity. In order to examine what effects this streaming medium has on the waves, linearly polarized waves are decomposed into left and right circularly polarized waves. Computation is made of analytic expressions valid to first order for the radial amplitude and phase dependence of these constituent waves. It is shown that after travelling a given distance r, these waves have different amplitudes and phases. The former result causes their superposition to become elliptical rather than linear. The latter causes the axis of the ellipse of polarization to rotate through a well-defined angle. Analytic expressions are obtained for the eccentricity of the ellipse and for the angle of rotation. In analogy with regular Faraday rotation, in which the plane of polarization of a linear polarized wave rotates, the effect is denoted as generalized Faraday rotation.

Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation in the fluid/plasma mechanics

NASA Astrophysics Data System (ADS)

Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Wang, Qi-Min

2016-09-01

Under investigation in this paper is a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation for the shallow water wave in a fluid or electrostatic wave potential in a plasma. Bilinear form, Bäcklund transformation and Lax pair are derived based on the binary Bell polynomials. Multi-soliton solutions are constructed via the Hirota’s method. Propagation and interaction of the solitons are illustrated graphically: (i) Through the asymptotic analysis, elastic and inelastic interactions between the two solitons are discussed analytically and graphically, respectively. The elastic interaction, amplitudes, velocities and shapes of the two solitons remain unchanged except for a phase shift. However, in the area of the inelastic interaction, amplitudes of the two solitons have a linear superposition. (ii) Elastic interactions among the three solitons indicate that the properties of the elastic interactions among the three solitons are similar to those between the two solitons. Moreover, oblique and overtaking interactions between the two solitons are displayed. Oblique interactions among the three solitons and interactions among the two parallel solitons and a single one are presented as well. (iii) Inelastic-elastic interactions imply that the interaction between the inelastic region and another one is elastic.

Wave processes in dusty plasma near the Moon’s surface

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

Morozova, T. I.; Kopnin, S. I.; Popel, S. I., E-mail: popel@iki.rssi.ru

2015-10-15

A plasma—dust system in the near-surface layer on the illuminated side of the Moon is described. The system involves photoelectrons, solar-wind electrons and ions, neutrals, and charged dust grains. Linear and nonlinear waves in the plasma near the Moon’s surface are discussed. It is noticed that the velocity distribution of photoelectrons can be represented as a superposition of two distribution functions characterized by different electron temperatures: lower energy electrons are knocked out of lunar regolith by photons with energies close to the work function of regolith, whereas higher energy electrons are knocked out by photons corresponding to the peak atmore » 10.2 eV in the solar radiation spectrum. The anisotropy of the electron velocity distribution function is distorted due to the solar wind motion with respect to photoelectrons and dust grains, which leads to the development of instability and excitation of high-frequency oscillations with frequencies in the range of Langmuir and electromagnetic waves. In addition, dust acoustic waves can be excited, e.g., near the lunar terminator. Solutions in the form of dust acoustic solitons corresponding to the parameters of the dust—plasma system in the near-surface layer of the illuminated Moon’s surface are found. Ranges of possible Mach numbers and soliton amplitudes are determined.« less

A Semi-Analytical Extraction Method for Interface and Bulk Density of States in Metal Oxide Thin-Film Transistors

PubMed Central

Chen, Weifeng; Wu, Weijing; Zhou, Lei; Xu, Miao; Wang, Lei; Peng, Junbiao

2018-01-01

A semi-analytical extraction method of interface and bulk density of states (DOS) is proposed by using the low-frequency capacitance–voltage characteristics and current–voltage characteristics of indium zinc oxide thin-film transistors (IZO TFTs). In this work, an exponential potential distribution along the depth direction of the active layer is assumed and confirmed by numerical solution of Poisson’s equation followed by device simulation. The interface DOS is obtained as a superposition of constant deep states and exponential tail states. Moreover, it is shown that the bulk DOS may be represented by the superposition of exponential deep states and exponential tail states. The extracted values of bulk DOS and interface DOS are further verified by comparing the measured transfer and output characteristics of IZO TFTs with the simulation results by a 2D device simulator ATLAS (Silvaco). As a result, the proposed extraction method may be useful for diagnosing and characterising metal oxide TFTs since it is fast to extract interface and bulk density of states (DOS) simultaneously. PMID:29534492

Antecedent Synoptic Environments Conducive to North American Polar/Subtropical Jet Superpositions

NASA Astrophysics Data System (ADS)

Winters, A. C.; Keyser, D.; Bosart, L. F.

2017-12-01

The atmosphere often exhibits a three-step pole-to-equator tropopause structure, with each break in the tropopause associated with a jet stream. The polar jet stream (PJ) typically resides in the break between the polar and subtropical tropopause and is positioned atop the strongly baroclinic, tropospheric-deep polar front around 50°N. The subtropical jet stream (STJ) resides in the break between the subtropical and the tropical tropopause and is situated on the poleward edge of the Hadley cell around 30°N. On occasion, the latitudinal separation between the PJ and the STJ can vanish, resulting in a vertical jet superposition. Prior case study work indicates that jet superpositions are often attended by a vigorous transverse vertical circulation that can directly impact the production of extreme weather over North America. Furthermore, this work suggests that there is considerable variability among antecedent environments conducive to the production of jet superpositions. These considerations motivate a comprehensive study to examine the synoptic-dynamic mechanisms that operate within the double-jet environment to produce North American jet superpositions. This study focuses on the identification of North American jet superposition events in the CFSR dataset during November-March 1979-2010. Superposition events will be classified into three characteristic types: "Polar Dominant" events will consist of events during which only the PJ is characterized by a substantial excursion from its climatological latitude band; "Subtropical Dominant" events will consist of events during which only the STJ is characterized by a substantial excursion from its climatological latitude band; and "Hybrid" events will consist of those events characterized by an excursion of both the PJ and STJ from their climatological latitude bands. Following their classification, frequency distributions of jet superpositions will be constructed to highlight the geographical locations most often associated with jet superpositions for each event type. PV inversion and composite analysis will also be performed on each event type in an effort to illustrate the antecedent environments and the dominant synoptic-dynamic mechanisms that favor the production of North American jet superpositions for each event type.

Dynamic Properties of Human Tympanic Membrane Based on Frequency-Temperature Superposition

PubMed Central

Zhang, Xiangming; Gan, Rong Z.

2012-01-01

The human tympanic membrane (TM) transfers sound in the ear canal into the mechanical vibration of the ossicles in the middle ear. The dynamic properties of TM directly affect the middle ear transfer function. The static or quasi-static mechanical properties of TM were reported in the literature, but the dynamic properties of TM over the auditory frequency range are very limited. In this paper, a new method was developed to measure the dynamic properties of human TM using the Dynamic-Mechanical Analyzer (DMA). The test was conducted at the frequency range of 1 to 40 Hz at three different temperatures: 5°, 25° and 37°C. The frequency-temperature superposition was applied to extend the testing frequency range to a much higher level (at least 3800 Hz). The generalized linear solid model was employed to describe the constitutive relation of the TM. The storage modulus E’ and the loss modulus E” were obtained from 11 specimens. The mean storage modulus was 15.1 MPa at 1 Hz and 27.6 MPa at 3800 Hz. The mean loss modulus was 0.28 MPa at 1 Hz and 4.1 MPa at 3800 Hz. The results show that the frequency-temperature superposition is a feasible approach to study the dynamic properties of the ear soft tissues. The dynamic properties of human TM obtained in this study provide a better description of the damping behavior of ear tissues. The properties can be transferred into the finite element (FE) model of the human ear to replace the Rayleigh type damping. The data reported here contribute to the biomechanics of the middle ear and improve the accuracy of the FE model for the human ear. PMID:22820983

Demonstration and implications when 50% beam combiners can behave as 0% or 100% reflector/transmitter inside some interferometers

NASA Astrophysics Data System (ADS)

Roychoudhuri, ChandraSekhar

2017-08-01

The purpose of this paper is to embolden students to raise basic questions regarding the feasibility of "indivisible single photon interference". We do this by presenting experimental results of well-known classical Mach-Zehnder interferometer (MZI) under two different conditions of beam alignment. We routinely do such experiments in our laboratories. In the first case, we align the light beams on the beam combiner (BC) with their Poynting vectors as perfectly collinear. The 50% dielectric boundary can now transmit 100% of the energy of both the beams into either one of the two MZI output ports, depending upon the relative phase between the two beams combined on the BC from the opposite directions. The dielectric boundary layer actively re-directs the energy from one beam to the other. This is pure classical superposition effect. In the second case, we combine the two beams on the BC with a small intersecting angle. Now the BC functions as a 50% beam splitter to both the beams. One can see spatial fringes as the relative phase varies with spatial distance by placing a photo detector array after the BC. At very low intensity, the quantum properties of the photo detector will become apparent because the photo electrons are discrete and are always bound quantum mechanically to its host molecular assembly; and not because light is definitely quantized. Students can learn to distinguish the pedagogical difference between the Superposition Principle (linear sum of wave amplitudes) and the Superposition Effect (square modulus of the sum of all the wave-induced stimulations) as observable intensity variations due to interaction with materials, classical or quantum.

Enhanced calculation of eigen-stress field and elastic energy in atomistic interdiffusion of alloys

NASA Astrophysics Data System (ADS)

Cecilia, José M.; Hernández-Díaz, A. M.; Castrillo, Pedro; Jiménez-Alonso, J. F.

2017-02-01

The structural evolution of alloys is affected by the elastic energy associated to eigen-stress fields. However, efficient calculations of the elastic energy in evolving geometries are actually a great challenge in promising atomistic simulation techniques such as Kinetic Monte Carlo (KMC) methods. In this paper, we report two complementary algorithms to calculate the eigen-stress field by linear superposition (a.k.a. LSA, Lineal Superposition Algorithm) and the elastic energy modification in atomistic interdiffusion of alloys (the Atom Exchange Elastic Energy Evaluation (AE4) Algorithm). LSA is shown to be appropriated for fast incremental stress calculation in highly nanostructured materials, whereas AE4 provides the required input for KMC and, additionally, it can be used to evaluate the accuracy of the eigen-stress field calculated by LSA. Consequently, they are suitable to be used on-the-fly with KMC. Both algorithms are massively parallel by their definition and thus well-suited for their parallelization on modern Graphics Processing Units (GPUs). Our computational studies confirm that we can obtain significant improvements compared to conventional Finite Element Methods, and the utilization of GPUs opens up new possibilities for the development of these methods in atomistic simulation of materials.

Effects of Aging-Time Reference on the Long Term Behavior of the IM7/K3B Composite

NASA Technical Reports Server (NTRS)

Veazie, David R.; Gates, Thomas S.

1998-01-01

An analytical study was undertaken to investigate the effects of the time-based shift reference on the long term behavior of the graphite reinforced thermoplastic polyimide composite IM7/K3B at elevated temperature. Creep compliance and the effects of physical aging on the time dependent response was measured for uniaxial loading at several isothermal conditions below the glass transition temperature (T(sub g). Two matrix dominated loading modes, shear and transverse, were investigated in tension and compression. The momentary sequenced creep/aging curves were collapsed through a horizontal (time) shift using the shortest, middle and longest aging time curve as the reference curve. Linear viscoelasticity was used to characterize the creep/recovery behavior and superposition techniques were used to establish the physical aging related material constants. The use of effective time expressions in a laminated plate model allowed for the prediction of long term creep compliance. The effect of using different reference curves with time/aging-time superposition was most sensitive to the physical aging shift rate at lower test temperatures. Depending on the loading mode, the reference curve used can result in a more accurate long term prediction, especially at lower test temperatures.

Interaction of Aquifer and River-Canal Network near Well Field.

PubMed

Ghosh, Narayan C; Mishra, Govinda C; Sandhu, Cornelius S S; Grischek, Thomas; Singh, Vikrant V

2015-01-01

The article presents semi-analytical mathematical models to asses (1) enhancements of seepage from a canal and (2) induced flow from a partially penetrating river in an unconfined aquifer consequent to groundwater withdrawal in a well field in the vicinity of the river and canal. The nonlinear exponential relation between seepage from a canal reach and hydraulic head in the aquifer beneath the canal reach is used for quantifying seepage from the canal reach. Hantush's (1967) basic solution for water table rise due to recharge from a rectangular spreading basin in absence of pumping well is used for generating unit pulse response function coefficients for water table rise in the aquifer. Duhamel's convolution theory and method of superposition are applied to obtain water table position due to pumping and recharge from different canal reaches. Hunt's (1999) basic solution for river depletion due to constant pumping from a well in the vicinity of a partially penetrating river is used to generate unit pulse response function coefficients. Applying convolution technique and superposition, treating the recharge from canal reaches as recharge through conceptual injection wells, river depletion consequent to variable pumping and recharge is quantified. The integrated model is applied to a case study in Haridwar (India). The well field consists of 22 pumping wells located in the vicinity of a perennial river and a canal network. The river bank filtrate portion consequent to pumping is quantified. © 2014, National GroundWater Association.

Periodic solutions with prescribed minimal period of vortex type problems in domains

NASA Astrophysics Data System (ADS)

Bartsch, Thomas; Sacchet, Matteo

2018-05-01

We consider Hamiltonian systems with two degrees of freedom of point vortex type for in a domain . In the classical point vortex context the Hamiltonian is of the form where is the regular part of a hydrodynamic Green function in Ω, is the Robin function: , and , are the vortex strengths. We prove the existence of infinitely many periodic solutions with prescribed minimal period that are superpositions of a slow motion of the center of vorticity close to a star-shaped level line of h and of a fast rotation of the two vortices around their center of vorticity. The proofs are based on a recent higher dimensional version of the Poincaré–Birkhoff theorem due to Fonda and Ureña.

Quantum computer games: Schrödinger cat and hounds

NASA Astrophysics Data System (ADS)

Gordon, Michal; Gordon, Goren

2012-05-01

The quantum computer game 'Schrödinger cat and hounds' is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. 'Schrödinger cat and hounds' demonstrates the effects of superposition, destructive and constructive interference, measurements and entanglement. More advanced concepts, like particle-wave duality and decoherence, can also be taught using the game as a model. The game that has an optimal solution in the classical version, can have many different solutions and a new balance of powers in the quantum world. Game-aided lectures were given to high-school students which showed that it is a valid and entertaining teaching platform.

Analytical solution of the transient temperature profile in gain medium of passively Q-switched microchip laser.

PubMed

Han, Xiahui; Li, Jianlang

2014-11-01

The transient temperature evolution in the gain medium of a continuous wave (CW) end-pumped passively Q-switched microchip (PQSM) laser is analyzed. By approximating the time-dependent population inversion density as a sawtooth function of time and treating the time-dependent pump absorption of a CW end-pumped PQSM laser as the superposition of an infinite series of short pumping pulses, the analytical expressions of transient temperature evolution and distribution in the gain medium for four- and three-level laser systems, respectively, are given. These analytical solutions are applied to evaluate the transient temperature evolution and distribution in the gain medium of CW end-pumped PQSM Nd:YAG and Yb:YAG lasers.

A TDDFT study of the ruthenium(II) polyazaaromatic complex [Ru(dppz)(phen) 2] 2+ in solution

NASA Astrophysics Data System (ADS)

Fantacci, Simona; De Angelis, Filippo; Sgamellotti, Antonio; Re, Nazzareno

2004-09-01

DFT/TDDFT calculations were performed to investigate the structural, electronic and optical properties of the [Ru(dppz)(phen) 2] 2+ complex in solution. TDDFT calculations in water show two groups of metal-to-ligand charge transfer (MLCT) transitions at ≈450 and 415 nm whose superposition gives account of the broad absorption band experimentally characterized at 440 nm. Also, a group of almost coincident MLCT transitions partially mixed with dppz intraligand π-π ∗ transitions centered at ≈380 nm is found to give rise to the narrow absorption band experimentally found at 380 nm. Our results provide insight into the hypochromic shifts experimentally characterized upon intercalation of the title complex into DNA.

Non-classical State via Superposition of Two Opposite Coherent States

NASA Astrophysics Data System (ADS)

Ren, Gang; Du, Jian-ming; Yu, Hai-jun

2018-04-01

We study the non-classical properties of the states generated by superpositions of two opposite coherent states with the arbitrary relative phase factors. We show that the relative phase factors plays an important role in these superpositions. We demonstrate this result by discussing their squeezing properties, quantum statistical properties and fidelity in principle.

Ultrafast creation of large Schrödinger cat states of an atom.

PubMed

Johnson, K G; Wong-Campos, J D; Neyenhuis, B; Mizrahi, J; Monroe, C

2017-09-26

Mesoscopic quantum superpositions, or Schrödinger cat states, are widely studied for fundamental investigations of quantum measurement and decoherence as well as applications in sensing and quantum information science. The generation and maintenance of such states relies upon a balance between efficient external coherent control of the system and sufficient isolation from the environment. Here we create a variety of cat states of a single trapped atom's motion in a harmonic oscillator using ultrafast laser pulses. These pulses produce high fidelity impulsive forces that separate the atom into widely separated positions, without restrictions that typically limit the speed of the interaction or the size and complexity of the resulting motional superposition. This allows us to quickly generate and measure cat states larger than previously achieved in a harmonic oscillator, and create complex multi-component superposition states in atoms.Generation of mesoscopic quantum superpositions requires both reliable coherent control and isolation from the environment. Here, the authors succeed in creating a variety of cat states of a single trapped atom, mapping spin superpositions into spatial superpositions using ultrafast laser pulses.

A Method for Calculating Strain Energy Release Rates in Preliminary Design of Composite Skin/Stringer Debonding Under Multi-Axial Loading

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Minguet, Pierre J.; OBrien, T. Kevin

1999-01-01

Three simple procedures were developed to determine strain energy release rates, G, in composite skin/stringer specimens for various combinations of unaxial and biaxial (in-plane/out-of-plane) loading conditions. These procedures may be used for parametric design studies in such a way that only a few finite element computations will be necessary for a study of many load combinations. The results were compared with mixed mode strain energy release rates calculated directly from nonlinear two-dimensional plane-strain finite element analyses using the virtual crack closure technique. The first procedure involved solving three unknown parameters needed to determine the energy release rates. Good agreement was obtained when the external loads were used in the expression derived. This superposition technique was only applicable if the structure exhibits a linear load/deflection behavior. Consequently, a second technique was derived which was applicable in the case of nonlinear load/deformation behavior. The technique involved calculating six unknown parameters from a set of six simultaneous linear equations with data from six nonlinear analyses to determine the energy release rates. This procedure was not time efficient, and hence, less appealing. A third procedure was developed to calculate mixed mode energy release rates as a function of delamination lengths. This procedure required only one nonlinear finite element analysis of the specimen with a single delamination length to obtain a reference solution for the energy release rates and the scale factors. The delamination was extended in three separate linear models of the local area in the vicinity of the delamination subjected to unit loads to obtain the distribution of G with delamination lengths. This set of sub-problems was Although additional modeling effort is required to create the sub- models, this local technique is efficient for parametric studies.

Experimental investigation of yawing-rolling coupling effects on unsteady aerodynamic characteristics of an aircraft

NASA Astrophysics Data System (ADS)

Shen, Lin; Huang, Da; Wu, Genxing

2018-05-01

In this paper, an aircraft model was tested in the wind tunnel with different degrees of yaw-roll coupling at different angles of attack. The dynamic increments of yawing and rolling moments are compared to study the coupling effects on damping characteristics. The characteristic time constants are calculated to study the changes of flow field structure related to coupling ratios. The damping characteristics and time lag effects of aerodynamic loads calculated by dynamic derivative method are also compared with experimental results to estimate the applicability of linear superposition principle at large angles of attack.

Alfven wave dispersion behavior in single- and multicomponent plasmas

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

Rahbarnia, K.; Grulke, O.; Klinger, T.

Dispersion relations of driven Alfven waves (AWs) are measured in single- and multicomponent plasmas consisting of mixtures of argon, helium, and oxygen in a magnetized linear cylindrical plasma device VINETA [C. Franck, O. Grulke, and T. Klinger, Phys. Plasmas 9, 3254 (2002)]. The decomposition of the measured three-dimensional magnetic field fluctuations and the corresponding parallel current pattern reveals that the wave field is a superposition of L- and R-wave components. The dispersion relation measurements agree well with calculations based on a multifluid Hall-magnetohydrodynamic model if the plasma resistivity is correctly taken into account.

Color enhancement for portable LCD displays in low-power mode

NASA Astrophysics Data System (ADS)

Shih, Kuang-Tsu; Huang, Tai-Hsiang; Chen, Homer H.

2011-09-01

Switching the backlight of handheld devices to low power mode saves energy but affects the color appearance of an image. In this paper, we consider the chroma degradation problem and propose an enhancement algorithm that incorporates the CIECAM02 appearance model to quantitatively characterize the problem. In the proposed algorithm, we enhance the color appearance of the image in low power mode by weighted linear superposition of the chroma of the image and that of the estimated dim-backlight image. Subjective tests are carried out to determine the perceptually optimal weighting and prove the effectiveness of our framework.

Manipulation of optical-pulse-imprinted memory in a Λ system

NASA Astrophysics Data System (ADS)

Gutiérrez-Cuevas, Rodrigo; Eberly, Joseph H.

2015-09-01

We examine coherent memory manipulation in a Λ -type medium, using the second-order solution presented by Groves, Clader, and Eberly [J. Phys. B: At. Mol. Opt. Phys. 46, 224005 (2013), 10.1088/0953-4075/46/22/224005] as a guide. The analytical solution obtained using the Darboux transformation and a nonlinear superposition principle describes complicated soliton-pulse dynamics which, by an appropriate choice of parameters, can be simplified to a well-defined sequence of pulses interacting with the medium. In this report, this solution is reviewed and put to test by means of a series of numerical simulations, encompassing all the parameter space and adding the effects of homogeneous broadening due to spontaneous emission. We find that even though the decohered results deviate from the analytical prediction they do follow a similar trend that could be used as a guide for future experiments.

Bessel-Gauss beams as rigorous solutions of the Helmholtz equation.

PubMed

April, Alexandre

2011-10-01

The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

Teleportation of Unknown Superpositions of Collective Atomic Coherent States

NASA Astrophysics Data System (ADS)

Zheng, Shi-Biao

2001-06-01

We propose a scheme to teleport an unknown superposition of two atomic coherent states with different phases. Our scheme is based on resonant and dispersive atom-field interaction. Our scheme provides a possibility of teleporting macroscopic superposition states of many atoms first time. The project supported by National Natural Science Foundation of China under Grant No. 60008003

Student Ability to Distinguish between Superposition States and Mixed States in Quantum Mechanics

ERIC Educational Resources Information Center

Passante, Gina; Emigh, Paul J.; Shaffer, Peter S.

2015-01-01

Superposition gives rise to the probabilistic nature of quantum mechanics and is therefore one of the concepts at the heart of quantum mechanics. Although we have found that many students can successfully use the idea of superposition to calculate the probabilities of different measurement outcomes, they are often unable to identify the…

Nonclassical Properties of Q-Deformed Superposition Light Field State

NASA Technical Reports Server (NTRS)

Ren, Min; Shenggui, Wang; Ma, Aiqun; Jiang, Zhuohong

1996-01-01

In this paper, the squeezing effect, the bunching effect and the anti-bunching effect of the superposition light field state which involving q-deformation vacuum state and q-Glauber coherent state are studied, the controllable q-parameter of the squeezing effect, the bunching effect and the anti-bunching effect of q-deformed superposition light field state are obtained.

Rapid sampling of stochastic displacements in Brownian dynamics simulations

NASA Astrophysics Data System (ADS)

Fiore, Andrew M.; Balboa Usabiaga, Florencio; Donev, Aleksandar; Swan, James W.

2017-03-01

We present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform fast Fourier transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. For geometrically dense microstructures (fractal dimension equal three), the performance is independent of volume fraction, while for tenuous microstructures (fractal dimension less than three), such as gels and polymer solutions, the performance improves with decreasing volume fraction. This is in stark contrast with other related linear-scaling methods such as the force coupling method and the fluctuating immersed boundary method, for which performance degrades with decreasing volume fraction. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4 ×106 particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the cost of computing Brownian displacements comparable to the cost of computing deterministic displacements in BD simulations. A high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.

Numerical research on the lateral global buckling characteristics of a high temperature and pressure pipeline with two initial imperfections

PubMed Central

Liu, Wenbin; Liu, Aimin

2018-01-01

With the exploitation of offshore oil and gas gradually moving to deep water, higher temperature differences and pressure differences are applied to the pipeline system, making the global buckling of the pipeline more serious. For unburied deep-water pipelines, the lateral buckling is the major buckling form. The initial imperfections widely exist in the pipeline system due to manufacture defects or the influence of uneven seabed, and the distribution and geometry features of initial imperfections are random. They can be divided into two kinds based on shape: single-arch imperfections and double-arch imperfections. This paper analyzed the global buckling process of a pipeline with 2 initial imperfections by using a numerical simulation method and revealed how the ratio of the initial imperfection’s space length to the imperfection’s wavelength and the combination of imperfections affects the buckling process. The results show that a pipeline with 2 initial imperfections may suffer the superposition of global buckling. The growth ratios of buckling displacement, axial force and bending moment in the superposition zone are several times larger than no buckling superposition pipeline. The ratio of the initial imperfection’s space length to the imperfection’s wavelength decides whether a pipeline suffers buckling superposition. The potential failure point of pipeline exhibiting buckling superposition is as same as the no buckling superposition pipeline, but the failure risk of pipeline exhibiting buckling superposition is much higher. The shape and direction of two nearby imperfections also affects the failure risk of pipeline exhibiting global buckling superposition. The failure risk of pipeline with two double-arch imperfections is higher than pipeline with two single-arch imperfections. PMID:29554123

On the Use of Material-Dependent Damping in ANSYS for Mode Superposition Transient Analysis

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

Nie, J.; Wei, X.

The mode superposition method is often used for dynamic analysis of complex structures, such as the seismic Category I structures in nuclear power plants, in place of the less efficient full method, which uses the full system matrices for calculation of the transient responses. In such applications, specification of material-dependent damping is usually desirable because complex structures can consist of multiple types of materials that may have different energy dissipation capabilities. A recent review of the ANSYS manual for several releases found that the use of material-dependent damping is not clearly explained for performing a mode superposition transient dynamic analysis.more » This paper includes several mode superposition transient dynamic analyses using different ways to specify damping in ANSYS, in order to determine how material-dependent damping can be specified conveniently in a mode superposition transient dynamic analysis.« less

Testing the quantum superposition principle: matter waves and beyond

NASA Astrophysics Data System (ADS)

Ulbricht, Hendrik

2015-05-01

New technological developments allow to explore the quantum properties of very complex systems, bringing the question of whether also macroscopic systems share such features, within experimental reach. The interest in this question is increased by the fact that, on the theory side, many suggest that the quantum superposition principle is not exact, departures from it being the larger, the more macroscopic the system. Testing the superposition principle intrinsically also means to test suggested extensions of quantum theory, so-called collapse models. We will report on three new proposals to experimentally test the superposition principle with nanoparticle interferometry, optomechanical devices and by spectroscopic experiments in the frequency domain. We will also report on the status of optical levitation and cooling experiments with nanoparticles in our labs, towards an Earth bound matter-wave interferometer to test the superposition principle for a particle mass of one million amu (atomic mass unit).

General Boundary Relations for a Source-Driven Antenna With Application to a Finite Cylindrical Conductor

DTIC Science & Technology

1961-08-22

current#» D !x and equivalent magnetic fields l\\ and Bj. According *to the principle of superposition, the complete Maxwellian Electro-magnetic Field...of d * Alembert «s equation 0»".’ ’■ ■’- v.2 A - /«’«-gjr A « - /t J, .(Al) . Using reasonable K.K*S. units to calculate, the solution is 4* Ä...COMMERCE WASHINGTON 2$, D . C. i U. S. JOINT PUBLICATIONS RESEARCH SERVICE 1636 CONNECTICUT AVE., N. W. WASHINGTON 25, D . G. Reproduced From

An ideal clamping analysis for a cross-ply laminate

NASA Technical Reports Server (NTRS)

Valisetty, R. R.; Murthy, P. L. N.; Rehfield, L. W.

1988-01-01

Different elementary clamping models are discussed for a three layer crossply laminate to study the sensitivity of clamping to the definition of cross-sectional rotation. All of these models leave a considerable residual warping at the edges. Using a complimentary energy principle and principle of superposition, an analysis is conducted to reduce this residual warping. This led to the identification of exact interior solution corresponding to the ideal clamping. This study also suggests a presence of stress singularities at the corners and between different layers near the fixed edge.

Universal Spatial Correlation Functions for Describing and Reconstructing Soil Microstructure

PubMed Central

Skvortsova, Elena B.; Mallants, Dirk

2015-01-01

Structural features of porous materials such as soil define the majority of its physical properties, including water infiltration and redistribution, multi-phase flow (e.g. simultaneous water/air flow, or gas exchange between biologically active soil root zone and atmosphere) and solute transport. To characterize soil microstructure, conventional soil science uses such metrics as pore size and pore-size distributions and thin section-derived morphological indicators. However, these descriptors provide only limited amount of information about the complex arrangement of soil structure and have limited capability to reconstruct structural features or predict physical properties. We introduce three different spatial correlation functions as a comprehensive tool to characterize soil microstructure: 1) two-point probability functions, 2) linear functions, and 3) two-point cluster functions. This novel approach was tested on thin-sections (2.21×2.21 cm2) representing eight soils with different pore space configurations. The two-point probability and linear correlation functions were subsequently used as a part of simulated annealing optimization procedures to reconstruct soil structure. Comparison of original and reconstructed images was based on morphological characteristics, cluster correlation functions, total number of pores and pore-size distribution. Results showed excellent agreement for soils with isolated pores, but relatively poor correspondence for soils exhibiting dual-porosity features (i.e. superposition of pores and micro-cracks). Insufficient information content in the correlation function sets used for reconstruction may have contributed to the observed discrepancies. Improved reconstructions may be obtained by adding cluster and other correlation functions into reconstruction sets. Correlation functions and the associated stochastic reconstruction algorithms introduced here are universally applicable in soil science, such as for soil classification, pore-scale modelling of soil properties, soil degradation monitoring, and description of spatial dynamics of soil microbial activity. PMID:26010779

Universal spatial correlation functions for describing and reconstructing soil microstructure.

PubMed

Karsanina, Marina V; Gerke, Kirill M; Skvortsova, Elena B; Mallants, Dirk

2015-01-01

Structural features of porous materials such as soil define the majority of its physical properties, including water infiltration and redistribution, multi-phase flow (e.g. simultaneous water/air flow, or gas exchange between biologically active soil root zone and atmosphere) and solute transport. To characterize soil microstructure, conventional soil science uses such metrics as pore size and pore-size distributions and thin section-derived morphological indicators. However, these descriptors provide only limited amount of information about the complex arrangement of soil structure and have limited capability to reconstruct structural features or predict physical properties. We introduce three different spatial correlation functions as a comprehensive tool to characterize soil microstructure: 1) two-point probability functions, 2) linear functions, and 3) two-point cluster functions. This novel approach was tested on thin-sections (2.21×2.21 cm2) representing eight soils with different pore space configurations. The two-point probability and linear correlation functions were subsequently used as a part of simulated annealing optimization procedures to reconstruct soil structure. Comparison of original and reconstructed images was based on morphological characteristics, cluster correlation functions, total number of pores and pore-size distribution. Results showed excellent agreement for soils with isolated pores, but relatively poor correspondence for soils exhibiting dual-porosity features (i.e. superposition of pores and micro-cracks). Insufficient information content in the correlation function sets used for reconstruction may have contributed to the observed discrepancies. Improved reconstructions may be obtained by adding cluster and other correlation functions into reconstruction sets. Correlation functions and the associated stochastic reconstruction algorithms introduced here are universally applicable in soil science, such as for soil classification, pore-scale modelling of soil properties, soil degradation monitoring, and description of spatial dynamics of soil microbial activity.

Frequency conversion by the transformation-optical analogue of the cosmological redshift

NASA Astrophysics Data System (ADS)

Ginis, Vincent; Tassin, Philippe; Craps, Ben; Veretennicoff, Irina

2011-10-01

Recently, there has been a lot of interest in electromagnetic analogues of general relativistic effects. Using the techniques of transformation optics, the material parameters of table-top devices have been calculated such that they implement several effects that occur in outer space, e.g., the implementation of an artificial event horizon inside an optical fiber, an inhomogeneous refractive index profile to mimic celestial mechanics, or an omnidirectional absorber based on an equivalence with black holes. In this communication, we show how we have extended the framework of transformation optics to a time-dependent metric-the Robertson-Walker metric, a popular model for our universe describing the cosmological redshift. This redshift occurs due to the expansion of the universe, where a photon of frequency ωem emitted at instance tem, will be measured at a different frequency ωobs at time tobs. The relation between these two frequencies is given by ωobsa(tobs) = ωema(tem), where a(t) is the time-dependent scale factor of the expanding universe. Our results show that the transformation-optical analogue of the Robertson-Walker metric is a medium with linear, isotropic, and homogeneous material parameters that evolve as a given function of time. The electromagnetic solutions inside such a medium are frequency shifted according to the cosmological redshift formula. Furthermore, we have demonstrated that a finite slab of such a material allows for the frequency conversion of an optical signal without the creation of unwanted sidebands. Because the medium is linear, the superposition principle remains applicable and arbitrary wavepackets can be converted [V. Ginis, P. Tassin, B. Craps, and I. Veretennicoff Opt. Express 18, 5350-5355 (2010)1].

Quantum state engineering by a coherent superposition of photon subtraction and addition

NASA Astrophysics Data System (ADS)

Lee, Su-Yong; Nha, Hyunchul

2011-10-01

We study a coherent superposition tâ+r↠of field annihilation and creation operator acting on continuous variable systems and propose its application for quantum state engineering. We propose an experimental scheme to implement this elementary coherent operation and discuss its usefulness to produce an arbitrary superposition of number states involving up to two photons.

Composite and case study analyses of the large-scale environments associated with West Pacific Polar and subtropical vertical jet superposition events

NASA Astrophysics Data System (ADS)

Handlos, Zachary J.

Though considerable research attention has been devoted to examination of the Northern Hemispheric polar and subtropical jet streams, relatively little has been directed toward understanding the circumstances that conspire to produce the relatively rare vertical superposition of these usually separate features. This dissertation investigates the structure and evolution of large-scale environments associated with jet superposition events in the northwest Pacific. An objective identification scheme, using NCEP/NCAR Reanalysis 1 data, is employed to identify all jet superpositions in the west Pacific (30-40°N, 135-175°E) for boreal winters (DJF) between 1979/80 - 2009/10. The analysis reveals that environments conducive to west Pacific jet superposition share several large-scale features usually associated with East Asian Winter Monsoon (EAWM) northerly cold surges, including the presence of an enhanced Hadley Cell-like circulation within the jet entrance region. It is further demonstrated that several EAWM indices are statistically significantly correlated with jet superposition frequency in the west Pacific. The life cycle of EAWM cold surges promotes interaction between tropical convection and internal jet dynamics. Low potential vorticity (PV), high theta e tropical boundary layer air, exhausted by anomalous convection in the west Pacific lower latitudes, is advected poleward towards the equatorward side of the jet in upper tropospheric isentropic layers resulting in anomalous anticyclonic wind shear that accelerates the jet. This, along with geostrophic cold air advection in the left jet entrance region that drives the polar tropopause downward through the jet core, promotes the development of the deep, vertical PV wall characteristic of superposed jets. West Pacific jet superpositions preferentially form within an environment favoring the aforementioned characteristics regardless of EAWM seasonal strength. Post-superposition, it is shown that the west Pacific jet extends eastward and is associated with an upper tropospheric cyclonic (anticyclonic) anomaly in its left (right) exit region. A downstream ridge is present over northwest Canada, and within the strong EAWM environment, a wavier flow over North America is observed relative to the neutral EAWM environment. Preliminary investigation of the two weak EAWM season superpositions reveals a Kona Low type feature post-superposition. This is associated with anomalous convection reminiscent of an atmospheric river southwest of Mexico.

Construction Method of Analytical Solutions to the Mathematical Physics Boundary Problems for Non-Canonical Domains

NASA Astrophysics Data System (ADS)

Mobarakeh, Pouyan Shakeri; Grinchenko, Victor T.

2015-06-01

The majority of practical cases of acoustics problems requires solving the boundary problems in non-canonical domains. Therefore construction of analytical solutions of mathematical physics boundary problems for non-canonical domains is both lucrative from the academic viewpoint, and very instrumental for elaboration of efficient algorithms of quantitative estimation of the field characteristics under study. One of the main solving ideologies for such problems is based on the superposition method that allows one to analyze a wide class of specific problems with domains which can be constructed as the union of canonically-shaped subdomains. It is also assumed that an analytical solution (or quasi-solution) can be constructed for each subdomain in one form or another. However, this case implies some difficulties in the construction of calculation algorithms, insofar as the boundary conditions are incompletely defined in the intervals, where the functions appearing in the general solution are orthogonal to each other. We discuss several typical examples of problems with such difficulties, we study their nature and identify the optimal methods to overcome them.

Model and prediction of stress relaxation of polyurethane fiber

NASA Astrophysics Data System (ADS)

You, Gexin; Wang, Chunyan; Mei, Shuqin; Yang, Bo; Zhou, Xiuwen

2018-03-01

In this study, the effect of small strain (less than 10%) on hydrogen bond (H-bond) and crystallinity of dry-spun polyurethane fiber was investigated with fourier transform infrared spectroscopy and x-ray diffractometer, respectively. The results showed that the H-bond of hard segments hardly broke and its degree of crystallinity scarcely varied below strain of 10%. The fiber stress relaxation behavior at 25 °C under small strain was researched using dynamic mechanical analyzer. The stress relaxation modulus constitutive equation was obtained by transforming the non-linear relationship between stress and time into the linear relationship between stress and strain. The stress relaxation modulus master curve at 25 °C was established in terms of short-term stress relaxation tests at elevated temperatures (35 °C, 45 °C, 65 °C and 75 °C) according to time-temperature superposition principle (TTS) to predict long-term behavior within 353 year.

The Madden-Julian Oscillation and the Indo-Pacific Warm Pool

NASA Astrophysics Data System (ADS)

Raymond, David J.; Fuchs, Željka

2018-04-01

A minimal model of the interaction of the Madden-Julian oscillation (MJO) with the Indo-Pacific warm pool is presented. This model is based on the linear superposition of the flow associated with a highly simplified treatment of the MJO plus the flow induced by the warm pool itself. Both of these components parameterize rainfall as proportional to the column water vapor, which in turn is governed by a linearized moisture equation in which WISHE (wind induced surface heat exchange) plays a governing role. The MJO component has maximum growth rate for planetary wavenumber 1 and is equatorially trapped with purely zonal winds. The warm pool component exhibits a complex flow pattern, differing significantly from the classical Gill model as a result of the mean easterly flow. The combination of the two produce a flow that reproduces many aspects of the observed global flow associated with the MJO.

Litigated Metal Clusters - Structures, Energy and Reactivity

DTIC Science & Technology

2016-04-01

projection superposition approximation ( PSA ) algorithm through a more careful consideration of how to calculate cross sections for elongated molecules...superposition approximation ( PSA ) is now complete. We have made it available free of charge to the scientific community on a dedicated website at UCSB. We...by AFOSR. We continued to improve the projection superposition approximation ( PSA ) algorithm through a more careful consideration of how to calculate

Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States.

PubMed

Yue, Fuyong; Wen, Dandan; Zhang, Chunmei; Gerardot, Brian D; Wang, Wei; Zhang, Shuang; Chen, Xianzhong

2017-04-01

A facile metasurface approach is shown to realize polarization-controllable multichannel superpositions of orbital angular momentum (OAM) states with various topological charges. By manipulating the polarization state of the incident light, four kinds of superpositions of OAM states are realized using a single metasurface consisting of space-variant arrays of gold nanoantennas. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Issues in vibration energy harvesting

NASA Astrophysics Data System (ADS)

Zhang, Hui; Corr, Lawrence R.; Ma, Tianwei

2018-05-01

In this study, fundamental issues related to bandwidth and nonlinear resonance in vibrational energy harvesting devices are investigated. The results show that using bandwidth as a criterion to measure device performance can be misleading. For a linear device, an enlarged bandwidth is achieved at the cost of sacrificing device performance near resonance, and thus widening the bandwidth may offer benefits only when the natural frequency of the linear device cannot match the dominant excitation frequency. For a nonlinear device, since the principle of superposition does not apply, the ''broadband" performance improvements achieved for single-frequency excitations may not be achievable for multi-frequency excitations. It is also shown that a large-amplitude response based on the traditional ''nonlinear resonance" does not always result in the optimal performance for a nonlinear device because of the negative work done by the excitation, which indicates energy is returned back to the excitation. Such undesired negative work is eliminated at global resonance, a generalized resonant condition for both linear and nonlinear systems. While the linear resonance is a special case of global resonance for a single-frequency excitation, the maximum potential of nonlinear energy harvesting can be reached for multi-frequency excitations by using global resonance to simultaneously harvest energy distributed over multiple frequencies.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

The conformal transformation of an airfoil into a straight line and its application to the inverse problem of airfoil theory

NASA Technical Reports Server (NTRS)

Mutterperl, William

1944-01-01

A method of conformal transformation is developed that maps an airfoil into a straight line, the line being chosen as the extended chord line of the airfoil. The mapping is accomplished by operating directly with the airfoil ordinates. The absence of any preliminary transformation is found to shorten the work substantially over that of previous methods. Use is made of the superposition of solutions to obtain a rigorous counterpart of the approximate methods of thin-airfoils theory. The method is applied to the solution of the direct and inverse problems for arbitrary airfoils and pressure distributions. Numerical examples are given. Applications to more general types of regions, in particular to biplanes and to cascades of airfoils, are indicated. (author)

Influence of temperature on the rheological behavior of a new fucose-containing bacterial exopolysaccharide.

PubMed

Cruz, Madalena; Freitas, Filomena; Torres, Cristiana A V; Reis, Maria A M; Alves, Vítor D

2011-05-01

The effect of temperature on the rheology of a new fucose-containing extracellular polysaccharide (EPS) was evaluated. The steady state data revealed a shear-thinning behavior, with the viscosity being immediately recovered when the shear rate was decreased. The mechanical spectra indicated viscous solutions with entangled polymer molecules in the range of temperatures studied (from 15 °C to 65 °C). In addition, the Time-Temperature Superposition principle was successfully applied and the Cox-Merz rule was valid, reinforcing the idea of a thermorheologically simple behavior for the EPS in aqueous solution. Furthermore, the viscous and viscoelastic properties at 25 °C were maintained after consecutive heating and cooling cycles, indicating a good thermal stability under temperature fluctuations. Copyright © 2011 Elsevier B.V. All rights reserved.

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

Volkoff, T. J., E-mail: adidasty@gmail.com

We motivate and introduce a class of “hierarchical” quantum superposition states of N coupled quantum oscillators. Unlike other well-known multimode photonic Schrödinger-cat states such as entangled coherent states, the hierarchical superposition states are characterized as two-branch superpositions of tensor products of single-mode Schrödinger-cat states. In addition to analyzing the photon statistics and quasiprobability distributions of prominent examples of these nonclassical states, we consider their usefulness for highprecision quantum metrology of nonlinear optical Hamiltonians and quantify their mode entanglement. We propose two methods for generating hierarchical superpositions in N = 2 coupled microwave cavities, exploiting currently existing quantum optical technology formore » generating entanglement between spatially separated electromagnetic field modes.« less

Space-variant polarization patterns of non-collinear Poincaré superpositions

NASA Astrophysics Data System (ADS)

Galvez, E. J.; Beach, K.; Zeosky, J. J.; Khajavi, B.

2015-03-01

We present analysis and measurements of the polarization patterns produced by non-collinear superpositions of Laguerre-Gauss spatial modes in orthogonal polarization states, which are known as Poincaré modes. Our findings agree with predictions (I. Freund Opt. Lett. 35, 148-150 (2010)), that superpositions containing a C-point lead to a rotation of the polarization ellipse in 3-dimensions. Here we do imaging polarimetry of superpositions of first- and zero-order spatial modes at relative beam angles of 0-4 arcmin. We find Poincaré-type polarization patterns showing fringes in polarization orientation, but which preserve the polarization-singularity index for all three cases of C-points: lemons, stars and monstars.

Non-coaxial superposition of vector vortex beams.

PubMed

Aadhi, A; Vaity, Pravin; Chithrabhanu, P; Reddy, Salla Gangi; Prabakar, Shashi; Singh, R P

2016-02-10

Vector vortex beams are classified into four types depending upon spatial variation in their polarization vector. We have generated all four of these types of vector vortex beams by using a modified polarization Sagnac interferometer with a vortex lens. Further, we have studied the non-coaxial superposition of two vector vortex beams. It is observed that the superposition of two vector vortex beams with same polarization singularity leads to a beam with another kind of polarization singularity in their interaction region. The results may be of importance in ultrahigh security of the polarization-encrypted data that utilizes vector vortex beams and multiple optical trapping with non-coaxial superposition of vector vortex beams. We verified our experimental results with theory.

Oblique superposition of two elliptically polarized lightwaves using geometric algebra: is energy-momentum conserved?

PubMed

Sze, Michelle Wynne C; Sugon, Quirino M; McNamara, Daniel J

2010-11-01

In this paper, we use Clifford (geometric) algebra Cl(3,0) to verify if electromagnetic energy-momentum density is still conserved for oblique superposition of two elliptically polarized plane waves with the same frequency. We show that energy-momentum conservation is valid at any time only for the superposition of two counter-propagating elliptically polarized plane waves. We show that the time-average energy-momentum of the superposition of two circularly polarized waves with opposite handedness is conserved regardless of the propagation directions of the waves. And, we show that the resulting momentum density of the superposed waves generally has a vector component perpendicular to the momentum densities of the individual waves.

ILT for double exposure lithography with conventional and novel materials

NASA Astrophysics Data System (ADS)

Poonawala, Amyn; Borodovsky, Yan; Milanfar, Peyman

2007-03-01

Multiple paths exists to provide lithography solutions pursuant to Moore's Law for next 3-5 generations of technology, yet each of those paths inevitably leads to solutions eventually requiring patterning at k I < 0.30 and below. In this article, we explore double exposure single development lithography for k I >= 0.25 (using conventional resist) and k1 < 0.25 (using new out-of-sight out-of-mind materials). For the case of k I >= 0.25, we propose a novel double exposure inverse lithography technique (ILT) to split the pattern. Our algorithm is based on our earlier proposed single exposure ILT framework, and works by decomposing the aerial image (instead of the target pattern) into two parts. It also resolves the phase conflicts automatically as part of the decomposition, and the combined aerial image obtained using the estimated masks has a superior contrast. For the case of k I < 0.25, we focus on analyzing the use of various dual patterning techniques enabled by the use of hypothetic materials with properties that allow for the violation of the linear superposition of intensities from the two exposures. We investigate the possible use of two materials: contrast enhancement layer (CEL) and two-photon absorption resists. We propose a mathematical model for CEL, define its characteristic properties, and derive fundamental bounds on the improvement in image log-slope. Simulation results demonstrate that double exposure single development lithography using CEL enables printing 80nm gratings using dry lithography. We also combine ILT, CEL, and DEL to synthesize 2-D patterns with k I = 0.185. Finally, we discuss the viability of two-photon absorption resists for double exposure lithography.

Non-Abelian black string solutions of N = (2,0) , d = 6 supergravity

NASA Astrophysics Data System (ADS)

Cano, Pablo A.; Ortín, Tomás; Santoli, Camilla

2016-12-01

We show that, when compactified on a circle, N = (2, 0), d = 6 supergravity coupled to 1 tensor multiplet and n V vector multiplets is dual to N = (2 , 0) , d = 6 supergravity coupled to just n T = n V + 1 tensor multiplets and no vector multiplets. Both theories reduce to the same models of N = 2 , d = 5 supergravity coupled to n V 5 = n V + 2 vector fields. We derive Buscher rules that relate solutions of these theories (and of the theory that one obtains by dualizing the 3-form field strength) admitting an isometry. Since the relations between the fields of N = 2 , d = 5 supergravity and those of the 6-dimensional theories are the same with or without gaugings, we construct supersymmetric non-Abelian solutions of the 6-dimensional gauged theories by uplifting the recently found 5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions describe the usual superpositions of strings and waves supplemented by a BPST instanton in the transverse directions, similar to the gauge dyonic string of Duff, Lü and Pope. One of the solutions obtained interpolates smoothly between two AdS3× S3 geometries with different radii.

Effect of concentration and temperature on the rheological behavior of collagen solution.

PubMed

Lai, Guoli; Li, Yang; Li, Guoying

2008-04-01

Dynamic viscoelastic properties of collagen solutions with concentrations of 0.5-1.5% (w/w) were characterized by means of oscillatory rheometry at temperatures ranging from 20 to 32.5 degrees C. All collagen solutions showed a shear-thinning flow behavior. The complex viscosity exhibited an exponential increase and the loss tangent decreased with the increase of collagen concentration (C(COL)) when the C(COL)> or =0.75%. Both storage modulus (G') and loss modulus (G'') increased with the increase of frequency and concentration, but decreased with the increase of temperature and behaved without regularity at 32.5 degrees C. The relaxation times decreased with the increase of temperature for 1.0% collagen solution. According to a three-zone model, dynamic modulus of collagen solutions showed terminal-zone and plateau-zone behavior when C(COL) was no more than 1.25% or the stated temperature was no more than 30 degrees C. The concentrated solution (1.5%) behaved being entirely in plateau zone. An application of the time-temperature superposition (TTS) allowed the construction of master curve and an Arrhenius-type TTS principle was used to yield the activation energy of 161.4 kJ mol(-1).

Quantifying the errors due to the superposition of analytical deformation sources

NASA Astrophysics Data System (ADS)

Neuberg, J. W.; Pascal, K.

2012-04-01

The displacement field due to magma movement in the subsurface is often modelled using a Mogi point source or a dislocation Okada source embedded in a homogeneous elastic half-space. When the magmatic system cannot be modelled by a single source it is often represented by several sources, their respective deformation fields are superimposed. However, in such a case the assumption of homogeneity in the half-space is violated and the interaction between sources in an elastic medium is neglected. In this investigation we have quantified the effects of neglecting the interaction between sources on the surface deformation field. To do so, we calculated the vertical and horizontal displacements for models with adjacent sources and we tested them against the solutions of corresponding numerical 3D finite element models. We implemented several models combining spherical pressure sources and dislocation sources, varying the pressure or dislocation of the sources and their relative position. We also investigated three numerical methods to model a dike as a dislocation tensile source or as a pressurized tabular crack. We found that the discrepancies between simple superposition of the displacement field and a fully interacting numerical solution depend mostly on the source types and on their spacing. The errors induced when neglecting the source interaction are expected to vary greatly with the physical and geometrical parameters of the model. We demonstrated that for certain scenarios these discrepancies can be neglected (<5%) when the sources are separated by at least 4 radii for two combined Mogi sources and by at least 3 radii for juxtaposed Mogi and Okada sources

Pressure solution and microfracturing in primary oil migration, Upper Cretaceous Austin Chalk, Texas Gulf Coast

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

Chanchani, J.; Berg, R.R.; Lee, C.I.

1996-09-01

The Upper Cretaceous Austin Chalk is a well known source rock and fractured reservoir in the Gulf Coast. Production is mainly from tectonic fractures, and the mechanism by which oil migrated from the matrix into the fractures is poorly understood. Microfracturing due to oil generation offers a possible explanation for the mechanism of the primary migration of oil in the Austin Chalk. Petrographic study shows that the major components of the primary migration system are the solution seams and the associated microfractures. Pressure solution is manifest as centimeter to millimeter-scale solution seams and smaller microseams. The solution seams are compositesmore » formed by the superposition of the smaller microseams. A significant amount of organic matter was concentrated in the seams along with other insoluble residue. Swarms of horizontal microfractures, many of them filled with calcite and other residue, are associated with the seams. Vertical, tectonic fractures that constitute the reservoir porosity, intersect the solution seams. Pressure solution concentrated organic matter within the solution seams and oil was generated there. It is postulated that the accompanying increase in fluid volume raised the pore pressures and fractured the rock. The newly created microfractures were avenues for migration of fluids from the seams, perhaps by microfracture propagation.« less

The effect of tandem-ovoid titanium applicator on points A, B, bladder, and rectum doses in gynecological brachytherapy using 192Ir.

PubMed

Sadeghi, Mohammad Hosein; Sina, Sedigheh; Mehdizadeh, Amir; Faghihi, Reza; Moharramzadeh, Vahed; Meigooni, Ali Soleimani

2018-02-01

The dosimetry procedure by simple superposition accounts only for the self-shielding of the source and does not take into account the attenuation of photons by the applicators. The purpose of this investigation is an estimation of the effects of the tandem and ovoid applicator on dose distribution inside the phantom by MCNP5 Monte Carlo simulations. In this study, the superposition method is used for obtaining the dose distribution in the phantom without using the applicator for a typical gynecological brachytherapy (superposition-1). Then, the sources are simulated inside the tandem and ovoid applicator to identify the effect of applicator attenuation (superposition-2), and the dose at points A, B, bladder, and rectum were compared with the results of superposition. The exact dwell positions, times of the source, and positions of the dosimetry points were determined in images of a patient and treatment data of an adult woman patient from a cancer center. The MCNP5 Monte Carlo (MC) code was used for simulation of the phantoms, applicators, and the sources. The results of this study showed no significant differences between the results of superposition method and the MC simulations for different dosimetry points. The difference in all important dosimetry points was found to be less than 5%. According to the results, applicator attenuation has no significant effect on the calculated points dose, the superposition method, adding the dose of each source obtained by the MC simulation, can estimate the dose to points A, B, bladder, and rectum with good accuracy.

Linear viscoelastic limits of asphalt concrete at low and intermediate temperatures

NASA Astrophysics Data System (ADS)

Mehta, Yusuf A.

The purpose of this dissertation is to demonstrate the hypothesis that a region at which the behavior of asphalt concrete can be represented as a linear viscoelastic material can be determined at low and intermediate temperatures considering the stresses and strains typically developed in the pavements under traffic loading. Six mixtures containing different aggregate gradations and nominal maximum aggregate sizes varying from 12.5 to 37.5 mm were used in this study. The asphalt binder grade was the same for all mixtures. The mixtures were compacted to 7 +/- 1% air voids, using the Superpave Gyratory Compactor. Tests were conducted at low temperatures (-20°C and -10°C), using the indirect tensile test machine, and at intermediate temperatures (4°C and 20°C), using the Superpave shear machine. To determine the linear viscoelastic range of asphalt concrete, a relaxation test for 150 s, followed by a creep test for another 150 s, was conducted at 150 and 200 microstrains (1 microstrain = 1 x 10-6), at -20°C, and at 150 and 300 microstrains, at -10°C. A creep test for 200 s, followed by a recovery test for another 200 s, was conducted at stress levels up to 800 kPa at 4°C and up to 500 kPa at 20°C. At -20°C and -10°C, the behavior of the mixtures was linear viscoelastic at 200 and 300 microstrains, respectively. At intermediate temperatures (4°C and 20°C), an envelope defining the linear and nonlinear region in terms of stress as a function of shear creep compliance was constructed for all the mixtures. For creep tests conducted at 20°C, it was discovered that the commonly used protocol to verify the proportionality condition of linear viscoelastic behavior was unable to detect the appearance of nonlinear behavior at certain imposed shear stress levels. Said nonlinear behavior was easily detected, however, when checking the satisfaction of the superposition condition. The envelope constructed for determining when the material becomes nonlinear should be valid for mixtures similar to the ones tested in this study. Different envelopes should be used in the case of mixtures containing a very soft or a very stiff polymer modified binder. At 4°C, the typical values of stresses and material properties of mixtures fell within the linear viscoelastic region, considering the typical shear creep compliance values at loading times and stresses experienced in the field. However, typical values at 20°C fell within a region in which some, but not all of the mixtures tested in this study behaved linearly. It is known that the behavior of asphalt concrete mixture changes from linear to nonlinear, depending on the temperature and loading conditions. However, this study is the first of its kind in which both the proportionality and the superposition condition were evaluated. The experimental design and the analysis procedures presented in this study can be applied to similar experiments that may be conducted in the future to evaluate linearity of different types of asphalt concrete mixtures.

Adhesion of Mineral and Soot Aerosols can Strongly Affect their Scattering and Absorption Properties

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Jana M.

2012-01-01

We use the numerically exact superposition T-matrix method to compute the optical cross sections and the Stokes scattering matrix for polydisperse mineral aerosols (modeled as homogeneous spheres) covered with a large number of much smaller soot particles. These results are compared with the Lorenz-Mie results for a uniform external mixture of mineral and soot aerosols. We show that the effect of soot particles adhering to large mineral particles can be to change the extinction and scattering cross sections and the asymmetry parameter quite substantially. The effect on the phase function and degree of linear polarization can be equally significant.

Transonic Shock-Wave/Boundary-Layer Interactions on an Oscillating Airfoil

NASA Technical Reports Server (NTRS)

Davis, Sanford S.; Malcolm, Gerald N.

1980-01-01

Unsteady aerodynamic loads were measured on an oscillating NACA 64A010 airfoil In the NASA Ames 11 by 11 ft Transonic Wind Tunnel. Data are presented to show the effect of the unsteady shock-wave/boundary-layer interaction on the fundamental frequency lift, moment, and pressure distributions. The data show that weak shock waves induce an unsteady pressure distribution that can be predicted quite well, while stronger shock waves cause complex frequency-dependent distributions due to flow separation. An experimental test of the principles of linearity and superposition showed that they hold for weak shock waves while flows with stronger shock waves cannot be superimposed.

Instabilities in rapid solidification of multi-component alloys

NASA Astrophysics Data System (ADS)

Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

Rapid solidification of multi-component liquids occurs in many modern applications such as additive manufacturing. In the present work the interface departures from equilibrium consist of the segregation coefficient and liquidus slope depending on front speed, the one-sided, frozen-temperature approximation, and the alloy behaving as the superposition of individual components. Linear-stability theory is applied, showing that the cellular and oscillatory instabilities of the binary case are modified. The addition of components tends to destabilize the interface while the addition of a single large-diffusivity material can entirely suppress the oscillatory mode. Multiple minima in the neutral curve for the cellular mode occur.

High resolution particle tracking method by suppressing the wavefront aberrations

NASA Astrophysics Data System (ADS)

Chang, Xinyu; Yang, Yuan; Kou, Li; Jin, Lei; Lu, Junsheng; Hu, Xiaodong

2018-01-01

Digital in-line holographic microscopy is one of the most efficient methods for particle tracking as it can precisely measure the axial position of particles. However, imaging systems are often limited by detector noise, image distortions and human operator misjudgment making the particles hard to locate. A general method is used to solve this problem. The normalized holograms of particles were reconstructed to the pupil plane and then fit to a linear superposition of the Zernike polynomial functions to suppress the aberrations. Relative experiments were implemented to validate the method and the results show that nanometer scale resolution was achieved even when the holograms were poorly recorded.

Coherent response of a semiconductor microcavity in the strong coupling regime

NASA Astrophysics Data System (ADS)

Cassabois, G.; Triques, A. L. C.; Ferreira, R.; Delalande, C.; Roussignol, Ph; Bogani, F.

2000-05-01

We have studied the coherent dynamics of a semiconductor microcavity by means of interferometric correlation measurements with subpicosecond time resolution in a backscattering geometry. Evidence is brought of the resolution of a homogeneous polariton line in an inhomogeneously broadened exciton system. Surprisingly, photon-like polaritons exhibit an inhomogeneous dephasing. Moreover, we observe an unexpected stationary coherence up to 8 ps for the lower polariton branch close to resonance. All these experimental results are well reproduced within the framework of a linear dispersion theory assuming a coherent superposition of the reflectivity and resonant Rayleigh scattering signals with a well-defined relative phase.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

FastMag: Fast micromagnetic simulator for complex magnetic structures (invited)

NASA Astrophysics Data System (ADS)

Chang, R.; Li, S.; Lubarda, M. V.; Livshitz, B.; Lomakin, V.

2011-04-01

A fast micromagnetic simulator (FastMag) for general problems is presented. FastMag solves the Landau-Lifshitz-Gilbert equation and can handle multiscale problems with a high computational efficiency. The simulator derives its high performance from efficient methods for evaluating the effective field and from implementations on massively parallel graphics processing unit (GPU) architectures. FastMag discretizes the computational domain into tetrahedral elements and therefore is highly flexible for general problems. The magnetostatic field is computed via the superposition principle for both volume and surface parts of the computational domain. This is accomplished by implementing efficient quadrature rules and analytical integration for overlapping elements in which the integral kernel is singular. Thus, discretized superposition integrals are computed using a nonuniform grid interpolation method, which evaluates the field from N sources at N collocated observers in O(N) operations. This approach allows handling objects of arbitrary shape, allows easily calculating of the field outside the magnetized domains, does not require solving a linear system of equations, and requires little memory. FastMag is implemented on GPUs with ?> GPU-central processing unit speed-ups of 2 orders of magnitude. Simulations are shown of a large array of magnetic dots and a recording head fully discretized down to the exchange length, with over a hundred million tetrahedral elements on an inexpensive desktop computer.

Entanglement and quantum superposition induced by a single photon

NASA Astrophysics Data System (ADS)

Lü, Xin-You; Zhu, Gui-Lei; Zheng, Li-Li; Wu, Ying

2018-03-01

We predict the occurrence of single-photon-induced entanglement and quantum superposition in a hybrid quantum model, introducing an optomechanical coupling into the Rabi model. Originally, it comes from the photon-dependent quantum property of the ground state featured by the proposed hybrid model. It is associated with a single-photon-induced quantum phase transition, and is immune to the A2 term of the spin-field interaction. Moreover, the obtained quantum superposition state is actually a squeezed cat state, which can significantly enhance precision in quantum metrology. This work offers an approach to manipulate entanglement and quantum superposition with a single photon, which might have potential applications in the engineering of new single-photon quantum devices, and also fundamentally broaden the regime of cavity QED.

An exploration in acoustic radiation force experienced by cylindrical shells via resonance scattering theory.

PubMed

Rajabi, Majid; Behzad, Mehdi

2014-04-01

In nonlinear acoustic regime, a body insonified by a sound field is known to experience a steady force that is called the acoustic radiation force (RF). This force is a second-order quantity of the velocity potential function of the ambient medium. Exploiting the sufficiency of linear solution representation of potential function in RF formulation, and following the classical resonance scattering theorem (RST) which suggests the scattered field as a superposition of the resonant field and a background (non-resonant) component, we will show that the radiation force is a composition of three components: background part, resonant part and their interaction. Due to the nonlinearity effects, each part contains the contribution of pure partial waves in addition to their mutual interaction. The numerical results propose the residue component (i.e., subtraction of the background component from the RF) as a good indicator of the contribution of circumferential surface waves in RF. Defining the modal series of radiation force function and its components, it will be shown that within each partial wave, the resonance contribution can be synthesized as the Breit-Wigner form for adequately none-close resonant frequencies. The proposed formulation may be helpful essentially due to its inherent value as a canonical subject in physical acoustics. Furthermore, it may make a tunnel through the circumferential resonance reducing effects on radiation forces. Copyright © 2013 Elsevier B.V. All rights reserved.

Internal wave mode resonant triads in an arbitrarly stratified finite-depth ocean with background rotation

NASA Astrophysics Data System (ADS)

Varma, Dheeraj; Mathur, Manikandan

2017-11-01

Internal tides generated by barotropic tides on bottom topography or the spatially compact near-inertial mixed layer currents excited by surface winds can be conveniently represented in the linear regime as a superposition of vertical modes at a given frequency in an arbitrarily stratified ocean of finite depth. Considering modes (m , n) at a frequency ω in the primary wave field, we derive the weakly nonlinear solution, which contains a secondary wave at 2 ω that diverges when it forms a resonant triad with the primary waves. In nonuniform stratifications, resonant triads are shown to occur when the horizontal component of the classical RTI criterion k->1 +k->2 +k->3 = 0 is satisfied along with a non-orthogonality criterion. In nonuniform stratifications with a pycnocline, infinitely more pairs of primary wave modes (m , n) result in RTI when compared to a uniform stratification. Further, two nearby high modes at around the near-inertial frequency often form a resonant triad with a low mode at 2 ω , reminiscent of the features of PSI near the critical latitude. The theoretical framework is then adapted to investigate RTI in two different scenarios: low-mode internal tide scattering over topography, and internal wave beams incident on a pycnocline. The authors thank the Ministry of Earth Sciences, Government of India for financial support under the Monsoon Mission Grant MM/2014/IND-002.

Determination of Nerve Fiber Diameter Distribution From Compound Action Potential: A Continuous Approach.

PubMed

Un, M Kerem; Kaghazchi, Hamed

2018-01-01

When a signal is initiated in the nerve, it is transmitted along each nerve fiber via an action potential (called single fiber action potential (SFAP)) which travels with a velocity that is related with the diameter of the fiber. The additive superposition of SFAPs constitutes the compound action potential (CAP) of the nerve. The fiber diameter distribution (FDD) in the nerve can be computed from the CAP data by solving an inverse problem. This is usually achieved by dividing the fibers into a finite number of diameter groups and solve a corresponding linear system to optimize FDD. However, number of fibers in a nerve can be measured sometimes in thousands and it is possible to assume a continuous distribution for the fiber diameters which leads to a gradient optimization problem. In this paper, we have evaluated this continuous approach to the solution of the inverse problem. We have utilized an analytical function for SFAP and an assumed a polynomial form for FDD. The inverse problem involves the optimization of polynomial coefficients to obtain the best estimate for the FDD. We have observed that an eighth order polynomial for FDD can capture both unimodal and bimodal fiber distributions present in vivo, even in case of noisy CAP data. The assumed FDD distribution regularizes the ill-conditioned inverse problem and produces good results.

Simulating pad-electrodes with high-definition arrays in transcranial electric stimulation

NASA Astrophysics Data System (ADS)

Kempe, René; Huang, Yu; Parra, Lucas C.

2014-04-01

Objective. Research studies on transcranial electric stimulation, including direct current, often use a computational model to provide guidance on the placing of sponge-electrode pads. However, the expertise and computational resources needed for finite element modeling (FEM) make modeling impractical in a clinical setting. Our objective is to make the exploration of different electrode configurations accessible to practitioners. We provide an efficient tool to estimate current distributions for arbitrary pad configurations while obviating the need for complex simulation software. Approach. To efficiently estimate current distributions for arbitrary pad configurations we propose to simulate pads with an array of high-definition (HD) electrodes and use an efficient linear superposition to then quickly evaluate different electrode configurations. Main results. Numerical results on ten different pad configurations on a normal individual show that electric field intensity simulated with the sampled array deviates from the solutions with pads by only 5% and the locations of peak magnitude fields have a 94% overlap when using a dense array of 336 electrodes. Significance. Computationally intensive FEM modeling of the HD array needs to be performed only once, perhaps on a set of standard heads that can be made available to multiple users. The present results confirm that by using these models one can now quickly and accurately explore and select pad-electrode montages to match a particular clinical need.

Quantum formalism for classical statistics

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-06-01

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.

The inviscid pressure field on the tip of a semi-infinite wing and its application to the formation of a tip vortex

NASA Technical Reports Server (NTRS)

Hall, G. F.; Shamroth, S. J.; Mcdonald, H.; Briley, W. R.

1976-01-01

A method was developed for determining the aerodynamic loads on the tip of an infinitely thin, swept, cambered semi-infinite wing at an angle of attack which is operating subsonically in an inviscid medium and is subjected to a sinusoidal gust. Under the assumption of linearized aerodynamics, the loads on the tip are obtained by superposition of the steady aerodynamic results for angle of attack and camber, and the unsteady results for the response to the sinusoidal gust. The near field disturbance pressures in the fluid surrounding the tip are obtained by assuming a dipole representation for the loading on the tip and calculating the pressures accordingly. The near field pressures are used to drive a reduced form of the Navier-Stokes equations which yield the tip vortex formation. The combined viscid-inviscid analysis is applied to determining the pressures and examining the vortex rollup in the vicinity of an unswept, uncambered wing moving steadily at a Mach number of 0.2 at an angle of attack of 0.1 rad. The viscous tip flow calculation shows features expected in the tip flow such as the qualitatively proper development of boundary layers on both the upper and lower airfoil surfaces. In addition, application of the viscous solution leads to the generation of a circular type flow pattern above the airfoil suction surface.

Fundamental solution of the problem of linear programming and method of its determination

NASA Technical Reports Server (NTRS)

Petrunin, S. V.

1978-01-01

The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

The consistency of positive fully fuzzy linear system

NASA Astrophysics Data System (ADS)

Malkawi, Ghassan O.; Alfifi, Hassan Y.

2017-11-01

In this paper, the consistency of fuzziness of positive solution of the n × n fully fuzzy linear system (P - FFLS) is studied based on its associated linear system (P - ALS). That can consist of the whole entries of triangular fuzzy numbers in a linear system without fuzzy operations. The nature of solution is differentiated in case of fuzzy solution, non-fuzzy solution and fuzzy non-positive solution. Moreover, the analysis reveals that the P - ALS is applicable to provide the set of infinite number of solutions. Numerical examples are presented to illustrate the proposed analysis.

The effect of tandem-ovoid titanium applicator on points A, B, bladder, and rectum doses in gynecological brachytherapy using 192Ir

PubMed Central

Sadeghi, Mohammad Hosein; Mehdizadeh, Amir; Faghihi, Reza; Moharramzadeh, Vahed; Meigooni, Ali Soleimani

2018-01-01

Purpose The dosimetry procedure by simple superposition accounts only for the self-shielding of the source and does not take into account the attenuation of photons by the applicators. The purpose of this investigation is an estimation of the effects of the tandem and ovoid applicator on dose distribution inside the phantom by MCNP5 Monte Carlo simulations. Material and methods In this study, the superposition method is used for obtaining the dose distribution in the phantom without using the applicator for a typical gynecological brachytherapy (superposition-1). Then, the sources are simulated inside the tandem and ovoid applicator to identify the effect of applicator attenuation (superposition-2), and the dose at points A, B, bladder, and rectum were compared with the results of superposition. The exact dwell positions, times of the source, and positions of the dosimetry points were determined in images of a patient and treatment data of an adult woman patient from a cancer center. The MCNP5 Monte Carlo (MC) code was used for simulation of the phantoms, applicators, and the sources. Results The results of this study showed no significant differences between the results of superposition method and the MC simulations for different dosimetry points. The difference in all important dosimetry points was found to be less than 5%. Conclusions According to the results, applicator attenuation has no significant effect on the calculated points dose, the superposition method, adding the dose of each source obtained by the MC simulation, can estimate the dose to points A, B, bladder, and rectum with good accuracy. PMID:29619061

Asymptotic co- and post-seismic displacements in a homogeneous Maxwell sphere

NASA Astrophysics Data System (ADS)

Tang, He; Sun, Wenke

2018-07-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, that is, via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

Asymptotic Co- and Post-seismic displacements in a homogeneous Maxwell sphere

NASA Astrophysics Data System (ADS)

Tang, He; Sun, Wenke

2018-05-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, i.e. via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity, and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

Molecular weight between entanglements for κ- and ι-carrageenans in an ionic liquid.

PubMed

Horinaka, Jun-ichi; Urabayashi, Yuhei; Wang, Xiaochen; Takigawa, Toshikazu

2014-08-01

The molecular weight between entanglements (Me) for κ- and ι-carrageenans, sulfated galactans, was examined in concentrated solutions using an ionic liquid 1-butyl-3-methylimidazolium acetate as a solvent. The dynamic viscoelasticity data for the solutions measured at different temperatures were overlapped according to the time-temperature superposition principle, and the obtained master curves exhibited the flow and rubbery plateau zones, being typical of concentrated polymer solutions having entanglement coupling. The values of Me for κ- and ι-carrageenans in the solutions were determined from the plateau moduli. Then the values of Me in the molten state (Me,melt) estimated as a material constant to be 6.6×10(3) and 7.2×10(3), respectively. The close values of Me,melt for κ- and ι-carrageenans indicate that 4-sulfate group of ι-carrageenan are not so influential for the entanglement network. Compared with agarose, a non-sulfate galactan, carrageenans have larger values of average spacing between entanglements. Copyright © 2014 Elsevier B.V. All rights reserved.

Constructive Development of the Solutions of Linear Equations in Introductory Ordinary Differential Equations

ERIC Educational Resources Information Center

Mallet, D. G.; McCue, S. W.

2009-01-01

The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to…

Accuracy of a teleported squeezed coherent-state superposition trapped into a high-Q cavity

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

Sales, J. S.; Silva, L. F. da; Almeida, N. G. de

2011-03-15

We propose a scheme to teleport a superposition of squeezed coherent states from one mode of a lossy cavity to one mode of a second lossy cavity. Based on current experimental capabilities, we present a calculation of the fidelity demonstrating that accurate quantum teleportation can be achieved for some parameters of the squeezed coherent states superposition. The signature of successful quantum teleportation is present in the negative values of the Wigner function.

Accuracy of a teleported squeezed coherent-state superposition trapped into a high-Q cavity

NASA Astrophysics Data System (ADS)

Sales, J. S.; da Silva, L. F.; de Almeida, N. G.

2011-03-01

We propose a scheme to teleport a superposition of squeezed coherent states from one mode of a lossy cavity to one mode of a second lossy cavity. Based on current experimental capabilities, we present a calculation of the fidelity demonstrating that accurate quantum teleportation can be achieved for some parameters of the squeezed coherent states superposition. The signature of successful quantum teleportation is present in the negative values of the Wigner function.

Classical analogous of quantum cosmological perfect fluid models

NASA Astrophysics Data System (ADS)

Batista, A. B.; Fabris, J. C.; Gonçalves, S. V. B.; Tossa, J.

2001-05-01

Quantization in the minisuperspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state pQ= ρQ is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase.

Calculation of compressible flow about three-dimensional inlets with auxiliary inlets, slats and vanes by means of a panel method

NASA Technical Reports Server (NTRS)

Hess, J. L.; Friedman, D. M.; Clark, R. W.

1985-01-01

An efficient and user oriented method was constructed for calculating flow in and about complex inlet configurations. Efficiency is attained by: (1) the use of a panel method; (2) a technique of superposition for obtaining solutions at any inlet operating condition; and (3) employment of an advanced matrix iteration technique for solving large full systems of equations, including the nonlinear equations for the Kutta condition. User concerns are addressed by the provision of several novel graphical output options that yield a more complete comprehension of the flowfield than was possible previously.

Coherent superposition of propagation-invariant laser beams

NASA Astrophysics Data System (ADS)

Soskind, R.; Soskind, M.; Soskind, Y. G.

2012-10-01

The coherent superposition of propagation-invariant laser beams represents an important beam-shaping technique, and results in new beam shapes which retain the unique property of propagation invariance. Propagation-invariant laser beam shapes depend on the order of the propagating beam, and include Hermite-Gaussian and Laguerre-Gaussian beams, as well as the recently introduced Ince-Gaussian beams which additionally depend on the beam ellipticity parameter. While the superposition of Hermite-Gaussian and Laguerre-Gaussian beams has been discussed in the past, the coherent superposition of Ince-Gaussian laser beams has not received significant attention in literature. In this paper, we present the formation of propagation-invariant laser beams based on the coherent superposition of Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian beams of different orders. We also show the resulting field distributions of the superimposed Ince-Gaussian laser beams as a function of the ellipticity parameter. By changing the beam ellipticity parameter, we compare the various shapes of the superimposed propagation-invariant laser beams transitioning from Laguerre-Gaussian beams at one ellipticity extreme to Hermite-Gaussian beams at the other extreme.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Superposition Quantification

NASA Astrophysics Data System (ADS)

Chang, Li-Na; Luo, Shun-Long; Sun, Yuan

2017-11-01

The principle of superposition is universal and lies at the heart of quantum theory. Although ever since the inception of quantum mechanics a century ago, superposition has occupied a central and pivotal place, rigorous and systematic studies of the quantification issue have attracted significant interests only in recent years, and many related problems remain to be investigated. In this work we introduce a figure of merit which quantifies superposition from an intuitive and direct perspective, investigate its fundamental properties, connect it to some coherence measures, illustrate it through several examples, and apply it to analyze wave-particle duality. Supported by Science Challenge Project under Grant No. TZ2016002, Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences, Grant under No. 2008DP173182

A systematical rheological study of polysaccharide from Sophora alopecuroides L. seeds.

PubMed

Wu, Yan; Guo, Rui; Cao, Nannan; Sun, Xiangjun; Sui, Zhongquan; Guo, Qingbin

2018-01-15

The rheological properties of polysaccharide (SAP) from Sophora alopecuroides L. seeds were systematically investigated by fitting different models. The steady flow testing indicated that SAP exhibited shear-thinning behaviors, which were enhanced with increasing concentration and decreasing temperature. This was demonstrated quantitatively by Williamson and Arrhenius models. According to the generalized Morris equation, SAP exhibited random coil conformation with the potential to form weak gel-like network. On the other hand, multiple results of dynamic tests confirmed the viscoelastic properties of SAP, showing oscillatory behaviors between a dilute solution and an elastic gel. Furthermore, SAP solutions were thermorheologically stable without remarkable energetic interactions or structural heterogeneity, since their rheological patterns were successfully applied to Time-temperature superposition (TTS) principle, modified Cole-Cole analysis and Cox-Merz rule. Copyright © 2017 Elsevier Ltd. All rights reserved.

Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

NASA Astrophysics Data System (ADS)

Zhang, Dong; Kushibiki, Junichi; Zou, Wei

2006-10-01

We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO2/specimen/SiO2 multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33-96 MHz. Regarding two different ultrasonic devices, the accuracies of the measurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.

SU-E-T-91: Accuracy of Dose Calculation Algorithms for Patients Undergoing Stereotactic Ablative Radiotherapy

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

Tajaldeen, A; Ramachandran, P; Geso, M

2015-06-15

Purpose: The purpose of this study was to investigate and quantify the variation in dose distributions in small field lung cancer radiotherapy using seven different dose calculation algorithms. Methods: The study was performed in 21 lung cancer patients who underwent Stereotactic Ablative Body Radiotherapy (SABR). Two different methods (i) Same dose coverage to the target volume (named as same dose method) (ii) Same monitor units in all algorithms (named as same monitor units) were used for studying the performance of seven different dose calculation algorithms in XiO and Eclipse treatment planning systems. The seven dose calculation algorithms include Superposition, Fastmore » superposition, Fast Fourier Transform ( FFT) Convolution, Clarkson, Anisotropic Analytic Algorithm (AAA), Acurous XB and pencil beam (PB) algorithms. Prior to this, a phantom study was performed to assess the accuracy of these algorithms. Superposition algorithm was used as a reference algorithm in this study. The treatment plans were compared using different dosimetric parameters including conformity, heterogeneity and dose fall off index. In addition to this, the dose to critical structures like lungs, heart, oesophagus and spinal cord were also studied. Statistical analysis was performed using Prism software. Results: The mean±stdev with conformity index for Superposition, Fast superposition, Clarkson and FFT convolution algorithms were 1.29±0.13, 1.31±0.16, 2.2±0.7 and 2.17±0.59 respectively whereas for AAA, pencil beam and Acurous XB were 1.4±0.27, 1.66±0.27 and 1.35±0.24 respectively. Conclusion: Our study showed significant variations among the seven different algorithms. Superposition and AcurosXB algorithms showed similar values for most of the dosimetric parameters. Clarkson, FFT convolution and pencil beam algorithms showed large differences as compared to superposition algorithms. Based on our study, we recommend Superposition and AcurosXB algorithms as the first choice of algorithms in lung cancer radiotherapy involving small fields. However, further investigation by Monte Carlo simulation is required to confirm our results.« less

Nonlinear gyrotropic motion of skyrmion in a magnetic nanodisk

NASA Astrophysics Data System (ADS)

Chen, Yi-fu; Li, Zhi-xiong; Zhou, Zhen-wei; Xia, Qing-lin; Nie, Yao-zhuang; Guo, Guang-hua

2018-07-01

We study the nonlinear gyrotropic motion of a magnetic skyrmion in a nanodisk by means of micromagnetic simulations. The skyrmion is driven by a linearly polarized harmonic field with the frequency of counterclockwise gyrotropic mode. It is found that the motion of the skyrmion displays different patterns with increasing field amplitude. In the linear regime of weak driving field, the skyrmion performs a single counterclockwise gyrotropic motion. The guiding center of the skyrmion moves along a helical line from the centre of the nanodisk to a stable circular orbit. The stable orbital radius increases linearly with the field amplitude. When the driving field is larger than a critical value, the skyrmion exhibits complex nonlinear motion. With the advance of time, the motion trajectory of the skyrmion goes through a series of evolution process, from a single circular motion to a bird nest-like and a flower-like trajectory and finally, to a gear-like steady-state motion. The frequency spectra show that except the counterclockwise gyrotropic mode, the clockwise gyrotropic mode is also nonlinearly excited and its amplitude increases with time. The complex motion trajectory of the skyrmion is the result of superposition of the two gyrotropic motions with changing amplitude. Both the linear and nonlinear gyrotropic motions of the skyrmion can be well described by a generalized Thiele's equation of motion.

Towards quantum superposition of a levitated nanodiamond with a NV center

NASA Astrophysics Data System (ADS)

Li, Tongcang

2015-05-01

Creating large Schrödinger's cat states with massive objects is one of the most challenging goals in quantum mechanics. We have previously achieved an important step of this goal by cooling the center-of-mass motion of a levitated microsphere from room temperature to millikelvin temperatures with feedback cooling. To generate spatial quantum superposition states with an optical cavity, however, requires a very strong quadratic coupling that is difficult to achieve. We proposed to optically trap a nanodiamond with a nitrogen-vacancy (NV) center in vacuum, and generate large spatial superposition states using the NV spin-optomechanical coupling in a strong magnetic gradient field. The large spatial superposition states can be used to study objective collapse theories of quantum mechanics. We have optically trapped nanodiamonds in air and are working towards this goal.

Three-dimensional semi-analytical solution to groundwater flow in confined and unconfined wedge-shaped aquifers

NASA Astrophysics Data System (ADS)

Sedghi, Mohammad Mahdi; Samani, Nozar; Sleep, Brent

2009-06-01

The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471-80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.

Mastering the Concepts of Geologic Time: Novice Students' Understanding of the Principles of Relative Age

NASA Astrophysics Data System (ADS)

Speta, M.; Reid, L.

2010-12-01

Misconceptions can adversely affect students’ mastery of the fundamental geoscience concepts necessary for development of the knowledge base required to become a professional geoscientist. In the fall of 2009, in-class learning assessments were introduced into a large (400 student) undergraduate introductory geoscience course to help students develop expert-like problem solving skills for geologic problems. They were also designed to reveal students’ misconceptions on geoscience concepts in order to help direct the course of instruction. These assessments were based on simple, real-world scenarios that geoscientists encounter in their research. One of these assessments focused on the application of concepts of geologic time. It asked students to give the relative ages of granite, schist and shale based on a sketch of two outcrops, and to describe the reasoning behind their answer. In order to test all of the principles of relative age, the assignment had two possible solutions. A post-course analysis of student responses on these assessments was carried out using a modified constant comparative analysis method to identify common misconceptions. This analysis revealed that 61% of students failed to identify both possible solutions. Furthermore, 55% of students applied the principle of superposition to intrusive igneous and metamorphic rocks, and 18% treated the once connected outcrops as having separate geologic histories. 56% of students could not support their proposed geologic history with appropriate reasoning. These results suggest that the principles of relative geologic time that students had the greatest difficulty with were when to apply the principle of superposition and how to apply the principle of original continuity. Students also had difficulty using the principles of relative age to provide appropriate scientific reasoning for their choices.

Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

NASA Astrophysics Data System (ADS)

Bakker, Mark

2010-08-01

A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.

Valley-polarized quantum transport generated by gauge fields in graphene

NASA Astrophysics Data System (ADS)

Settnes, Mikkel; Garcia, Jose H.; Roche, Stephan

2017-09-01

We report on the possibility to simultaneously generate in graphene a bulk valley-polarized dissipative transport and a quantum valley Hall effect by combining strain-induced gauge fields and real magnetic fields. Such unique phenomenon results from a ‘resonance/anti-resonance’ effect driven by the superposition/cancellation of superimposed gauge fields which differently affect time reversal symmetry. The onset of a valley-polarized Hall current concomitant to a dissipative valley-polarized current flow in the opposite valley is revealed by a {{e}2}/h Hall conductivity plateau. We employ efficient linear scaling Kubo transport methods combined with a valley projection scheme to access valley-dependent conductivities and show that the results are robust against disorder.

Dielectric spectroscopy in aqueous solutions of oligosaccharides: Experiment meets simulation

NASA Astrophysics Data System (ADS)

Weingärtner, Hermann; Knocks, Andrea; Boresch, Stefan; Höchtl, Peter; Steinhauser, Othmar

2001-07-01

We report the frequency-dependent complex dielectric permittivity of aqueous solutions of the homologous saccharides D(+)-glucose, maltose, and maltotriose in the frequency range 200 MHz⩽ν⩽20 GHz. For each solute, solutions having concentrations between 0.01 and 1 mol dm-3 were studied. In all measured spectra two dispersion/loss regions could be discerned. With the exception of the two most concentrated maltotriose solutions, a good description of the spectra by the superposition of two Debye processes was possible. The amplitudes and correlation times of the glucose and maltose solutions determined from fits of the experimental data were compared to those obtained in an earlier molecular dynamics study of such systems; the overall agreement between experiment and simulation is quite satisfactory. A dielectric component analysis of the simulation results permitted a more detailed assignment of the relaxation processes occurring on the molecular level. The physical picture emerging from this analysis is compared with traditional hydration models used in the interpretation of measured dielectric data. It is shown that the usual standard models do not capture an important contribution arising from cross terms due to dipolar interactions between solute and water, as well as between hydration water and bulk water. This finding suggests that conventional approaches to determine molecular dipole moments of the solutes may be problematic. This is certainly the case for solutes with small molecular dipole moments, but strong solute-solvent interactions, such as the saccharides studied here.

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Physical aging effects on the compressive linear viscoelastic creep of IM7/K3B composite

NASA Technical Reports Server (NTRS)

Veazie, David R.; Gates, Thomas S.

1995-01-01

An experimental study was undertaken to establish the viscoelastic behavior of 1M7/K3B composite in compression at elevated temperature. Creep compliance, strain recovery and the effects of physical aging on the time dependent response was measured for uniaxial loading at several isothermal conditions below the glass transition temperature (T(g)). The IM7/K3B composite is a graphite reinforced thermoplastic polyimide with a T(g) of approximately 240 C. In a composite, the two matrix dominated compliance terms associated with time dependent behavior occur in the transverse and shear directions. Linear viscoelasticity was used to characterize the creep/recovery behavior and superposition techniques were used to establish the physical aging related material constants. Creep strain was converted to compliance and measured as a function of test time and aging time. Results included creep compliance master curves, physical aging shift factors and shift rates. The description of the unique experimental techniques required for compressive testing is also given.

Control of polarization rotation in nonlinear propagation of fully structured light

NASA Astrophysics Data System (ADS)

Gibson, Christopher J.; Bevington, Patrick; Oppo, Gian-Luca; Yao, Alison M.

2018-03-01

Knowing and controlling the spatial polarization distribution of a beam is of importance in applications such as optical tweezing, imaging, material processing, and communications. Here we show how the polarization distribution is affected by both linear and nonlinear (self-focusing) propagation. We derive an analytical expression for the polarization rotation of fully structured light (FSL) beams during linear propagation and show that the observed rotation is due entirely to the difference in Gouy phase between the two eigenmodes comprising the FSL beams, in excellent agreement with numerical simulations. We also explore the effect of cross-phase modulation due to a self-focusing (Kerr) nonlinearity and show that polarization rotation can be controlled by changing the eigenmodes of the superposition, and physical parameters such as the beam size, the amount of Kerr nonlinearity, and the input power. Finally, we show that by biasing cylindrical vector beams to have elliptical polarization, we can vary the polarization state from radial through spiral to azimuthal using nonlinear propagation.

Stationary bubbles and their tunneling channels toward trivial geometry

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

Chen, Pisin; Yeom, Dong-han; Domènech, Guillem

2016-04-01

In the path integral approach, one has to sum over all histories that start from the same initial condition in order to obtain the final condition as a superposition of histories. Applying this into black hole dynamics, we consider stable and unstable stationary bubbles as a reasonable and regular initial condition. We find examples where the bubble can either form a black hole or tunnel toward a trivial geometry, i.e., with no singularity nor event horizon. We investigate the dynamics and tunneling channels of true vacuum bubbles for various tensions. In particular, in line with the idea of superposition ofmore » geometries, we build a classically stable stationary thin-shell solution in a Minkowski background where its fate is probabilistically given by non-perturbative effects. Since there exists a tunneling channel toward a trivial geometry in the entire path integral, the entire information is encoded in the wave function. This demonstrates that the unitarity is preserved and there is no loss of information when viewed from the entire wave function of the universe, whereas a semi-classical observer, who can see only a definitive geometry, would find an effective loss of information. This may provide a resolution to the information loss dilemma.« less

Stationary bubbles and their tunneling channels toward trivial geometry

DOE PAGES

Chen, Pisin; Domènech, Guillem; Sasaki, Misao; ...

2016-04-07

In the path integral approach, one has to sum over all histories that start from the same initial condition in order to obtain the final condition as a superposition of histories. Applying this into black hole dynamics, we consider stable and unstable stationary bubbles as a reasonable and regular initial condition. We find examples where the bubble can either form a black hole or tunnel toward a trivial geometry, i.e., with no singularity nor event horizon. We investigate the dynamics and tunneling channels of true vacuum bubbles for various tensions. In particular, in line with the idea of superposition ofmore » geometries, we build a classically stable stationary thin-shell solution in a Minkowski background where its fate is probabilistically given by non-perturbative effects. Since there exists a tunneling channel toward a trivial geometry in the entire path integral, the entire information is encoded in the wave function. This demonstrates that the unitarity is preserved and there is no loss of information when viewed from the entire wave function of the universe, whereas a semi-classical observer, who can see only a definitive geometry, would find an effective loss of information. Ultimately, this may provide a resolution to the information loss dilemma.« less

Fracture toughness of brittle materials determined with chevron notch specimens

NASA Technical Reports Server (NTRS)

Shannon, J. L., Jr.; Bursey, R. T.; Munz, D.; Pierce, W. S.

1980-01-01

The use of chevron-notch specimens for determining the plane strain fracture toughness (K sub Ic) of brittle materials is discussed. Three chevron-notch specimens were investigated: short bar, short rod, and four-point-bend. The dimensionless stress intensity coefficient used in computing K sub Ic is derived for the short bar specimen from the superposition of ligament-dependent and ligament-independent solutions for the straight through crack, and also from experimental compliance calibrations. Coefficients for the four-point-bend specimen were developed by the same superposition procedure, and with additional refinement using the slice model of Bluhm. Short rod specimen stress intensity coefficients were determined only by experimental compliance calibration. Performance of the three chevron-notch specimens and their stress intensity factor relations were evaluated by tests on hot-pressed silicon nitride and sintered aluminum oxide. Results obtained with the short bar and the four-point-bend specimens on silicon nitride are in good agreement and relatively free of specimen geometry and size effects within the range investigated. Results on aluminum oxide were affected by specimen size and chevron-notch geometry, believed due to a rising crack growth resistance curve for the material. Only the results for the short bar specimen are presented in detail.

Nonlinear Diophantine equation 11 x +13 y = z 2

NASA Astrophysics Data System (ADS)

Sugandha, A.; Tripena, A.; Prabowo, A.; Sukono, F.

2018-03-01

This research aims to obtaining the solutions (if any) from the Non Linear Diophantine equation of 11 x + 13 y = z 2. There are 3 possibilities to obtain the solutions (if any) from the Non Linear Diophantine equation, namely single, multiple, and no solution. This research is conducted in two stages: (1) by utilizing simulation to obtain the solutions (if any) from the Non Linear Diophantine equation of 11 x + 13 y = z 2 and (2) by utilizing congruency theory with its characteristics proven that the Non Linear Diophantine equation has no solution for non negative whole numbers (integers) of x, y, z.

GENERAL: The Analytic Solution of Schrödinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

NASA Astrophysics Data System (ADS)

Hu, Xian-Quan; Luo, Guang; Cui, Li-Peng; Li, Fang-Yu; Niu, Lian-Bin

2009-03-01

The analytic solution of the radial Schrödinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrödinger equation is V(r) = α1r8 + α2r3 + α3r2 + β3r-1 + β2r-3 + β1r-4. Generally speaking, there is only an approximate solution, but not analytic solution for Schrödinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrödinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schrödinger equation; and lastly, they discuss the solutions and make conclusions.

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

Góźdź, A., E-mail: andrzej.gozdz@umcs.lublin.pl; Góźdź, M., E-mail: mgozdz@kft.umcs.lublin.pl

The theory of neutrino oscillations rests on the assumption, that the interaction basis and the physical (mass) basis of neutrino states are different. Therefore neutrino is produced in a certain welldefined superposition of three mass eigenstates, which propagate separately and may be detected as a different superposition. This is called flavor oscillations. It is, however, not clear why neutrinos behave this way, i.e., what is the underlying mechanism which leads to the production of a superposition of physical states in a single reaction. In this paper we argue, that one of the reasons may be connected with the temporal structuremore » of the process. In order to discuss the role of time in processes on the quantum level, we use a special formulation of the quantum mechanics, which is based on the projection time evolution. We arrive at the conclusion, that for short reaction times the formation of a superposition of states of similar masses is natural.« less

Experimental superposition of orders of quantum gates

PubMed Central

Procopio, Lorenzo M.; Moqanaki, Amir; Araújo, Mateus; Costa, Fabio; Alonso Calafell, Irati; Dowd, Emma G.; Hamel, Deny R.; Rozema, Lee A.; Brukner, Časlav; Walther, Philip

2015-01-01

Quantum computers achieve a speed-up by placing quantum bits (qubits) in superpositions of different states. However, it has recently been appreciated that quantum mechanics also allows one to ‘superimpose different operations'. Furthermore, it has been shown that using a qubit to coherently control the gate order allows one to accomplish a task—determining if two gates commute or anti-commute—with fewer gate uses than any known quantum algorithm. Here we experimentally demonstrate this advantage, in a photonic context, using a second qubit to control the order in which two gates are applied to a first qubit. We create the required superposition of gate orders by using additional degrees of freedom of the photons encoding our qubits. The new resource we exploit can be interpreted as a superposition of causal orders, and could allow quantum algorithms to be implemented with an efficiency unlikely to be achieved on a fixed-gate-order quantum computer. PMID:26250107

Solution of linear systems by a singular perturbation technique

NASA Technical Reports Server (NTRS)

Ardema, M. D.

1976-01-01

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

A linear programming approach to reconstructing subcellular structures from confocal images for automated generation of representative 3D cellular models.

PubMed

Wood, Scott T; Dean, Brian C; Dean, Delphine

2013-04-01

This paper presents a novel computer vision algorithm to analyze 3D stacks of confocal images of fluorescently stained single cells. The goal of the algorithm is to create representative in silico model structures that can be imported into finite element analysis software for mechanical characterization. Segmentation of cell and nucleus boundaries is accomplished via standard thresholding methods. Using novel linear programming methods, a representative actin stress fiber network is generated by computing a linear superposition of fibers having minimum discrepancy compared with an experimental 3D confocal image. Qualitative validation is performed through analysis of seven 3D confocal image stacks of adherent vascular smooth muscle cells (VSMCs) grown in 2D culture. The presented method is able to automatically generate 3D geometries of the cell's boundary, nucleus, and representative F-actin network based on standard cell microscopy data. These geometries can be used for direct importation and implementation in structural finite element models for analysis of the mechanics of a single cell to potentially speed discoveries in the fields of regenerative medicine, mechanobiology, and drug discovery. Copyright © 2012 Elsevier B.V. All rights reserved.

Molecular Mobility in Phase Segregated Bottlebrush Block Copolymer Melts

NASA Astrophysics Data System (ADS)

Yavitt, Benjamin; Gai, Yue; Song, Dongpo; Winter, H. Henning; Watkins, James

We investigate the linear viscoelastic behavior of poly(styrene)-block-poly(ethylene oxide) (PS-b-PEO) brush block copolymer (BBCP) materials over a range of vol. fractions and with side chain lengths below the entanglement molecular weights. The high chain mobility of the brush architecture results in rapid micro-phase segregation of the brush copolymer segments, which occurs during thermal annealing at mild temperatures. Master curves of the dynamic moduli were obtained by time-temperature superposition. The reduced degree of chain entanglements leads to a unique liquid-like rheology similar to that of bottlebrush homopolymers, even in the phase segregated state. We also explore the alignment of phase segregated domains at exceptionally low strain amplitudes (γ = 0.01) and mild processing temperatures using small angle X-ray scattering (SAXS). Domain orientation occurred readily at strains within the linear viscoelastic regime without noticeable effect on the moduli. This interplay of high molecular mobility and rapid phase segregation that are exhibited simultaneously in BBCPs is in contrast to the behavior of conventional linear block copolymer (LBCP) analogs and opens up new possibilities for processing BBCP materials for a wide range of nanotechnology applications. NSF Center for Hierarchical Manufacturing at the University of Massachusetts, Amherst (CMMI-1025020).

Unique Properties and Prospects: Quantum Theory of the Orbital Angular Momentum of Ince-Gauss Beams

NASA Astrophysics Data System (ADS)

Plick, William; Krenn, Mario; Fickler, Robert; Ramelow, Sven; Zeilinger, Anton

2012-02-01

The Ince-Gauss modes represent a new addition to the standard solutions to the paraxial wave equation. Parametrized by the ellipticity of the beam, they span the solution space between the Hermite-Gauss and the Laguerre-Gauss modes. These beams may be decomposed in either basis, and single photons in the Ince-Gauss modes exist naturally as superpositions of either Laguerre-Gauss or Hermite-Gauss modes. We present the fully quantum theory of the orbital angular momentum of these beams. Interesting features that arise are: stable beams with fractional orbital angular momentum, non-monotonic behavior of the OAM with respect to ellipticity, and the possibility of orthogonal modes possessing the same OAM. We believe that these modes may open up a fully new parameter space for quantum informatics and communication, and thus are worthy of thorough study.

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

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

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

A study of tyre cavity resonance and noise reduction using inner trim

NASA Astrophysics Data System (ADS)

Mohamed, Zamri; Wang, Xu

2015-01-01

A study of tyre inner trim as a method for reducing tyre cavity resonance noise is presented. The tyre is modelled as a rectangular toroid where only the outside shell is flexible. A modal series solution of the sound pressure frequency response inside the tyre cavity is derived from the wave equation using modal superposition. In the solution with the rigid and flexible wall boundary condition, the effect of placing a trim layer onto the inner surface of the tyre tread plate wall is reflected by adding a damping loss term in the sound pressure frequency response function. The numerical simulation result was then compared with the result obtained from a roving impact test performed on a tyre. The results show that selective trim material may be effective for reducing the structure-borne noise magnitude resulting from the tyre cavity resonance.

Modal sound transmission loss of a single leaf panel: Asymptotic solutions.

PubMed

Wang, Chong

2015-12-01

In a previously published paper [C. Wang, J. Acoust. Soc. Am. 137(6), 3514-3522 (2015)], the modal sound transmission coefficients of a single leaf panel were discussed with regard to the inter-modal coupling effects. By incorporating such effect into the equivalent modal radiation impedance, which is directly related to the modal sound transmission coefficient of each mode, the overall sound transmission loss for both normal and randomized sound incidences was computed through a simple modal superposition. Benefiting from the analytical expressions of the equivalent modal impedance and modal transmission coefficients, in this paper, behaviors of modal sound transmission coefficients in several typical frequency ranges are discussed in detail. Asymptotic solutions are also given for the panels with relatively low bending stiffnesses, for which the sound transmission loss has been assumed to follow the mass law of a limp panel. Results are also compared to numerical analysis and the renowned mass law theories.

A sparse equivalent source method for near-field acoustic holography.

PubMed

Fernandez-Grande, Efren; Xenaki, Angeliki; Gerstoft, Peter

2017-01-01

This study examines a near-field acoustic holography method consisting of a sparse formulation of the equivalent source method, based on the compressive sensing (CS) framework. The method, denoted Compressive-Equivalent Source Method (C-ESM), encourages spatially sparse solutions (based on the superposition of few waves) that are accurate when the acoustic sources are spatially localized. The importance of obtaining a non-redundant representation, i.e., a sensing matrix with low column coherence, and the inherent ill-conditioning of near-field reconstruction problems is addressed. Numerical and experimental results on a classical guitar and on a highly reactive dipole-like source are presented. C-ESM is valid beyond the conventional sampling limits, making wide-band reconstruction possible. Spatially extended sources can also be addressed with C-ESM, although in this case the obtained solution does not recover the spatial extent of the source.

Nanoprobe diffusion in entangled polymer solutions: Linear vs. unconcatenated ring chains

NASA Astrophysics Data System (ADS)

Nahali, Negar; Rosa, Angelo

2018-05-01

We employ large-scale molecular dynamics computer simulations to study the problem of nanoprobe diffusion in entangled solutions of linear polymers and unknotted and unconcatenated circular (ring) polymers. By tuning both the diameter of the nanoprobe and the density of the solution, we show that nanoprobes of diameter smaller than the entanglement distance (tube diameter) of the solution display the same (Rouse-like) behavior in solutions of both polymer architectures. Instead, nanoprobes with larger diameters appear to diffuse markedly faster in solutions of rings than in solutions of linear chains. Finally, by analysing the distribution functions of spatial displacements, we find that nanoprobe motion in rings' solutions shows both Gaussian and ergodic behaviors, in all regimes considered, while, in solutions of linear chains, nanoprobes exceeding the size of the tube diameter show a transition to non-Gaussian and non-ergodic motion. Our results emphasize the role of chain architecture in the motion of nanoprobes dispersed in polymer solutions.

Anomaly General Circulation Models.

NASA Astrophysics Data System (ADS)

Navarra, Antonio

The feasibility of the anomaly model is assessed using barotropic and baroclinic models. In the barotropic case, both a stationary and a time-dependent model has been formulated and constructed, whereas only the stationary, linear case is considered in the baroclinic case. Results from the barotropic model indicate that a relation between the stationary solution and the time-averaged non-linear solution exists. The stationary linear baroclinic solution can therefore be considered with some confidence. The linear baroclinic anomaly model poses a formidable mathematical problem because it is necessary to solve a gigantic linear system to obtain the solution. A new method to find solution of large linear system, based on a projection on the Krylov subspace is shown to be successful when applied to the linearized baroclinic anomaly model. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be inverted to obtain the solution. With an appropriate setting of the damping parameters, the iterative Krylov method reaches a solution even using a Krylov subspace ten times smaller than the original space of the problem. This generality allows the treatment of the important problem of linear waves in the atmosphere. A larger class (nonzonally symmetric) of basic states can now be treated for the baroclinic primitive equations. These problem leads to large unsymmetrical linear systems of order 10000 and more which can now be successfully tackled by the Krylov method. The (R7) linear anomaly model is used to investigate extensively the linear response to equatorial and mid-latitude prescribed heating. The results indicate that the solution is deeply affected by the presence of the stationary waves in the basic state. The instability of the asymmetric flows, first pointed out by Simmons et al. (1983), is active also in the baroclinic case. However, the presence of baroclinic processes modifies the dominant response. The most sensitive areas are identified; they correspond to north Japan, the Pole and Greenland regions. A limited set of higher resolution (R15) experiments indicate that this situation is still present and enhanced at higher resolution. The linear anomaly model is also applied to a realistic case. (Abstract shortened with permission of author.).

A novel algorithm for the calculation of physical and biological irradiation quantities in scanned ion beam therapy: the beamlet superposition approach

NASA Astrophysics Data System (ADS)

Russo, G.; Attili, A.; Battistoni, G.; Bertrand, D.; Bourhaleb, F.; Cappucci, F.; Ciocca, M.; Mairani, A.; Milian, F. M.; Molinelli, S.; Morone, M. C.; Muraro, S.; Orts, T.; Patera, V.; Sala, P.; Schmitt, E.; Vivaldo, G.; Marchetto, F.

2016-01-01

The calculation algorithm of a modern treatment planning system for ion-beam radiotherapy should ideally be able to deal with different ion species (e.g. protons and carbon ions), to provide relative biological effectiveness (RBE) evaluations and to describe different beam lines. In this work we propose a new approach for ion irradiation outcomes computations, the beamlet superposition (BS) model, which satisfies these requirements. This model applies and extends the concepts of previous fluence-weighted pencil-beam algorithms to quantities of radiobiological interest other than dose, i.e. RBE- and LET-related quantities. It describes an ion beam through a beam-line specific, weighted superposition of universal beamlets. The universal physical and radiobiological irradiation effect of the beamlets on a representative set of water-like tissues is evaluated once, coupling the per-track information derived from FLUKA Monte Carlo simulations with the radiobiological effectiveness provided by the microdosimetric kinetic model and the local effect model. Thanks to an extension of the superposition concept, the beamlet irradiation action superposition is applicable for the evaluation of dose, RBE and LET distributions. The weight function for the beamlets superposition is derived from the beam phase space density at the patient entrance. A general beam model commissioning procedure is proposed, which has successfully been tested on the CNAO beam line. The BS model provides the evaluation of different irradiation quantities for different ions, the adaptability permitted by weight functions and the evaluation speed of analitical approaches. Benchmarking plans in simple geometries and clinical plans are shown to demonstrate the model capabilities.

Receptivity of the compressible mixing layer

NASA Astrophysics Data System (ADS)

Barone, Matthew F.; Lele, Sanjiva K.

2005-09-01

Receptivity of compressible mixing layers to general source distributions is examined by a combined theoretical/computational approach. The properties of solutions to the adjoint Navier Stokes equations are exploited to derive expressions for receptivity in terms of the local value of the adjoint solution. The result is a description of receptivity for arbitrary small-amplitude mass, momentum, and heat sources in the vicinity of a mixing-layer flow, including the edge-scattering effects due to the presence of a splitter plate of finite width. The adjoint solutions are examined in detail for a Mach 1.2 mixing-layer flow. The near field of the adjoint solution reveals regions of relatively high receptivity to direct forcing within the mixing layer, with receptivity to nearby acoustic sources depending on the source type and position. Receptivity ‘nodes’ are present at certain locations near the splitter plate edge where the flow is not sensitive to forcing. The presence of the nodes is explained by interpretation of the adjoint solution as the superposition of incident and scattered fields. The adjoint solution within the boundary layer upstream of the splitter-plate trailing edge reveals a mechanism for transfer of energy from boundary-layer stability modes to Kelvin Helmholtz modes. Extension of the adjoint solution to the far field using a Kirchhoff surface gives the receptivity of the mixing layer to incident sound from distant sources.

Compact piezoelectric micromotor with a single bulk lead zirconate titanate stator

NASA Astrophysics Data System (ADS)

Yan, Liang; Lan, Hua; Jiao, Zongxia; Chen, Chin-Yin; Chen, I.-Ming

2013-04-01

The advance of micro/nanotechnology promotes the development of micromotors in recent years. In this article, a compact piezoelectric ultrasonic micromotor with a single bulk lead zirconate titanate stator is proposed. A traveling wave is generated by superposition of bending modes with 90° phase difference excited by d15 inverse piezoelectric effects. The operating principle simplifies the system structure significantly, and provides a miniaturization solution. A research prototype with the size of 0.75× 0.75×1.55 mm is developed. It can produce start-up torque of 0.27μNmand maximum speed of 2760 r/min at 14RMS.

Transport toward a well in highly heterogeneous aquifer

NASA Astrophysics Data System (ADS)

Di Dato, Mariaines; de Barros, Felipe P. J.; Bellin, Alberto; Fiori, Aldo

2017-04-01

Solute transport toward a well is a challenging subject in subsurface hydrology since the complexity of the mathematical model is tremendously increased by the non-uniformity of the mean flow and heterogeneity of the formation. Up to date, analytical solutions for such flow configurations are limited to low heterogeneous conditions. On the other hand, numerical simulations in 3D highly heterogeneous formations are computationally expensive and plagued by numerical errors. In this work we propose an analytical solution for the Breakthrough Curve (BTC) at the well for an instantaneous linear injection across the aquifer's thickness for any degree of heterogeneity of the porous medium. Our solution makes use of the Multi Indicator Model-Self Consistent Approximation (MIMSCA), by which the aquifer is conceptualized as an ensemble of blocks of constant hydraulic conductivity K randomly drawn from a lognormal distribution. In order to apply MIMSCA, we assume the flow as locally uniform, given that K is uniform within the block. With this approximation, the travel time to the well is equal to the superposition of the time spent by the solute particle within each block. We emphasize that, despite the approximations introduced, the model is able to reproduce the laboratory experiment of [1] without the need to fit any transport parameters. In this work, we present results for two different injection modes: a resident injection (e.g., residual DNAPL) and a flux proportional injection (e.g., leakage from a passive well). The proposed methodology allows to quantify the BTC at the well as a function of few parameters such as the injection mode and the statistical structure of the aquifer (geometric mean, variance and integral scale of the hydraulic conductivity field). Results illustrate that the release condition has a strong impact on the shape of the BTC. Furthermore, the difference between different injection modes increases with the heterogeneity of the K-field. The importance of the both injection mode and heterogeneity degree are also elucidated on the early and late solute arrival times at the well. Finally, we show how travel times become ergodic only for very thick aquifers, even in case of mild heterogeneity. We emphasize that the present framework has a practical validity, giving an affordable, although approximated, first estimation of mass arrival at an extraction well. References [1] Fernàndez-Garcia, D., T. H. Illangasekare, and H. Rajaram (2004), Conservative and sorptive forced-gradient and uniform flow tracer tests in a three-dimensional laboratory test aquifer, Water Resour. Res., 40, W10103, doi:10.1029/2004WR003112.

Polarization and propagation characteristics of switchable first-order azimuthally asymmetric beam generated in dual-mode fiber.

PubMed

Khan, Saba N; Chatterjee, Sudip K; Chaudhuri, Partha Roy

2015-02-20

We report here the controlled generation of a linearly polarized first-order azimuthally asymmetric beam (F-AAB) in a dual-mode fiber (DMF) by appropriate superposition of selectively excited zeroth-order vector modes that are doughnut-shaped azimuthally symmetric beams (D-ASBs). We first demonstrate continually switching polarization mode structures having an identical two-lobe intensity profile (i.e., intra-F-AAB conversion). Then, under a distinct launching state, we generate mode structures progressively toggling between the doughnut-shaped profile and two-lobe pattern having dissimilar polarization orientations (i.e., F-AAB to D-ASB conversion). Interestingly, a decentralized elliptical Gaussian beam possessing homogenous spatial polarization is obtained by enhancing the contribution of the fundamental mode (HE₁₁/LP₀₁) in selectively excited F-AAB. A smoothly varying azimuth of the input beam in this situation resulted in redistribution of transverse energy procuring a unique and exciting unconventional two-grain T-polarized beam having mutually orthogonal state of polarization (SOP). All of the above three were achieved under a given set of launching conditions (tilt/offset) of a Gaussian mode (TEM₀₀) devised with changing SOP of the input beam. A strong modulation in the output beam characteristics was also observed with the variation in propagation distance (for a fixed input SOP) owing to the large difference in propagation constants of the participating modes (LP₀₁ and one of the F-AABs). Finally, this particular study led to a design for a low-cost highly sensitive strain measuring device based on tracking the centroid movement of the output intensity pattern. Each of our experimentally observed intensity/polarization distributions is theoretically mapped on a one-to-one basis considering a linear superposition of appropriately excited LP basis modes of the waveguide toward a complete understanding of the polarization and mode propagation in the dual-mode structure.

GPU-accelerated Monte Carlo convolution/superposition implementation for dose calculation.

PubMed

Zhou, Bo; Yu, Cedric X; Chen, Danny Z; Hu, X Sharon

2010-11-01

Dose calculation is a key component in radiation treatment planning systems. Its performance and accuracy are crucial to the quality of treatment plans as emerging advanced radiation therapy technologies are exerting ever tighter constraints on dose calculation. A common practice is to choose either a deterministic method such as the convolution/superposition (CS) method for speed or a Monte Carlo (MC) method for accuracy. The goal of this work is to boost the performance of a hybrid Monte Carlo convolution/superposition (MCCS) method by devising a graphics processing unit (GPU) implementation so as to make the method practical for day-to-day usage. Although the MCCS algorithm combines the merits of MC fluence generation and CS fluence transport, it is still not fast enough to be used as a day-to-day planning tool. To alleviate the speed issue of MC algorithms, the authors adopted MCCS as their target method and implemented a GPU-based version. In order to fully utilize the GPU computing power, the MCCS algorithm is modified to match the GPU hardware architecture. The performance of the authors' GPU-based implementation on an Nvidia GTX260 card is compared to a multithreaded software implementation on a quad-core system. A speedup in the range of 6.7-11.4x is observed for the clinical cases used. The less than 2% statistical fluctuation also indicates that the accuracy of the authors' GPU-based implementation is in good agreement with the results from the quad-core CPU implementation. This work shows that GPU is a feasible and cost-efficient solution compared to other alternatives such as using cluster machines or field-programmable gate arrays for satisfying the increasing demands on computation speed and accuracy of dose calculation. But there are also inherent limitations of using GPU for accelerating MC-type applications, which are also analyzed in detail in this article.

Rogue waves and W-shaped solitons in the multiple self-induced transparency system.

PubMed

Wang, Xin; Liu, Chong; Wang, Lei

2017-09-01

We study localized nonlinear waves on a plane wave background in the multiple self-induced transparency (SIT) system, which describes an important enhancement of the amplification and control of optical waves compared to the single SIT system. A hierarchy of exact multiparametric rational solutions in a compact determinant representation is presented. We demonstrate that this family of solutions contain known rogue wave solutions and unusual W-shaped soliton solutions. State transitions between the fundamental rogue waves and W-shaped solitons as well as higher-order nonlinear superposition modes are revealed in the zero-frequency perturbation region by the suitable choice for the background wavenumber of the electric field component. Particularly, it is found that the multiple SIT system can admit both stationary and nonstationary W-shaped solitons in contrast to the stationary results in the single SIT system. Moreover, the W-shaped soliton complex which is formed by a certain number of fundamental W-shaped solitons with zero phase parameters and its decomposition mechanism in the case of the nonzero phase parameters are shown. Meanwhile, some important characteristics of the nonlinear waves including trajectories and spectrum are discussed through the numerical and analytical methods.

Propagation of large-amplitude waves on dielectric liquid sheets in a tangential electric field: exact solutions in three-dimensional geometry.

PubMed

Zubarev, Nikolay M; Zubareva, Olga V

2010-10-01

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.

Analytical model of a corona discharge from a conical electrode under saturation

NASA Astrophysics Data System (ADS)

Boltachev, G. Sh.; Zubarev, N. M.

2012-11-01

Exact partial solutions are found for the electric field distribution in the outer region of a stationary unipolar corona discharge from an ideal conical needle in the space-charge-limited current mode with allowance for the electric field dependence of the ion mobility. It is assumed that only the very tip of the cone is responsible for the discharge, i.e., that the ionization zone is a point. The solutions are obtained by joining the spherically symmetric potential distribution in the drift space and the self-similar potential distribution in the space-charge-free region. Such solutions are outside the framework of the conventional Deutsch approximation, according to which the space charge insignificantly influences the shape of equipotential surfaces and electric lines of force. The dependence is derived of the corona discharge saturation current on the apex angle of the conical electrode and applied potential difference. A simple analytical model is suggested that describes drift in the point-plane electrode geometry under saturation as a superposition of two exact solutions for the field potential. In terms of this model, the angular distribution of the current density over the massive plane electrode is derived, which agrees well with Warburg's empirical law.

Dark-dark-soliton dynamics in two density-coupled Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Morera, I.; Mateo, A. Muñoz; Polls, A.; Juliá-Díaz, B.

2018-04-01

We study the one-dimensional dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate (g >0 ). By using an adiabatic perturbation theory in the parameter g12/g , we show that, contrary to the case of two solitons in scalar condensates, the interactions between solitons are attractive when the interparticle interactions between condensates are repulsive g12>0 . As a result, the relative motion of dark solitons with equal chemical potential μ is well approximated by harmonic oscillations of angular frequency wr=(μ /ℏ ) √{(8 /15 ) g12/g } . We also show that, in finite systems, the resonance of this anomalous excitation mode with the spin-density mode of lowest energy gives rise to alternating dynamical instability and stability fringes as a function of the perturbative parameter. In the presence of harmonic trapping (with angular frequency Ω ) the solitons are driven by the superposition of two harmonic motions at a frequency given by w2=(Ω/√{2 }) 2+wr2 . When g12<0 , these two oscillators compete to give rise to an overall effective potential that can be either single well or double well through a pitchfork bifurcation. All our theoretical results are compared with numerical solutions of the Gross-Pitaevskii equation for the dynamics and the Bogoliubov equations for the linear stability. A good agreement is found between them.

A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

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

Shao, Yan-Lin, E-mail: yanlin.shao@dnvgl.com; Faltinsen, Odd M.

2014-10-01

We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods,more » e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.« less

Linearization instability for generic gravity in AdS spacetime

NASA Astrophysics Data System (ADS)

Altas, Emel; Tekin, Bayram

2018-01-01

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

Linear-time reconstruction of zero-recombinant Mendelian inheritance on pedigrees without mating loops.

PubMed

Liu, Lan; Jiang, Tao

2007-01-01

With the launch of the international HapMap project, the haplotype inference problem has attracted a great deal of attention in the computational biology community recently. In this paper, we study the question of how to efficiently infer haplotypes from genotypes of individuals related by a pedigree without mating loops, assuming that the hereditary process was free of mutations (i.e. the Mendelian law of inheritance) and recombinants. We model the haplotype inference problem as a system of linear equations as in [10] and present an (optimal) linear-time (i.e. O(mn) time) algorithm to generate a particular solution (A particular solution of any linear system is an assignment of numerical values to the variables in the system which satisfies the equations in the system.) to the haplotype inference problem, where m is the number of loci (or markers) in a genotype and n is the number of individuals in the pedigree. Moreover, the algorithm also provides a general solution (A general solution of any linear system is denoted by the span of a basis in the solution space to its associated homogeneous system, offset from the origin by a vector, namely by any particular solution. A general solution for ZRHC is very useful in practice because it allows the end user to efficiently enumerate all solutions for ZRHC and performs tasks such as random sampling.) in O(mn2) time, which is optimal because the size of a general solution could be as large as Theta(mn2). The key ingredients of our construction are (i) a fast consistency checking procedure for the system of linear equations introduced in [10] based on a careful investigation of the relationship between the equations (ii) a novel linear-time method for solving linear equations without invoking the Gaussian elimination method. Although such a fast method for solving equations is not known for general systems of linear equations, we take advantage of the underlying loop-free pedigree graph and some special properties of the linear equations.

Hybrid reconstruction of field-reversed configurations

NASA Astrophysics Data System (ADS)

Steinhauer, Loren; TAE Team

2016-10-01

Field-reversed configurations (FRC) are poorly represented by fluid-based models and require instead an ion-distribution function. Two such populations are needed since ``core'' ions are roughly restricted to the region inside the separatrix, whereas ``periphery'' ions can escape along open field lines. The Vlasov equation governs the distribution, the general solution to which is an arbitrary function of the constants of motion (Hamiltonian, canonical angular momentum). Only a small subset of such distributions are realistic in view of collisions, which smooth the distribution, and instabilities, which reorganize the field structure. Collisions and end loss are included if the distribution is a solution to the Fokker-Planck (FP) equation. Vlasov and FP solutions are nearly identical in weakly-collisional plasmas. Numerical construction of such equilibria requires solving both Ampere's law for the magnetic flux variable and the ponderous task of a full velocity-space integration at each point. The latter can be done analytically by expressing the distribution as the superposition of simple basis elements. This procedure allows rapid reconstruction of evolving equilibria based on limited diagnostic observables in FRC experiments.

Stability analysis of the Peregrine solution via squared eigenfunctions

NASA Astrophysics Data System (ADS)

Schober, C. M.; Strawn, M.

2017-10-01

A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

Final Aperture Superposition Technique applied to fast calculation of electron output factors and depth dose curves

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

Faddegon, B.A.; Villarreal-Barajas, J.E.; Mt. Diablo Regional Cancer Center, 2450 East Street, Concord, California

2005-11-15

The Final Aperture Superposition Technique (FAST) is described and applied to accurate, near instantaneous calculation of the relative output factor (ROF) and central axis percentage depth dose curve (PDD) for clinical electron beams used in radiotherapy. FAST is based on precalculation of dose at select points for the two extreme situations of a fully open final aperture and a final aperture with no opening (fully shielded). This technique is different than conventional superposition of dose deposition kernels: The precalculated dose is differential in position of the electron or photon at the downstream surface of the insert. The calculation for amore » particular aperture (x-ray jaws or MLC, insert in electron applicator) is done with superposition of the precalculated dose data, using the open field data over the open part of the aperture and the fully shielded data over the remainder. The calculation takes explicit account of all interactions in the shielded region of the aperture except the collimator effect: Particles that pass from the open part into the shielded part, or visa versa. For the clinical demonstration, FAST was compared to full Monte Carlo simulation of 10x10,2.5x2.5, and 2x8 cm{sup 2} inserts. Dose was calculated to 0.5% precision in 0.4x0.4x0.2 cm{sup 3} voxels, spaced at 0.2 cm depth intervals along the central axis, using detailed Monte Carlo simulation of the treatment head of a commercial linear accelerator for six different electron beams with energies of 6-21 MeV. Each simulation took several hours on a personal computer with a 1.7 Mhz processor. The calculation for the individual inserts, done with superposition, was completed in under a second on the same PC. Since simulations for the pre calculation are only performed once, higher precision and resolution can be obtained without increasing the calculation time for individual inserts. Fully shielded contributions were largest for small fields and high beam energy, at the surface, reaching a maximum of 5.6% at 21 MeV. Contributions from the collimator effect were largest for the large field size, high beam energy, and shallow depths, reaching a maximum of 4.7% at 21 MeV. Both shielding contributions and the collimator effect need to be taken into account to achieve an accuracy of 2%. FAST takes explicit account of the shielding contributions. With the collimator effect set to that of the largest field in the FAST calculation, the difference in dose on the central axis (product of ROF and PDD) between FAST and full simulation was generally under 2%. The maximum difference of 2.5% exceeded the statistical precision of the calculation by four standard deviations. This occurred at 18 MeV for the 2.5x2.5 cm{sup 2} field. The differences are due to the method used to account for the collimator effect.« less

The Fundamental Solution of the Linearized Navier Stokes Equations for Spinning Bodies in Three Spatial Dimensions Time Dependent Case

NASA Astrophysics Data System (ADS)

Thomann, Enrique A.; Guenther, Ronald B.

2006-02-01

Explicit formulae for the fundamental solution of the linearized time dependent Navier Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L p (R 3), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.

MPT Prediction of Aircraft-Engine Fan Noise

NASA Technical Reports Server (NTRS)

Connell, Stuart D.

2004-01-01

A collection of computer programs has been developed that implements a procedure for predicting multiple-pure-tone (MPT) noise generated by fan blades of an aircraft engine (e.g., a turbofan engine). MPT noise arises when the fan is operating with supersonic relative tip Mach No. Under this flow condition, there is a strong upstream running shock. The strength and position of this shock are very sensitive to blade geometry variations. For a fan where all the blades are identical, the primary tone observed upstream of the fan will be the blade passing frequency. If there are small variations in geometry between blades, then tones below the blade passing frequency arise MPTs. Stagger angle differences as small as 0.1 can give rise to significant MPT. It is also noted that MPT noise is more pronounced when the fan is operating in an unstarted mode. Computational results using a three-dimensional flow solver to compute the complete annulus flow with non-uniform fans indicate that MPT noise can be estimated in a relatively simple way. Hence, once the effect of a typical geometry variation of one blade in an otherwise uniform blade row is known, the effect of all the blades being different can be quickly computed via superposition. Two computer programs that were developed as part of this work are used in conjunction with a user s computational fluid dynamics (CFD) code to predict MPT spectra for a fan with a specified set of geometric variations: (1) The first program ROTBLD reads the users CFD solution files for a single blade passage via an API (Application Program Interface). There are options to replicate and perturb the geometry with typical variations stagger, camber, thickness, and pitch. The multi-passage CFD solution files are then written in the user s file format using the API. (2) The second program SUPERPOSE requires two input files: the first is the circumferential upstream pressure distribution extracted from the CFD solution on the multi-passage mesh, the second file defines the geometry variations of each blade in a complete fan. Superposition is used to predict the spectra resulting from the geometric variations.

Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions.

PubMed

Harris, Frank E

2016-05-28

Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance rij. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validated by showing that they yield correct results for a large number of integrals published by other investigators.

Probing the degenerate states of V-point singularities.

PubMed

Ram, B S Bhargava; Sharma, Anurag; Senthilkumaran, Paramasivam

2017-09-15

V-points are polarization singularities in spatially varying linearly polarized optical fields and are characterized by the Poincare-Hopf index η. Each V-point singularity is a superposition of two oppositely signed orbital angular momentum states in two orthogonal spin angular momentum states. Hence, a V-point singularity has zero net angular momentum. V-points with given |η| have the same (amplitude) intensity distribution but have four degenerate polarization distributions. Each of these four degenerate states also produce identical diffraction patterns. Hence to distinguish these degenerate states experimentally, we present in this Letter a method involving a combination of polarization transformation and diffraction. This method also shows the possibility of using polarization singularities in place of phase singularities in optical communication and quantum information processing.

Computer modeling the fatigue crack growth rate behavior of metals in corrosive environments

NASA Technical Reports Server (NTRS)

Richey, Edward, III; Wilson, Allen W.; Pope, Jonathan M.; Gangloff, Richard P.

1994-01-01

The objective of this task was to develop a method to digitize FCP (fatigue crack propagation) kinetics data, generally presented in terms of extensive da/dN-Delta K pairs, to produce a file for subsequent linear superposition or curve-fitting analysis. The method that was developed is specific to the Numonics 2400 Digitablet and is comparable to commercially available software products as Digimatic(sup TM 4). Experiments demonstrated that the errors introduced by the photocopying of literature data, and digitization, are small compared to those inherent in laboratory methods to characterize FCP in benign and aggressive environments. The digitizing procedure was employed to obtain fifteen crack growth rate data sets for several aerospace alloys in aggressive environments.

Entanglement Potential Versus Negativity of Wigner Function for SUP-Operated Quantum States

NASA Astrophysics Data System (ADS)

Chatterjee, Arpita

2018-02-01

We construct a distinct category of nonclassical quantum states by applying a superposition of products (SUP) of field annihilation (\\hat {a}) and creation (\\hat {a}^{\\dagger }) operators of the type (s\\hat {a}\\hat {a}^{\\dagger }+t\\hat {a}^{\\dagger }\\hat {a}), with s2+t2=1, upon thermal and even coherent states. We allow these SUP operated states to undergo a decoherence process and then describe the nonclassical features of the resulted field by using the entanglement potential (EP) and the negativity of the Wigner distribution function. Our analysis reveals that both the measures are reduced in the linear loss process. The partial negativity of the Wigner function disappears when losses exceed 50% but EP exists always.

Binary chromatographic data and estimation of adsorbent porosities. [data for system n-heptane/n-pentane

NASA Technical Reports Server (NTRS)

Meisch, A. J.

1972-01-01

Data for the system n-pentane/n-heptane on porous Chromosorb-102 adsorbent were obtained at 150, 175, and 200 C for mixtures containing zero to 100% n-pentane by weight. Prior results showing limitations on superposition of pure component data to predict multicomponent chromatograms were verified. The thermodynamic parameter MR0 was found to be a linear function of sample composition. A nonporous adsorbent failed to separate the system because of large input sample dispersions. A proposed automated data processing scheme involving magnetic tape recording of the detector signals and processing by a minicomputer was rejected because of resolution limitations of the available a/d converters. Preliminary data on porosity and pore size distributions of the adsorbents were obtained.

Recovery time in quantum dynamics of wave packets

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

Strekalov, M. L., E-mail: strekalov@kinetics.nsc.ru

2017-01-15

A wave packet formed by a linear superposition of bound states with an arbitrary energy spectrum returns arbitrarily close to the initial state after a quite long time. A method in which quantum recovery times are calculated exactly is developed. In particular, an exact analytic expression is derived for the recovery time in the limiting case of a two-level system. In the general case, the reciprocal recovery time is proportional to the Gauss distribution that depends on two parameters (mean value and variance of the return probability). The dependence of the recovery time on the mean excitation level of themore » system is established. The recovery time is the longest for the maximal excitation level.« less

Analysis of the tensile stress-strain behavior of elastomers at constant strain rates. I - Criteria for separability of the time and strain effects

NASA Technical Reports Server (NTRS)

Hong, S. D.; Fedors, R. F.; Schwarzl, F.; Moacanin, J.; Landel, R. F.

1981-01-01

A theoretical analysis of the tensile stress-strain relation of elastomers at constant strain rate is presented which shows that the time and the stress effect are separable if the experimental time scale coincides with a segment of the relaxation modulus that can be described by a single power law. It is also shown that time-strain separability is valid if the strain function is linearly proportional to the Cauchy strain, and that when time-strain separability holds, two strain-dependent quantities can be obtained experimentally. In the case where time and strain effect are not separable, superposition can be achieved only by using temperature and strain-dependent shift factors.

Using Musical Intervals to Demonstrate Superposition of Waves and Fourier Analysis

ERIC Educational Resources Information Center

LoPresto, Michael C.

2013-01-01

What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.

High-order harmonic generation of CO and N2 molecules under linearly- and bi circularly-polarized laser pulses by TD-DFT

NASA Astrophysics Data System (ADS)

Koushki, A. M.; Sadighi-Bonabi, R.; Mohsen-Nia, M.; Irani, E.

2018-07-01

We present a method for high-order harmonics generation of N2 and CO molecules under two-color circularly polarized counter-rotating laser pulses at frequencies of and 2. Pulse envelope in this investigation is sin-squared and the intensity of each laser beam is with ten-optical cycle (o.c.). We show that an isolated pulse with a pulse duration shorter than 20 attosecond from the superposition of several harmonics can be generated. Both two-color linearly- and bicircularly-polarized laser pulses are considered. Our results have also been compared with the outcomes of the previous theoretical works as well as experiment observations. It is found that for CO molecule, the bicircularly-polarized laser pulses are superior and more efficient, and it can generate narrower attosecond pulses than the linearly-polarized pulses. While for N2 molecule, the two-color linearly-polarized pulses are more efficient, and it can generate narrower attosecond pulses than the bicircularly-polarized pulses. Furthermore, in order to demonstrate the origin of red- and blue-shifts in high-harmonic spectra, the effect of pulse duration on the high-order harmonics spectra is investigated. In addition, to obtain imaging on the temporal dependence of the electron densities, the time dependent electron localization function is used. Moreover, in order to study of the quantum trajectory of electrons, time-frequency analysis is utilized.

Crack displacement sensing and measurement in concrete using circular grating moire fringes and pattern matching

NASA Astrophysics Data System (ADS)

Chan, H. M.; Yen, K. S.; Ratnam, M. M.

2008-09-01

The moire method has been extensively studied in the past and applied in various engineering applications. Several techniques are available for generating the moire fringes in these applications, which include moire interferometry, projection moire, shadow moire, moire deflectometry etc. Most of these methods use the superposition of linear gratings to generate the moire patterns. The use of non-linear gratings, such as circular, radial and elongated gratings has received less attention from the research community. The potential of non-linear gratings in engineering measurement has been realized in a limited number of applications, such as rotation measurement, measurement of linear displacement, measurement of expansion coefficients of materials and measurement of strain distribution. In this work, circular gratings of different pitch were applied to the sensing and measurement of crack displacement in concrete structures. Gratings of pitch 0.50 mm and 0.55 mm were generated using computer software and attached to two overlapping acrylic plates that were bonded to either side of the crack. The resulting moire patterns were captured using a standard digital camera and compared with a set of reference patterns generated using a precision positioning stage. Using several image pre-processing stages, such as filtering and morphological operations, and pattern matching the magnitude displacements along two orthogonal axes can be detected with a resolution of 0.05 mm.

A stopping criterion for the iterative solution of partial differential equations

NASA Astrophysics Data System (ADS)

Rao, Kaustubh; Malan, Paul; Perot, J. Blair

2018-01-01

A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.

On the sighted ancestry of blindness - exceptionally preserved eyes of Mesozoic polychelidan lobsters.

PubMed

Audo, Denis; Haug, Joachim T; Haug, Carolin; Charbonnier, Sylvain; Schweigert, Günter; Müller, Carsten H G; Harzsch, Steffen

2016-01-01

Modern representatives of Polychelida (Polychelidae) are considered to be entirely blind and have largely reduced eyes, possibly as an adaptation to deep-sea environments. Fossil species of Polychelida, however, appear to have well-developed compound eyes preserved as anterior bulges with distinct sculpturation. We documented the shapes and sizes of eyes and ommatidia based upon exceptionally preserved fossil polychelidans from Binton (Hettangian, United-Kingdom), Osteno (Sinemurian, Italy), Posidonia Shale (Toarcian, Germany), La Voulte-sur-Rhône (Callovian, France), and Solnhofen-type plattenkalks (Kimmeridgian-Tithonian, Germany). For purposes of comparison, sizes of the eyes of several other polychelidans without preserved ommatidia were documented. Sizes of ommatidia and eyes were statistically compared against carapace length, taxonomic group, and outcrop. Nine species possess eyes with square facets; Rosenfeldia oppeli (Woodward, 1866), however, displays hexagonal facets. The sizes of eyes and ommatidia are a function of carapace length. No significant differences were discerned between polychelidans from different outcrops; Eryonidae, however, have significantly smaller eyes than other groups. Fossil eyes bearing square facets are similar to the reflective superposition eyes found in many extant decapods. As such, they are the earliest example of superposition eyes. As reflective superposition is considered plesiomorphic for Reptantia, this optic type was probably retained in Polychelida. The two smallest specimens, a Palaeopentacheles roettenbacheri (Münster, 1839) and a Hellerocaris falloti (Van Straelen, 1923), are interpreted as juveniles. Both possess square-shaped facets, a typical post-larval feature. The eye morphology of these small specimens, which are far smaller than many extant eryoneicus larvae, suggests that Jurassic polychelidans did not develop via giant eryoneicus larvae. In contrast, another species we examined, Rosenfeldia oppeli (Woodward, 1866), did not possess square-shaped facets, but rather hexagonal ones, which suggests that this species did not possess reflective superposition eyes. The hexagonal facets may indicate either another type of superposition eye (refractive or parabolic superposition), or an apposition eye. As decapod larvae possess apposition eyes with hexagonal facets, it is most parsimonious to consider eyes of R. oppeli as apposition eyes evolved through paedomorphic heterochrony. Polychelidan probably originally had reflective superposition. R. oppeli, however, probably gained apposition eyes through paedomorphosis.

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

NASA Astrophysics Data System (ADS)

Daoud, M.; Ahl Laamara, R.

2012-07-01

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl-Heisenberg, SU(2) and SU(1,1) coherent states which interpolate between Werner and Greenberger-Horne-Zeilinger states.

Programmable superpositions of Ising configurations

NASA Astrophysics Data System (ADS)

Sieberer, Lukas M.; Lechner, Wolfgang

2018-05-01

We present a framework to prepare superpositions of bit strings, i.e., many-body spin configurations, with deterministic programmable probabilities. The spin configurations are encoded in the degenerate ground states of the lattice-gauge representation of an all-to-all connected Ising spin glass. The ground-state manifold is invariant under variations of the gauge degrees of freedom, which take the form of four-body parity constraints. Our framework makes use of these degrees of freedom by individually tuning them to dynamically prepare programmable superpositions. The dynamics combines an adiabatic protocol with controlled diabatic transitions. We derive an effective model that allows one to determine the control parameters efficiently even for large system sizes.

Linear adsorption of nonionic organic compounds from water onto hydrophilic minerals: Silica and alumina

USGS Publications Warehouse

Su, Y.-H.; Zhu, Y.-G.; Sheng, G.; Chiou, C.T.

2006-01-01

To characterize the linear adsorption phenomena in aqueous nonionic organic solute-mineral systems, the adsorption isotherms of some low-molecular- weightnonpolar nonionic solutes (1,2,3-trichlorobenzene, lindane, phenanthrene, and pyrene) and polar nonionic solutes (1,3-dinitrobenzene and 2,4-dinitrotoluene) from single-and binary-solute solutions on hydrophilic silica and alumina were established. Toward this objective, the influences of temperature, ionic strength, and pH on adsorption were also determined. It is found that linear adsorption exhibits low exothermic heats and practically no adsorptive competition. The solute-solid configuration and the adsorptive force consistent with these effects were hypothesized. For nonpolar solutes, the adsorption occurs presumably by London (dispersion) forces onto a water film above the mineral surface. For polar solutes, the adsorption is also assisted by polar-group interactions. The reduced adsorptive forces of solutes with hydrophilic minerals due to physical separation by the water film and the low fractions of the water-film surface covered by solutes offer a theoretical basis for linear solute adsorption, low exothermic heats, and no adsorptive competition. The postulated adsorptive forces are supported by observations that ionic strength or pH poses no effect on the adsorption of nonpolar solutes while it exhibits a significant effect on the uptake of polar solutes. ?? 2006 American Chemical Society.

Statistical properties of superimposed stationary spike trains.

PubMed

Deger, Moritz; Helias, Moritz; Boucsein, Clemens; Rotter, Stefan

2012-06-01

The Poisson process is an often employed model for the activity of neuronal populations. It is known, though, that superpositions of realistic, non- Poisson spike trains are not in general Poisson processes, not even for large numbers of superimposed processes. Here we construct superimposed spike trains from intracellular in vivo recordings from rat neocortex neurons and compare their statistics to specific point process models. The constructed superimposed spike trains reveal strong deviations from the Poisson model. We find that superpositions of model spike trains that take the effective refractoriness of the neurons into account yield a much better description. A minimal model of this kind is the Poisson process with dead-time (PPD). For this process, and for superpositions thereof, we obtain analytical expressions for some second-order statistical quantities-like the count variability, inter-spike interval (ISI) variability and ISI correlations-and demonstrate the match with the in vivo data. We conclude that effective refractoriness is the key property that shapes the statistical properties of the superposition spike trains. We present new, efficient algorithms to generate superpositions of PPDs and of gamma processes that can be used to provide more realistic background input in simulations of networks of spiking neurons. Using these generators, we show in simulations that neurons which receive superimposed spike trains as input are highly sensitive for the statistical effects induced by neuronal refractoriness.

The Evolution and Development of Neural Superposition

PubMed Central

Agi, Egemen; Langen, Marion; Altschuler, Steven J.; Wu, Lani F.; Zimmermann, Timo

2014-01-01

Visual systems have a rich history as model systems for the discovery and understanding of basic principles underlying neuronal connectivity. The compound eyes of insects consist of up to thousands of small unit eyes that are connected by photoreceptor axons to set up a visual map in the brain. The photoreceptor axon terminals thereby represent neighboring points seen in the environment in neighboring synaptic units in the brain. Neural superposition is a special case of such a wiring principle, where photoreceptors from different unit eyes that receive the same input converge upon the same synaptic units in the brain. This wiring principle is remarkable, because each photoreceptor in a single unit eye receives different input and each individual axon, among thousands others in the brain, must be sorted together with those few axons that have the same input. Key aspects of neural superposition have been described as early as 1907. Since then neuroscientists, evolutionary and developmental biologists have been fascinated by how such a complicated wiring principle could evolve, how it is genetically encoded, and how it is developmentally realized. In this review article, we will discuss current ideas about the evolutionary origin and developmental program of neural superposition. Our goal is to identify in what way the special case of neural superposition can help us answer more general questions about the evolution and development of genetically “hard-wired” synaptic connectivity in the brain. PMID:24912630

The evolution and development of neural superposition.

PubMed

Agi, Egemen; Langen, Marion; Altschuler, Steven J; Wu, Lani F; Zimmermann, Timo; Hiesinger, Peter Robin

2014-01-01

Visual systems have a rich history as model systems for the discovery and understanding of basic principles underlying neuronal connectivity. The compound eyes of insects consist of up to thousands of small unit eyes that are connected by photoreceptor axons to set up a visual map in the brain. The photoreceptor axon terminals thereby represent neighboring points seen in the environment in neighboring synaptic units in the brain. Neural superposition is a special case of such a wiring principle, where photoreceptors from different unit eyes that receive the same input converge upon the same synaptic units in the brain. This wiring principle is remarkable, because each photoreceptor in a single unit eye receives different input and each individual axon, among thousands others in the brain, must be sorted together with those few axons that have the same input. Key aspects of neural superposition have been described as early as 1907. Since then neuroscientists, evolutionary and developmental biologists have been fascinated by how such a complicated wiring principle could evolve, how it is genetically encoded, and how it is developmentally realized. In this review article, we will discuss current ideas about the evolutionary origin and developmental program of neural superposition. Our goal is to identify in what way the special case of neural superposition can help us answer more general questions about the evolution and development of genetically "hard-wired" synaptic connectivity in the brain.

Conditions for Stabilizability of Linear Switched Systems

NASA Astrophysics Data System (ADS)

Minh, Vu Trieu

2011-06-01

This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence.

Dynamic growth of mixed-mode shear cracks

USGS Publications Warehouse

Andrews, D.J.

1994-01-01

A pure mode II (in-plane) shear crack cannot propagate spontaneously at a speed between the Rayleigh and S-wave speeds, but a three-dimensional (3D) or two-dimensional (2D) mixed-mode shear crack can propagate in this range, being driven by the mode III (antiplane) component. Two different analytic solutions have been proposed for the mode II component in this case. The first is the solution valid for crack speed less than the Rayleigh speed. When applied above the Rayleigh speed, it predicts a negative stress intensity factor, which implies that energy is generated at the crack tip. Burridge proposed a second solution, which is continuous at the crack tip, but has a singularity in slip velocity at the Rayleigh wave. Spontaneous propagation of a mixed-mode rupture has been calculated with a slip-weakening friction law, in which the slip velocity vector is colinear with the total traction vector. Spontaneous trans-Rayleigh rupture speed has been found. The solution depends on the absolute stress level. The solution for the in-plane component appears to be a superposition of smeared-out versions of the two analytic solutions. The proportion of the first solution increases with increasing absolute stress. The amplitude of the negative in-plane traction pulse is less than the absolute final sliding traction, so that total in-plane traction does not reverse. The azimuth of the slip velocity vector varies rapidly between the onset of slip and the arrival of the Rayleigh wave. The variation is larger at smaller absolute stress.

Topological view of quantum tunneling coherent destruction

NASA Astrophysics Data System (ADS)

Bernardini, Alex E.; Chinaglia, Mariana

2017-08-01

Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support quantum mechanical zero mode and first excited state analytical solutions. Reporting about a symmetry breaking that supports the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state, two inequivalent topological scenarios are supposed to drive stable tunneling and coherent tunneling destruction respectively. A complete prospect of the Wigner function dynamics, vector field fluxes and the time dependence of stagnation points is obtained for the analytical potentials that support stable and tachyonic modes.

The Decoherence and Interference of Cosmological Arrows of Time for a de Sitter Universe with Quantum Fluctuations

NASA Astrophysics Data System (ADS)

Rotondo, Marcello; Nambu, Yasusada

2018-06-01

We consider the superposition of two semiclassical solutions of the Wheeler-DeWitt equation for a de Sitter universe, describing a quantized scalar vacuum propagating in a universe that is contracting in one case and expanding in the other, each identifying a opposite cosmological arrow of time. We discuss the suppression of the interference terms between the two arrows of time due to environment-induced decoherence caused by modes of the scalar vacuum crossing the Hubble horizon. Furthermore, we quantify the effect of the interference on the expectation value of the observable field mode correlations, with respect to an observer that we identify with the spatial geometry.

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

NASA Astrophysics Data System (ADS)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

Decoherence-free evolution of time-dependent superposition states of two-level systems and thermal effects

NASA Astrophysics Data System (ADS)

Prado, F. O.; de Almeida, N. G.; Duzzioni, E. I.; Moussa, M. H. Y.; Villas-Boas, C. J.

2011-07-01

In this paper we detail some results advanced in a recent letter [Prado , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.102.073008 102, 073008 (2009).] showing how to engineer reservoirs for two-level systems at absolute zero by means of a time-dependent master equation leading to a nonstationary superposition equilibrium state. We also present a general recipe showing how to build nonadiabatic coherent evolutions of a fermionic system interacting with a bosonic mode and investigate the influence of thermal reservoirs at finite temperature on the fidelity of the protected superposition state. Our analytical results are supported by numerical analysis of the full Hamiltonian model.

Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication

NASA Astrophysics Data System (ADS)

Guérin, Philippe Allard; Feix, Adrien; Araújo, Mateus; Brukner, Časlav

2016-09-01

In communication complexity, a number of distant parties have the task of calculating a distributed function of their inputs, while minimizing the amount of communication between them. It is known that with quantum resources, such as entanglement and quantum channels, one can obtain significant reductions in the communication complexity of some tasks. In this work, we study the role of the quantum superposition of the direction of communication as a resource for communication complexity. We present a tripartite communication task for which such a superposition allows for an exponential saving in communication, compared to one-way quantum (or classical) communication; the advantage also holds when we allow for protocols with bounded error probability.

Detection of Linear Polarization from SNR Cassiopeia A at Low Radio Frequencies

NASA Astrophysics Data System (ADS)

Raja, Wasim; Deshpande, Avinash A.

2015-03-01

We report detection of the weak but significant linear polarization from the Supernova Remnant Cas A at low radio frequencies (327 MHz) using the GMRT. The spectro-polarimetric data (16 MHz bandwidth with 256 spectral channels) was analyzed using the technique of Faraday Tomography. Ascertaining association of this weak polarization to the source is non-trivial in the presence of the remnant instrumental polarization (<1% in our case) - the expected anti-correlation ρlp,x, between the linear polarized intensity and the soft X-ray counts gets masked by the correlation between the Stokes-I dependent instrumental leakage and the X-radiation that is spatially correlated with Stokes-I, if ρ lp,x is computed naively. Hence, we compute ρ lp,x using pixels within ultra narrow bins of Stokes-I within which the instrumental leakage is expected to remain constant, and establish the anti-correlation as well as the correspondence of this correlation with the mean X-ray profile (Figure 1). Given the angular and RM-resolution in our data, the observed depolarization relative to that at higher frequencies, implies that the mixing of thermal and non-thermal plasma within the source might be occurring on spatial scales ~ 1000 AU, assuming random superposition of polarization states.

Manipulation of ultracold Rb atoms using a single linearly chirped laser pulse.

PubMed

Collins, T A; Malinovskaya, S A

2012-06-15

At ultracold temperatures, atoms are free from thermal motion, which makes them ideal objects of investigations aiming to advance high-precision spectroscopy, metrology, quantum computation, producing Bose condensates, etc. The quantum state of ultracold atoms may be created and manipulated by making use of quantum control methods employing low-intensity pulses. We theoretically investigate population dynamics of ultracold Rb vapor induced by nanosecond linearly chirped pulses having kW/cm2 beam intensity and show a possibility of controllable population transfer between hyperfine (HpF) levels of 5(2)/S(1/2) state through Raman transitions. Satisfying the one-photon resonance condition with the lowest of the HpF states of 5(2)/P(1/2) or 5(2)/P(3/2) state allows us to enter the adiabatic region of population transfer at very low field intensities, such that corresponding Rabi frequencies are less than or equal to the HpF splitting. This methodology provides a robust way to create a specifically designed superposition state in Rb in the basis of HpF levels and perform state manipulation controllable on the picosecond-to-nanosecond time scale.

An instability of hyperbolic space under the Yang-Mills flow

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

Gegenberg, Jack; Day, Andrew C.; Liu, Haitao

2014-04-15

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of constant curvature. We analytically solve the linearized flow equations for a large class of perturbations to the fixed point corresponding to hyperbolic 3-space. These can be expressed as a linear superposition of distinct modes, some of which are exponentially growing along the flow. The growing modes imply the divergence ofmore » the (gauge invariant) perturbative torsion for a wide class of initial data, indicating an instability of the background geometry that we confirm with numeric simulations in the partially compactified case. There are stable modes with zero torsion, but all the unstable modes are torsion-full. This leads us to speculate that the instability is induced by the torsion degrees of freedom present in the Yang-Mills flow.« less

Linear analysis of active-medium two-beam accelerator

NASA Astrophysics Data System (ADS)

Voin, Miron; Schächter, Levi

2015-07-01

We present detailed development of the linear theory of wakefield amplification by active medium and its possible application to a two-beam accelerator (TBA) is discussed. A relativistic train of triggering microbunches traveling along a vacuum channel in an active medium confined by a cylindrical waveguide excites Cherenkov wake in the medium. The wake is a superposition of azimuthally symmetric transverse magnetic modes propagating along a confining waveguide, with a phase velocity equal to the velocity of the triggering bunches. The structure may be designed in such a way that the frequency of one of the modes is close to active-medium resonant frequency, resulting in amplification of the former and domination of a single mode far behind the trigger bunches. Another electron bunch placed in proper phase with the amplified wakefield may be accelerated by the latter. Importantly, the energy for acceleration is provided by the active medium and not the drive bunch as in a traditional TBA. Based on a simplified model, we analyze extensively the impact of various parameters on the wakefield amplification process.

Galvanic vestibular stimulation combines with Earth-horizontal rotation in roll to induce the illusion of translation.

PubMed

Schneider, Erich; Bartl, Klaus; Glasauer, Stefan

2009-05-01

Human head rotation in roll around an earth-horizontal axis constitutes a vestibular stimulus that, by its rotational component, acts on the semicircular canals (SCC) and that, by its tilt of the gravity vector, also acts on the otoliths. Galvanic vestibular stimulation (GVS) is thought to resemble mainly a rotation in roll. A superposition of sinusoidal GVS with a natural earth-horizontal roll movement was therefore applied in order to cancel the rotation effects and to isolate the otolith activation. By self-adjusting the amplitude and phase of GVS, subjects were able to minimize their sensation of rotation and to generate the perception of a linear translation. The final adjustments are in the range of a model that predicts SCC activation during natural rotations and GVS. This indicates that the tilt-translation ambiguity of the otoliths is resolved by SCC-otolith interaction. It is concluded that GVS might be able to cancel rotations in roll and that the residual tilt of the gravitoinertial force is possibly interpreted as a linear translation.

Dynamics in Complex Coacervates

NASA Astrophysics Data System (ADS)

Perry, Sarah

Understanding the dynamics of a material provides detailed information about the self-assembly, structure, and intermolecular interactions present in a material. While rheological methods have long been used for the characterization of complex coacervate-based materials, it remains a challenge to predict the dynamics for a new system of materials. Furthermore, most work reports only qualitative trends exist as to how parameters such as charge stoichiometry, ionic strength, and polymer chain length impact self-assembly and material dynamics, and there is little information on the effects of polymer architecture or the organization of charges within a polymer. We seek to link thermodynamic studies of coacervation phase behavior with material dynamics through a carefully-controlled, systematic study of coacervate linear viscoelasticity for different polymer chemistries. We couple various methods of characterizing the dynamics of polymer-based complex coacervates, including the time-salt superposition methods developed first by Spruijt and coworkers to establish a more mechanistic strategy for comparing the material dynamics and linear viscoelasticity of different systems. Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for support of this research.

A physically based connection between fractional calculus and fractal geometry

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

Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

2014-11-15

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

Studies of nonlinear interactions between counter-propagating Alfv'en waves in the LAPD

NASA Astrophysics Data System (ADS)

Auerbach, D. W.; Perez, J. C.; Carter, T. A.; Boldyrev, S.

2007-11-01

From a weak turbulence point of view, nonlinear interactions between shear Alfv'en waves are fundamental to the energy cascade in low-frequency magnetic turbulence. We report here on an experimental study of counter-propagating Alfv'en wave interactions in the Large Plasma Device (LAPD) at UCLA. Colliding, orthogonally polarized kinetic Alfv'en waves are generated by two antennae, separated by 5m along the guide magnetic field. Magnetic field and langmuir probes record plasma behavior between the antennae. When each antenna is operated separately, linearly polarized Alfv'en waves propagate in opposite directions along the guide field. When two antennae simultaneously excite counter propagating waves, we observe multiple side bands in the frequency domain, whose amplitude scales quadratically with wave amplitude. In the spatial domain we observe non-linear superposition in the 2D structure of the waves and spectral broadening in the perpendicular wave-number spectrum. This indicates the presence of nonlinear interaction of the counter propagating Alfv'en waves, and opens the possiblity to investigate Alfv'enic plasma turbulence in controlled and reproducible laboratory experiments.

Interrelation of creep and relaxation: a modeling approach for ligaments.

PubMed

Lakes, R S; Vanderby, R

1999-12-01

Experimental data (Thornton et al., 1997) show that relaxation proceeds more rapidly (a greater slope on a log-log scale) than creep in ligament, a fact not explained by linear viscoelasticity. An interrelation between creep and relaxation is therefore developed for ligaments based on a single-integral nonlinear superposition model. This interrelation differs from the convolution relation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e., the stress-strain curve is concave up as observed in ligament. We also show that it is inconsistent to assume a Fung-type constitutive law (Fung, 1972) for both creep and relaxation. Using the published data of Thornton et al. (1997), the nonlinear interrelation developed herein predicts creep behavior from relaxation data well (R > or = 0.998). Although data are limited and the causal mechanisms associated with viscoelastic tissue behavior are complex, continuum concepts demonstrated here appear capable of interrelating creep and relaxation with fidelity.

Dynamic modulation of visual and electrosensory gains for locomotor control

PubMed Central

Sutton, Erin E.; Demir, Alican; Stamper, Sarah A.; Fortune, Eric S.; Cowan, Noah J.

2016-01-01

Animal nervous systems resolve sensory conflict for the control of movement. For example, the glass knifefish, Eigenmannia virescens, relies on visual and electrosensory feedback as it swims to maintain position within a moving refuge. To study how signals from these two parallel sensory streams are used in refuge tracking, we constructed a novel augmented reality apparatus that enables the independent manipulation of visual and electrosensory cues to freely swimming fish (n = 5). We evaluated the linearity of multisensory integration, the change to the relative perceptual weights given to vision and electrosense in relation to sensory salience, and the effect of the magnitude of sensory conflict on sensorimotor gain. First, we found that tracking behaviour obeys superposition of the sensory inputs, suggesting linear sensorimotor integration. In addition, fish rely more on vision when electrosensory salience is reduced, suggesting that fish dynamically alter sensorimotor gains in a manner consistent with Bayesian integration. However, the magnitude of sensory conflict did not significantly affect sensorimotor gain. These studies lay the theoretical and experimental groundwork for future work investigating multisensory control of locomotion. PMID:27170650

Influence of composition fluctuations on the linear viscoelastic properties of symmetric diblock copolymers near the order-disorder transition

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

Hickey, Robert J.; Gillard, Timothy M.; Lodge, Timothy P.

2015-08-28

Rheological evidence of composition fluctuations in disordered diblock copolymers near the order disorder transition (ODT) has been documented in the literature over the past three decades, characterized by a failure of time–temperature superposition (tTS) to reduce linear dynamic mechanical spectroscopy (DMS) data in the terminal viscoelastic regime to a temperature-independent form. However, for some materials, most notably poly(styrene-b-isoprene) (PS–PI), no signature of these rheological features has been found. We present small-angle X-ray scattering (SAXS) results on symmetric poly(cyclohexylethylene-b-ethylene) (PCHE–PE) diblock copolymers that confirm the presence of fluctuations in the disordered state and DMS measurements that also show no sign ofmore » the features ascribed to composition fluctuations. Assessment of DMS results published on five different diblock copolymer systems leads us to conclude that the effects of composition fluctuations can be masked by highly asymmetric block dynamics, thereby resolving a long-standing disagreement in the literature and reinforcing the importance of mechanical contrast in understanding the dynamics of ordered and disordered block polymers.« less

Calculating Interaction Energies Using First Principle Theories: Consideration of Basis Set Superposition Error and Fragment Relaxation

ERIC Educational Resources Information Center

Bowen, J. Philip; Sorensen, Jennifer B.; Kirschner, Karl N.

2007-01-01

The analysis explains the basis set superposition error (BSSE) and fragment relaxation involved in calculating the interaction energies using various first principle theories. Interacting the correlated fragment and increasing the size of the basis set can help in decreasing the BSSE to a great extent.

Teleportation of a general two-mode coherent-state superposition via attenuated quantum channels with ideal and/or threshold detectors

NASA Astrophysics Data System (ADS)

An, Nguyen Ba

2009-04-01

Three novel probabilistic yet conclusive schemes are proposed to teleport a general two-mode coherent-state superposition via attenuated quantum channels with ideal and/or threshold detectors. The calculated total success probability is highest (lowest) when only ideal (threshold) detectors are used.

The principle of superposition in human prehension.

PubMed

Zatsiorsky, Vladimir M; Latash, Mark L; Gao, Fan; Shim, Jae Kun

2004-03-01

The experimental evidence supports the validity of the principle of superposition for multi-finger prehension in humans. Forces and moments of individual digits are defined by two independent commands: "Grasp the object stronger/weaker to prevent slipping" and "Maintain the rotational equilibrium of the object". The effects of the two commands are summed up.

Simulated Holograms: A Simple Introduction to Holography.

ERIC Educational Resources Information Center

Dittmann, H.; Schneider, W. B.

1992-01-01

Describes a project that uses a computer and a dot matrix printer to simulate the holographic recording process of simple object structures. The process' four steps are (1) superposition of waves; (2) representing the superposition of a plane reference wave on the monitor screen; (3) photographic reduction of the images; and (4) reconstruction of…

Measurement of the Mutual Interference Between Independent Bluetooth Devices

NASA Astrophysics Data System (ADS)

Schoof, Adrien; Ter Haseborg, Jan Luiken

In this paper the field superposition of commercial Bluetooth transmitters is examined. The superposition is measured for miscellaneous analyzer filter bandwidths, transmitter combinations and numbers. Also the commonness of the collisions is measured. Finally the spatial field distributions of standalone and Bluetooth equipped devices are measured and will be presented and discussed.

Classification of ligand molecules in PDB with graph match-based structural superposition.

PubMed

Shionyu-Mitsuyama, Clara; Hijikata, Atsushi; Tsuji, Toshiyuki; Shirai, Tsuyoshi

2016-12-01

The fast heuristic graph match algorithm for small molecules, COMPLIG, was improved by adding a structural superposition process to verify the atom-atom matching. The modified method was used to classify the small molecule ligands in the Protein Data Bank (PDB) by their three-dimensional structures, and 16,660 types of ligands in the PDB were classified into 7561 clusters. In contrast, a classification by a previous method (without structure superposition) generated 3371 clusters from the same ligand set. The characteristic feature in the current classification system is the increased number of singleton clusters, which contained only one ligand molecule in a cluster. Inspections of the singletons in the current classification system but not in the previous one implied that the major factors for the isolation were differences in chirality, cyclic conformations, separation of substructures, and bond length. Comparisons between current and previous classification systems revealed that the superposition-based classification was effective in clustering functionally related ligands, such as drugs targeted to specific biological processes, owing to the strictness of the atom-atom matching.

Multiple quantum coherence spectroscopy.

PubMed

Mathew, Nathan A; Yurs, Lena A; Block, Stephen B; Pakoulev, Andrei V; Kornau, Kathryn M; Wright, John C

2009-08-20

Multiple quantum coherences provide a powerful approach for studies of complex systems because increasing the number of quantum states in a quantum mechanical superposition state increases the selectivity of a spectroscopic measurement. We show that frequency domain multiple quantum coherence multidimensional spectroscopy can create these superposition states using different frequency excitation pulses. The superposition state is created using two excitation frequencies to excite the symmetric and asymmetric stretch modes in a rhodium dicarbonyl chelate and the dynamic Stark effect to climb the vibrational ladders involving different overtone and combination band states. A monochromator resolves the free induction decay of different coherences comprising the superposition state. The three spectral dimensions provide the selectivity required to observe 19 different spectral features associated with fully coherent nonlinear processes involving up to 11 interactions with the excitation fields. The different features act as spectroscopic probes of the diagonal and off-diagonal parts of the molecular potential energy hypersurface. This approach can be considered as a coherent pump-probe spectroscopy where the pump is a series of excitation pulses that prepares a multiple quantum coherence and the probe is another series of pulses that creates the output coherence.

Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates

NASA Astrophysics Data System (ADS)

Moxley, Frederick Ira; Dowling, Jonathan P.; Dai, Weizhong; Byrnes, Tim

2016-05-01

We investigate prospects of using counter-rotating vortex superposition states in nonequilibrium exciton-polariton Bose-Einstein condensates for the purposes of Sagnac interferometry. We first investigate the stability of vortex-antivortex superposition states, and show that they survive at steady state in a variety of configurations. Counter-rotating vortex superpositions are of potential interest to gyroscope and seismometer applications for detecting rotations. Methods of improving the sensitivity are investigated by targeting high momentum states via metastable condensation, and the application of periodic lattices. The sensitivity of the polariton gyroscope is compared to its optical and atomic counterparts. Due to the large interferometer areas in optical systems and small de Broglie wavelengths for atomic BECs, the sensitivity per detected photon is found to be considerably less for the polariton gyroscope than with competing methods. However, polariton gyroscopes have an advantage over atomic BECs in a high signal-to-noise ratio, and have other practical advantages such as room-temperature operation, area independence, and robust design. We estimate that the final sensitivities including signal-to-noise aspects are competitive with existing methods.

Improved Pedagogy for Linear Differential Equations by Reconsidering How We Measure the Size of Solutions

ERIC Educational Resources Information Center

Tisdell, Christopher C.

2017-01-01

For over 50 years, the learning of teaching of "a priori" bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to "a priori" bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving…

Potentials of mean force for biomolecular simulations: Theory and test on alanine dipeptide

NASA Astrophysics Data System (ADS)

Pellegrini, Matteo; Grønbech-Jensen, Niels; Doniach, Sebastian

1996-06-01

We describe a technique for generating potentials of mean force (PMF) between solutes in an aqueous solution. We first generate solute-solvent correlation functions (CF) using Monte Carlo (MC) simulations in which we place a single atom solute in a periodic boundary box containing a few hundred water molecules. We then make use of the Kirkwood superposition approximation, where the 3-body correlation function is approximated as the product of 2-body CFs, to describe the mean water density around two solutes. Computing the force generated on the solutes by this average water density allows us to compute potentials of mean force between the two solutes. For charged solutes an additional approximation involving dielectric screening is made, by setting the dielectric constant of water to ɛ=80. These potentials account, in an approximate manner, for the average effect of water on the atoms. Following the work of Pettitt and Karplus [Chem. Phys. Lett. 121, 194 (1985)], we approximate the n-body potential of mean force as a sum of the pairwise potentials of mean force. This allows us to run simulations of biomolecules without introducing explicit water, hence gaining several orders of magnitude in efficiency with respect to standard molecular dynamics techniques. We demonstrate the validity of this technique by first comparing the PMFs for methane-methane and sodium-chloride generated with this procedure, with those calculated with a standard Monte Carlo simulation with explicit water. We then compare the results of the free energy profiles between the equilibria of alanine dipeptide generated by the two methods.

Employment of Gibbs-Donnan-based concepts for interpretation of the properties of linear polyelectrolyte solutions

USGS Publications Warehouse

Marinsky, J.A.; Reddy, M.M.

1991-01-01

Earlier research has shown that the acid dissociation and metal ion complexation equilibria of linear, weak-acid polyelectrolytes and their cross-linked gel analogues are similarly sensitive to the counterion concentration levels of their solutions. Gibbs-Donnan-based concepts, applicable to the gel, are equally applicable to the linear polyelectrolyte for the accommodation of this sensitivity to ionic strength. This result is presumed to indicate that the linear polyelectrolyte in solution develops counterion-concentrating regions that closely resemble the gel phase of their analogues. Advantage has been taken of this description of linear polyelectrolytes to estimate the solvent uptake by these regions. ?? 1991 American Chemical Society.

Toward quantum superposition of living organisms

NASA Astrophysics Data System (ADS)

Romero-Isart, Oriol; Juan, Mathieu L.; Quidant, Romain; Cirac, J. Ignacio

2010-03-01

The most striking feature of quantum mechanics is the existence of superposition states, where an object appears to be in different situations at the same time. The existence of such states has been previously tested with small objects, such as atoms, ions, electrons and photons (Zoller et al 2005 Eur. Phys. J. D 36 203-28), and even with molecules (Arndt et al 1999 Nature 401 680-2). More recently, it has been shown that it is possible to create superpositions of collections of photons (Deléglise et al 2008 Nature 455 510-14), atoms (Hammerer et al 2008 arXiv:0807.3358) or Cooper pairs (Friedman et al 2000 Nature 406 43-6). Very recent progress in optomechanical systems may soon allow us to create superpositions of even larger objects, such as micro-sized mirrors or cantilevers (Marshall et al 2003 Phys. Rev. Lett. 91 130401; Kippenberg and Vahala 2008 Science 321 1172-6 Marquardt and Girvin 2009 Physics 2 40; Favero and Karrai 2009 Nature Photon. 3 201-5), and thus to test quantum mechanical phenomena at larger scales. Here we propose a method to cool down and create quantum superpositions of the motion of sub-wavelength, arbitrarily shaped dielectric objects trapped inside a high-finesse cavity at a very low pressure. Our method is ideally suited for the smallest living organisms, such as viruses, which survive under low-vacuum pressures (Rothschild and Mancinelli 2001 Nature 406 1092-101) and optically behave as dielectric objects (Ashkin and Dziedzic 1987 Science 235 1517-20). This opens up the possibility of testing the quantum nature of living organisms by creating quantum superposition states in very much the same spirit as the original Schrödinger's cat 'gedanken' paradigm (Schrödinger 1935 Naturwissenschaften 23 807-12, 823-8, 844-9). We anticipate that our paper will be a starting point for experimentally addressing fundamental questions, such as the role of life and consciousness in quantum mechanics.

Capture zones for simple aquifers

USGS Publications Warehouse

McElwee, Carl D.

1991-01-01

Capture zones showing the area influenced by a well within a certain time are useful for both aquifer protection and cleanup. If hydrodynamic dispersion is neglected, a deterministic curve defines the capture zone. Analytical expressions for the capture zones can be derived for simple aquifers. However, the capture zone equations are transcendental and cannot be explicitly solved for the coordinates of the capture zone boundary. Fortunately, an iterative scheme allows the solution to proceed quickly and efficiently even on a modest personal computer. Three forms of the analytical solution must be used in an iterative scheme to cover the entire region of interest, after the extreme values of the x coordinate are determined by an iterative solution. The resulting solution is a discrete one, and usually 100-1000 intervals along the x-axis are necessary for a smooth definition of the capture zone. The presented program is written in FORTRAN and has been used in a variety of computing environments. No graphics capability is included with the program; it is assumed the user has access to a commercial package. The superposition of capture zones for multiple wells is expected to be satisfactory if the spacing is not too close. Because this program deals with simple aquifers, the results rarely will be the final word in a real application.

Linearized simulation of flow over wind farms and complex terrains.

PubMed

Segalini, Antonio

2017-04-13

The flow over complex terrains and wind farms is estimated here by numerically solving the linearized Navier-Stokes equations. The equations are linearized around the unperturbed incoming wind profile, here assumed logarithmic. The Boussinesq approximation is used to model the Reynolds stress with a prescribed turbulent eddy viscosity profile. Without requiring the boundary-layer approximation, two new linear equations are obtained for the vertical velocity and the wall-normal vorticity, with a reduction in the computational cost by a factor of 8 when compared with a primitive-variables formulation. The presence of terrain elevation is introduced as a vertical coordinate shift, while forestry or wind turbines are included as body forces, without any assumption about the wake structure for the turbines. The model is first validated against some available experiments and simulations, and then a simulation of a wind farm over a Gaussian hill is performed. The speed-up effect of the hill is clearly beneficial in terms of the available momentum upstream of the crest, while downstream of it the opposite can be said as the turbines face a decreased wind speed. Also, the presence of the hill introduces an additional spanwise velocity component that may also affect the turbines' operations. The linear superposition of the flow over the hill and the flow over the farm alone provided a first estimation of the wind speed along the farm, with discrepancies of the same order of magnitude for the spanwise velocity. Finally, the possibility of using a parabolic set of equations to obtain the turbulent kinetic energy after the linearized model is investigated with promising results.This article is part of the themed issue 'Wind energy in complex terrains'. © 2017 The Author(s).

Linearized simulation of flow over wind farms and complex terrains

NASA Astrophysics Data System (ADS)

Segalini, Antonio

2017-03-01

The flow over complex terrains and wind farms is estimated here by numerically solving the linearized Navier-Stokes equations. The equations are linearized around the unperturbed incoming wind profile, here assumed logarithmic. The Boussinesq approximation is used to model the Reynolds stress with a prescribed turbulent eddy viscosity profile. Without requiring the boundary-layer approximation, two new linear equations are obtained for the vertical velocity and the wall-normal vorticity, with a reduction in the computational cost by a factor of 8 when compared with a primitive-variables formulation. The presence of terrain elevation is introduced as a vertical coordinate shift, while forestry or wind turbines are included as body forces, without any assumption about the wake structure for the turbines. The model is first validated against some available experiments and simulations, and then a simulation of a wind farm over a Gaussian hill is performed. The speed-up effect of the hill is clearly beneficial in terms of the available momentum upstream of the crest, while downstream of it the opposite can be said as the turbines face a decreased wind speed. Also, the presence of the hill introduces an additional spanwise velocity component that may also affect the turbines' operations. The linear superposition of the flow over the hill and the flow over the farm alone provided a first estimation of the wind speed along the farm, with discrepancies of the same order of magnitude for the spanwise velocity. Finally, the possibility of using a parabolic set of equations to obtain the turbulent kinetic energy after the linearized model is investigated with promising results. This article is part of the themed issue 'Wind energy in complex terrains'.

Bäcklund transformation, infinitely-many conservation laws, solitary and periodic waves of an extended (3 + 1)-dimensional Jimbo-Miwa equation with time-dependent coefficients

NASA Astrophysics Data System (ADS)

Deng, Gao-Fu; Gao, Yi-Tian; Gao, Xin-Yi

2018-07-01

In this paper, an extended (3+1)-dimensional Jimbo-Miwa equation with time-dependent coefficients is investigated, which comes from the second member of the Kadomtsev-Petviashvili hierarchy and is shown to be conditionally integrable. Bilinear form, Bäcklund transformation, Lax pair and infinitely-many conservation laws are derived via the binary Bell polynomials and symbolic computation. With the help of the bilinear form, one-, two- and three-soliton solutions are obtained via the Hirota method, one-periodic wave solutions are constructed via the Riemann theta function. Additionally, propagation and interaction of the solitons are investigated analytically and graphically, from which we find that the interaction between the solitons is elastic and the time-dependent coefficients can affect the soliton velocities, but the soliton amplitudes remain unchanged. One-periodic waves approach the one-solitary waves with the amplitudes vanishing and can be viewed as a superposition of the overlapping solitary waves, placed one period apart.

Vector semirational rogue waves and modulation instability for the coupled higher-order nonlinear Schrödinger equations in the birefringent optical fibers.

PubMed

Sun, Wen-Rong; Liu, De-Yin; Xie, Xi-Yang

2017-04-01

We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrödinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics. We show that the bright-dark type vector solitons (or breather-like vector solitons) with nonconstant speed interplay with Akhmediev breathers, Kuznetsov-Ma solitons, and rogue waves. By adjusting parameters, we note that the rogue wave and bright-dark soliton merge, generating the boomeron-type bright-dark solitons. We prove that the rogue wave can be excited in the baseband modulation instability regime. These results may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.

On the superposition of strengthening mechanisms in dispersion strengthened alloys and metal-matrix nanocomposites: Considerations of stress and energy

NASA Astrophysics Data System (ADS)

Ferguson, J. B.; Schultz, Benjamin F.; Venugopalan, Dev; Lopez, Hugo F.; Rohatgi, Pradeep K.; Cho, Kyu; Kim, Chang-Soo

2014-03-01

Yield strength improvement in dispersion strengthened alloys and nano particle-reinforced composites by well-known strengthening mechanisms such as solid solution, grain refinement, coherent and incoherent dispersed particles, and increased dislocation density resulting from work-hardening can all be described individually. However, there is no agreed upon description of how these mechanisms combine to determine the yield strength. In this work, we propose an analytical yield strength prediction model combining arithmetic and quadratic addition approaches based on the consideration of two types of yielding mechanisms; stress-activated and energy-activated. Using data available in the literature for materials of differing grain sizes, we consider the cases of solid solutions and coherent precipitates to show that they follow stress-activated behavior. Then, we applied our model with some empirical parameters to precipitationhardenable materials of various grain sizes in both coherent and incoherent precipitate conditions, which demonstrated that grain boundary and Orowan-strengthening can be treated as energy-activated mechanisms.

Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2012-01-01

A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

Diffraction of a plane wave by a three-dimensional corner

NASA Technical Reports Server (NTRS)

Ting, L.; Kung, F.

1971-01-01

By the superposition of the conical solution for the diffraction of a plane pulse by a three dimensional corner, the solution for a general incident plane wave is constructed. A numerical program is presented for the computation of the pressure distribution on the surface due to an incident plane wave of any wave form and at any incident angle. Numerical examples are presented to show the pressure signature at several points on the surface due to incident wave with a front shock wave, two shock waves in succession, or a compression wave with same peak pressure. The examples show that when the distance of a point on the surface from the edges or the vertex is comparable to the distance for the front pressure raise to reach the maximum, the peak pressure at that point can be much less than that given by a regular reflection, because the diffracted wave front arrives at that point prior to the arrival of the peak incident wave.

Electrostatic interaction between dissimilar colloids at fluid interfaces

NASA Astrophysics Data System (ADS)

Majee, Arghya; Schmetzer, Timo; Bier, Markus

2018-04-01

The electrostatic interaction between two nonidentical, moderately charged colloids situated in close proximity of each other at a fluid interface is studied. By resorting to a well-justified model system, this problem is analytically solved within the framework of linearized Poisson-Boltzmann density functional theory. The resulting interaction comprises a surface and a line part, both of which, as functions of the interparticle separation, show a rich behavior including monotonic as well as nonmonotonic variations. In almost all cases, these variations cannot be captured correctly by using the superposition approximation. Moreover, expressions for the surface tensions, the line tensions and the fluid-fluid interfacial tension, which are all independent of the interparticle separation, are obtained. Our results are expected to be particularly useful for emulsions stabilized by oppositely charged particles.

Estimation of multiple accelerated motions using chirp-Fourier transform and clustering.

PubMed

Alexiadis, Dimitrios S; Sergiadis, George D

2007-01-01

Motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed, which, however, cannot handle both time-varying and multiple motions. Extending previously published ideas, we present an efficient method for estimating multiple, linearly time-varying motions. It is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals. From this viewpoint, one can exploit established signal processing tools such as the chirp-Fourier transform. It is shown that accelerated motion results in energy concentration along planes in the 4-D space: spatial frequencies-temporal frequency-chirp rate. Using fuzzy c-planes clustering, we estimate the plane/motion parameters. The effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted.

An analytical approach to the rise velocity of periodic bubble trains in non-Newtonian fluids.

PubMed

Frank, X; Li, H Z; Funfschilling, D

2005-01-01

The present study aims at providing insight into the acceleration mechanism of a bubble chain rising in shear-thinning viscoelastic fluids. The experimental investigation by the Particle Image Velocimetry (PIV), birefringence visualisation and rheological simulation shows that two aspects are central to bubble interactions in such media: the stress creation by the passage of bubbles, and their relaxation due to the fluid's memory forming an evanescent corridor of reduced viscosity. Interactions between bubbles were taken into account mainly through a linear superposition of the stress evolution behind each bubble. An analytical approach together with the rheological consideration was developed to compute the rise velocity of a bubble chain in function of the injection period and bubble volume. The model predictions compare satisfactorily with the experimental investigation.

Mass Spectrometry Using Nanomechanical Systems: Beyond the Point-Mass Approximation.

PubMed

Sader, John E; Hanay, M Selim; Neumann, Adam P; Roukes, Michael L

2018-03-14

The mass measurement of single molecules, in real time, is performed routinely using resonant nanomechanical devices. This approach models the molecules as point particles. A recent development now allows the spatial extent (and, indeed, image) of the adsorbate to be characterized using multimode measurements ( Hanay , M. S. , Nature Nanotechnol. , 10 , 2015 , pp 339 - 344 ). This "inertial imaging" capability is achieved through virtual re-engineering of the resonator's vibrating modes, by linear superposition of their measured frequency shifts. Here, we present a complementary and simplified methodology for the analysis of these inertial imaging measurements that exhibits similar performance while streamlining implementation. This development, together with the software that we provide, enables the broad implementation of inertial imaging that opens the door to a range of novel characterization studies of nanoscale adsorbates.

Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions

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

Harris, Frank E., E-mail: harris@qtp.ufl.edu

Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance r{sub ij}. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validatedmore » by showing that they yield correct results for a large number of integrals published by other investigators.« less

A phoenics model for the triaxial loading of an initially cylindrical mass of rate-type material with provisions for bulging and yield

NASA Technical Reports Server (NTRS)

French, K. W., Jr.

1986-01-01

This work traces the response of a granular material via the Ten Coefficient Truesdell rate-type constituitive model into the simplest meaningful loading: the triaxial test configuration. A functional relation has been posed for computing the rather peculiar relation between average applied stress and average porosity. Using that relation an attack has been mounted on the dilemma that exists between dynamic and constitutive use of the pressure variable; that is relating dynamic pressure, thermodynamic pressure, stress deviator and higher stress invariants. The resolution was as a linear superposition with a one-way feedback, in that while the dynamic component could not effect the constituitive component, the converse was not true since density appears in the momentum transport relation.

Mechanically fastened composite laminates subjected to combined bearing-bypass and shear loading

NASA Technical Reports Server (NTRS)

Madenci, Erdogan

1993-01-01

Bolts and rivets provide a means of load transfer in the construction of aircraft. However, they give rise to stress concentrations and are often the source and location of static and fatigue failures. Furthermore, fastener holes are prone to cracks during take-off and landing. These cracks present the most common origin of structural failures in aircraft. Therefore, accurate determination of the contact stresses associated with such loaded holes in mechanically fastened joints is essential to reliable strength evaluation and failure prediction. As the laminate is subjected to loading, the contact region, whose extent is not known, develops between the fastener and the hole boundary through this contact region, which consists of slip and no-slip zones due to friction. The presence of the unknown contact stress distribution over the contact region between the pin and the composite laminate, material anisotropy, friction between the pin and the laminate, pin-hole clearance, combined bearing-bypass and shear loading, and finite geometry of the laminate result in a complex non-linear problem. In the case of bearing-bypass loading in compression, this non-linear problem is further complicated by the presence of dual contact regions. Previous research concerning the analysis of mechanical joints subjected to combined bearing-bypass and shear loading is non-existent. In the case of bearing-bypass loading only, except for the study conducted by Naik and Crews (1991), others employed the concept of superposition which is not valid for this non-linear problem. Naik and Crews applied a linear finite element analysis with conditions along the pin-hole contact region specified as displacement constraint equations. The major shortcoming of this method is that the variation of the contract region as a function of the applied load should be known a priori. Also, their analysis is limited to symmetric geometry and material systems, and frictionless boundary conditions. Since the contact stress distribution and the contact region are not known a priori, they did not directly impose the boundary conditions appropriate for modelling the contact and on-contact regions between the fastener and the hole. Furthermore, finite element analysis is not suitable for iterative design calculations for optimizing laminate construction in the presence of fasteners under complex loading conditions. In this study, the solution method developed by Madenci and Ileri (1992a,b) has been extended to determine the contact stresses in mechanical joints under combined bearing-bypass and shear loading, and bearing-bypass loading in compression resulting in dual contact regions.

Multiple solution of linear algebraic systems by an iterative method with recomputed preconditioner in the analysis of microstrip structures

NASA Astrophysics Data System (ADS)

Ahunov, Roman R.; Kuksenko, Sergey P.; Gazizov, Talgat R.

2016-06-01

A multiple solution of linear algebraic systems with dense matrix by iterative methods is considered. To accelerate the process, the recomputing of the preconditioning matrix is used. A priory condition of the recomputing based on change of the arithmetic mean of the current solution time during the multiple solution is proposed. To confirm the effectiveness of the proposed approach, the numerical experiments using iterative methods BiCGStab and CGS for four different sets of matrices on two examples of microstrip structures are carried out. For solution of 100 linear systems the acceleration up to 1.6 times, compared to the approach without recomputing, is obtained.

The principle of superposition in human prehension

PubMed Central

Zatsiorsky, Vladimir M.; Latash, Mark L.; Gao, Fan; Shim, Jae Kun

2010-01-01

SUMMARY The experimental evidence supports the validity of the principle of superposition for multi-finger prehension in humans. Forces and moments of individual digits are defined by two independent commands: “Grasp the object stronger/weaker to prevent slipping” and “Maintain the rotational equilibrium of the object”. The effects of the two commands are summed up. PMID:20186284

Dissecting ion-specific dielectric spectra of sodium-halide solutions into solvation water and ionic contributions.

PubMed

Rinne, Klaus F; Gekle, Stephan; Netz, Roland R

2014-12-07

Using extensive equilibrium molecular dynamics simulations we determine the dielectric spectra of aqueous solutions of NaF, NaCl, NaBr, and NaI. The ion-specific and concentration-dependent shifts of the static dielectric constants and the dielectric relaxation times match experimental results very well, which serves as a validation of the classical and non-polarizable ionic force fields used. The purely ionic contribution to the dielectric response is negligible, but determines the conductivity of the salt solutions. The ion-water cross correlation contribution is negative and reduces the total dielectric response by about 5%-10% for 1 M solutions. The dominating water dielectric response is decomposed into different water solvation shells and ion-pair configurations, by this the spectral blue shift and the dielectric decrement of salt solutions with increasing salt concentration is demonstrated to be primarily caused by first-solvation shell water. With rising salt concentration the simulated spectra show more pronounced deviations from a single-Debye form and can be well described by a Cole-Cole fit, in quantitative agreement with experiments. Our spectral decomposition into ionic and different water solvation shell contributions does not render the individual contributions more Debye-like, this suggests the non-Debye-like character of the dielectric spectra of salt solutions not to be due to the superposition of different elementary relaxation processes with different relaxation times. Rather, the non-Debye-like character is likely to be an inherent spectral signature of solvation water around ions.

Are Cloned Quantum States Macroscopic?

NASA Astrophysics Data System (ADS)

Fröwis, F.; Dür, W.

2012-10-01

We study quantum states produced by optimal phase covariant quantum cloners. We argue that cloned quantum superpositions are not macroscopic superpositions in the spirit of Schrödinger’s cat, despite their large particle number. This is indicated by calculating several measures for macroscopic superpositions from the literature, as well as by investigating the distinguishability of the two superposed cloned states. The latter rapidly diminishes when considering imperfect detectors or noisy states and does not increase with the system size. In contrast, we find that cloned quantum states themselves are macroscopic, in the sense of both proposed measures and their usefulness in quantum metrology with an optimal scaling in system size. We investigate the applicability of cloned states for parameter estimation in the presence of different kinds of noise.

Superposition and detection of two helical beams for optical orbital angular momentum communication

NASA Astrophysics Data System (ADS)

Liu, Yi-Dong; Gao, Chunqing; Gao, Mingwei; Qi, Xiaoqing; Weber, Horst

2008-07-01

A loop-like system with a Dove prism is used to generate a collinear superposition of two helical beams with different azimuthal quantum numbers in this manuscript. After the generation of the helical beams distributed on the circle centered at the optical axis by using a binary amplitude grating, the diffractive field is separated into two polarized ones with the same distribution. Rotated by the Dove prism in the loop-like system in counter directions and combined together, the two fields will generate the collinear superposition of two helical beams in certain direction. The experiment shows consistency with the theoretical analysis. This method has potential applications in optical communication by using orbital angular momentum of laser beams (optical vortices).

Optical information encryption based on incoherent superposition with the help of the QR code

NASA Astrophysics Data System (ADS)

Qin, Yi; Gong, Qiong

2014-01-01

In this paper, a novel optical information encryption approach is proposed with the help of QR code. This method is based on the concept of incoherent superposition which we introduce for the first time. The information to be encrypted is first transformed into the corresponding QR code, and thereafter the QR code is further encrypted into two phase only masks analytically by use of the intensity superposition of two diffraction wave fields. The proposed method has several advantages over the previous interference-based method, such as a higher security level, a better robustness against noise attack, a more relaxed work condition, and so on. Numerical simulation results and actual smartphone collected results are shown to validate our proposal.

Solving Modal Equations of Motion with Initial Conditions Using MSC/NASTRAN DMAP. Part 2; Coupled Versus Uncoupled Integration

NASA Technical Reports Server (NTRS)

Barnett, Alan R.; Ibrahim, Omar M.; Abdallah, Ayman A.; Sullivan, Timothy L.

1993-01-01

By utilizing MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) in an existing NASA Lewis Research Center coupled loads methodology, solving modal equations of motion with initial conditions is possible using either coupled (Newmark-Beta) or uncoupled (exact mode superposition) integration available within module TRD1. Both the coupled and newly developed exact mode superposition methods have been used to perform transient analyses of various space systems. However, experience has shown that in most cases, significant time savings are realized when the equations of motion are integrated using the uncoupled solver instead of the coupled solver. Through the results of a real-world engineering analysis, advantages of using the exact mode superposition methodology are illustrated.

Near-field interferometry of a free-falling nanoparticle from a point-like source

NASA Astrophysics Data System (ADS)

Bateman, James; Nimmrichter, Stefan; Hornberger, Klaus; Ulbricht, Hendrik

2014-09-01

Matter-wave interferometry performed with massive objects elucidates their wave nature and thus tests the quantum superposition principle at large scales. Whereas standard quantum theory places no limit on particle size, alternative, yet untested theories—conceived to explain the apparent quantum to classical transition—forbid macroscopic superpositions. Here we propose an interferometer with a levitated, optically cooled and then free-falling silicon nanoparticle in the mass range of one million atomic mass units, delocalized over >150 nm. The scheme employs the near-field Talbot effect with a single standing-wave laser pulse as a phase grating. Our analysis, which accounts for all relevant sources of decoherence, indicates that this is a viable route towards macroscopic high-mass superpositions using available technology.

Slowing Quantum Decoherence by Squeezing in Phase Space

NASA Astrophysics Data System (ADS)

Le Jeannic, H.; Cavaillès, A.; Huang, K.; Filip, R.; Laurat, J.

2018-02-01

Non-Gaussian states, and specifically the paradigmatic cat state, are well known to be very sensitive to losses. When propagating through damping channels, these states quickly lose their nonclassical features and the associated negative oscillations of their Wigner function. However, by squeezing the superposition states, the decoherence process can be qualitatively changed and substantially slowed down. Here, as a first example, we experimentally observe the reduced decoherence of squeezed optical coherent-state superpositions through a lossy channel. To quantify the robustness of states, we introduce a combination of a decaying value and a rate of decay of the Wigner function negativity. This work, which uses squeezing as an ancillary Gaussian resource, opens new possibilities to protect and manipulate quantum superpositions in phase space.

Quantum state engineering of light with continuous-wave optical parametric oscillators.

PubMed

Morin, Olivier; Liu, Jianli; Huang, Kun; Barbosa, Felippe; Fabre, Claude; Laurat, Julien

2014-05-30

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics(1,2). Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems(3). We focus here on the use of a continuous-wave optical parametric oscillator(3,4). This system is based on a non-linear χ(2) crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states(5). Generating directly such states is a difficult task and would require strong χ(3) non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.

Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform.

PubMed

Kannan, R; Ievlev, A V; Laanait, N; Ziatdinov, M A; Vasudevan, R K; Jesse, S; Kalinin, S V

2018-01-01

Many spectral responses in materials science, physics, and chemistry experiments can be characterized as resulting from the superposition of a number of more basic individual spectra. In this context, unmixing is defined as the problem of determining the individual spectra, given measurements of multiple spectra that are spatially resolved across samples, as well as the determination of the corresponding abundance maps indicating the local weighting of each individual spectrum. Matrix factorization is a popular linear unmixing technique that considers that the mixture model between the individual spectra and the spatial maps is linear. Here, we present a tutorial paper targeted at domain scientists to introduce linear unmixing techniques, to facilitate greater understanding of spectroscopic imaging data. We detail a matrix factorization framework that can incorporate different domain information through various parameters of the matrix factorization method. We demonstrate many domain-specific examples to explain the expressivity of the matrix factorization framework and show how the appropriate use of domain-specific constraints such as non-negativity and sum-to-one abundance result in physically meaningful spectral decompositions that are more readily interpretable. Our aim is not only to explain the off-the-shelf available tools, but to add additional constraints when ready-made algorithms are unavailable for the task. All examples use the scalable open source implementation from https://github.com/ramkikannan/nmflibrary that can run from small laptops to supercomputers, creating a user-wide platform for rapid dissemination and adoption across scientific disciplines.

Transverse vibration and buckling of a cantilevered beam with tip body under constant axial base acceleration

NASA Technical Reports Server (NTRS)

Storch, J.; Gates, S.

1983-01-01

The planar transverse bending behavior of a uniform cantilevered beam with rigid tip body subject to constant axial base acceleration was analyzed. The beam is inextensible and capable of small elastic transverse bending deformations only. Two classes of tip bodies are recognized: (1) mass centers located along the beam tip tangent line; and (2) mass centers with arbitrary offset towards the beam attachment point. The steady state response is studied for the beam end condition cases: free, tip mass, tip body with restricted mass center offset, and tip body with arbitrary mass center offset. The first three cases constitute classical Euler buckling problems, and the characteristic equation for the critical loads/accelerations are determined. For the last case a unique steady state solution exists. The free vibration response is examined for the two classes of tip body. The characteristic equation, eigenfunctions and their orthogonality properties are obtained for the case of restricted mass center offset. The vibration problem is nonhomogeneous for the case of arbitrary mass center offset. The exact solution is obtained as a sum of the steady state solution and a superposition of simple harmonic motions.

A Gaussian beam method for ultrasonic non-destructive evaluation modeling

NASA Astrophysics Data System (ADS)

Jacquet, O.; Leymarie, N.; Cassereau, D.

2018-05-01

The propagation of high-frequency ultrasonic body waves can be efficiently estimated with a semi-analytic Dynamic Ray Tracing approach using paraxial approximation. Although this asymptotic field estimation avoids the computational cost of numerical methods, it may encounter several limitations in reproducing identified highly interferential features. Nevertheless, some can be managed by allowing paraxial quantities to be complex-valued. This gives rise to localized solutions, known as paraxial Gaussian beams. Whereas their propagation and transmission/reflection laws are well-defined, the fact remains that the adopted complexification introduces additional initial conditions. While their choice is usually performed according to strategies specifically tailored to limited applications, a Gabor frame method has been implemented to indiscriminately initialize a reasonable number of paraxial Gaussian beams. Since this method can be applied for an usefully wide range of ultrasonic transducers, the typical case of the time-harmonic piston radiator is investigated. Compared to the commonly used Multi-Gaussian Beam model [1], a better agreement is obtained throughout the radiated field between the results of numerical integration (or analytical on-axis solution) and the resulting Gaussian beam superposition. Sparsity of the proposed solution is also discussed.

Modeling 2D and 3D periodic nanostructuring of materials with ultrafast laser pulses (Conference Presentation)

NASA Astrophysics Data System (ADS)

Colombier, Jean-Philippe; Rudenko, Anton; Bévillon, Emile; Zhang, Hao; Itina, Tatiana E.; Stoian, Razvan

2017-03-01

Generation of periodic arrangements of matter on materials irradiated by laser fields of uniform and isotropic energy distribution is a key issue in controlling laser structuring processes below the diffractive limit. Using three-dimensional finite-difference time-domain methods, we evaluate energy deposition patterns below a material's rough surface [1] and in bulk dielectric materials containing randomly distributed nano-inhomogeneities [2]. We show that both surface and volume patterns can be attributed to spatially ordered electromagnetic solutions of linear and nonlinear Maxwell equations. In particular, simulations revealed that anisotropic energy deposition results from the coherent superposition of the incident and the inhomogeneity-scattered light waves. Transient electronic response is also analyzed by kinetic equations of free electron excitation/relaxation processes for dielectrics and by ab initio calculations for metals. They show that for nonplasmonic metals, ultrafast carrier excitation can drastically affect electronic structures, driving a transient surface plasmonic state with high consequences for optical resonances generation [3]. Comparing condition formations of 2D laser-induced periodic surface structures (LIPSS) and 3D self-organized nanogratings, we will discuss the role of collective scattering of nanoroughness and the feedback-driven growth of the nanostructures. [1] H. Zhang, J.P. Colombier, C. Li, N. Faure, G. Cheng, and R. Stoian, Physical Review B 92, 174109 (2015). [2] A. Rudenko, J.P. Colombier, and T.E. Itina, Physical Review B 93 (7), 075427 (2016). [3] E. Bévillon, J.P. Colombier, V. Recoules, H. Zhang, C. Li and R. Stoian, Physical Review B 93 (16), 165416 (2016).

Assessing the impact of non-tidal atmospheric loading on a Kalman filter-based terrestrial reference frame

NASA Astrophysics Data System (ADS)

Abbondanza, Claudio; Altamimi, Zuheir; Chin, Toshio; Collilieux, Xavier; Dach, Rolf; Gross, Richard; Heflin, Michael; König, Rolf; Lemoine, Frank; Macmillan, Dan; Parker, Jay; van Dam, Tonie; Wu, Xiaoping

2014-05-01

The International Terrestrial Reference Frame (ITRF) adopts a piece-wise linear model to parameterize regularized station positions and velocities. The space-geodetic (SG) solutions from VLBI, SLR, GPS and DORIS used as input in the ITRF combination process account for tidal loading deformations, but ignore the non-tidal part. As a result, the non-linear signal observed in the time series of SG-derived station positions in part reflects non-tidal loading displacements not introduced in the SG data reduction. In this analysis, we assess the impact of non-tidal atmospheric loading (NTAL) corrections on the TRF computation. Focusing on the a-posteriori approach, (i) the NTAL model derived from the National Centre for Environmental Prediction (NCEP) surface pressure is removed from the SINEX files of the SG solutions used as inputs to the TRF determinations; (ii) adopting a Kalman-filter based approach, two distinct linear TRFs are estimated combining the 4 SG solutions with (corrected TRF solution) and without the NTAL displacements (standard TRF solution). Linear fits (offset and atmospheric velocity) of the NTAL displacements removed during step (i) are estimated accounting for the station position discontinuities introduced in the SG solutions and adopting different weighting strategies. The NTAL-derived (atmospheric) velocity fields are compared to those obtained from the TRF reductions during step (ii). The consistency between the atmospheric and the TRF-derived velocity fields is examined. We show how the presence of station position discontinuities in SG solutions degrades the agreement between the velocity fields and compare the effect of different weighting structure adopted while estimating the linear fits to the NTAL displacements. Finally, we evaluate the effect of restoring the atmospheric velocities determined through the linear fits of the NTAL displacements to the single-technique linear reference frames obtained by stacking the standard SG SINEX files. Differences between the velocity fields obtained restoring the NTAL displacements and the standard stacked linear reference frames are discussed.

Schwarz maps of algebraic linear ordinary differential equations

NASA Astrophysics Data System (ADS)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

Operator Factorization and the Solution of Second-Order Linear Ordinary Differential Equations

ERIC Educational Resources Information Center

Robin, W.

2007-01-01

The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential equations (ODE). Using the operator factorization approach, the general second-order linear ODE is solved, exactly, in quadratures and the resulting…

Scattering and Absorption Properties of Polydisperse Wavelength-sized Particles Covered with Much Smaller Grains

NASA Technical Reports Server (NTRS)

Dlugach, Jana M.; Mishchenko, Michael I.; Mackowski, Daniel W.

2012-01-01

Using the results of direct, numerically exact computer solutions of the Maxwell equations, we analyze scattering and absorption characteristics of polydisperse compound particles in the form of wavelength-sized spheres covered with a large number of much smaller spherical grains.The results pertain to the complex refractive indices1.55 + i0.0003,1.55 + i0.3, and 3 + i0.1. We show that the optical effects of dusting wavelength-sized hosts by microscopic grains can vary depending on the number and size of the grains as well as on the complex refractive index. Our computations also demonstrate the high efficiency of the new superposition T-matrix code developed for use on distributed memory computer clusters.

A Noniterative Technique for the Direct Implementation of Well Bore Boundary Conditions in Three-Dimensional Heterogeneous Formations

NASA Astrophysics Data System (ADS)

Sudicky, E. A.; Unger, A. J. A.; Lacombe, S.

1995-02-01

A noniterative algorithm for handling prescribed well bore boundary conditions while pumping or injecting fluid in a three-dimensional heterogeneous aquifer is described. The algorithm is formulated by superimposing conductive one-dimensional line elements representing the well screen onto the three-dimensional matrix elements epresenting the aquifer. Storage in the well casing is also naturally accommodated by the superposition of the line elements. The numerical algorithm is verified by comparison with results obtained from the solution of Papadopulos and Cooper (1967). A large-scale example problem involving groundwater extraction from a partially penetrating pumping well located in a highly heterogeneous confined aquifer is presented to demonstrate the utility of the approach.

Drawings and Ideas of Physics Teacher Candidates Relating to the Superposition Principle on a Continuous Rope

ERIC Educational Resources Information Center

Sengoren, Serap Kaya; Tanel, Rabia; Kavcar, Nevzat

2006-01-01

The superposition principle is used to explain many phenomena in physics. Incomplete knowledge about this topic at a basic level leads to physics students having problems in the future. As long as prospective physics teachers have difficulties in the subject, it is inevitable that high school students will have the same difficulties. The aim of…

Nano confinement effects on dynamic and viscoelastic properties of Selenium Films

NASA Astrophysics Data System (ADS)

Yoon, Heedong; McKenna, Gregory

2015-03-01

In current study, we use a novel nano bubble inflation technique to study nano confinement effects on the dynamic and viscoelastic properties of physical vapor deposited Selenium films. Film thicknesses ranged from 60 to 260 nm. Creep experiments were performed for the temperatures ranging from Tg,macroscopic-14 °C to Tg,\\ macroscopic + 19 °C. Time temperature superposition and time thickness superposition were applied to create reduced creep curves, and those were compared with macroscopic data [J. Non-Cryst. Solids. 2002, 307, 790-801]. The results showed that the time temperature superposition was applicable in the glassy relaxation regime to the steady-state plateau regime. However in the long time response of the creep compliance, time thickness superposition failed due to the thickness dependence on the steady-state plateau. It was observed that the steady state compliance increased with film thickness. The thickness dependence on the plateau stiffening followed a power law of DPlateau ~ h2.46, which is greater than observed in organic polymers where the exponents observed range from 0.83 to 2.0 [Macromolecules. 2012, 45 (5), 2453-2459]. National Science Foundation Grant No. CHE 1112416 and John R. Bradford Endowment at Texas Tech

Dosimetric verification of radiation therapy including intensity modulated treatments, using an amorphous-silicon electronic portal imaging device

NASA Astrophysics Data System (ADS)

Chytyk-Praznik, Krista Joy

Radiation therapy is continuously increasing in complexity due to technological innovation in delivery techniques, necessitating thorough dosimetric verification. Comparing accurately predicted portal dose images to measured images obtained during patient treatment can determine if a particular treatment was delivered correctly. The goal of this thesis was to create a method to predict portal dose images that was versatile and accurate enough to use in a clinical setting. All measured images in this work were obtained with an amorphous silicon electronic portal imaging device (a-Si EPID), but the technique is applicable to any planar imager. A detailed, physics-motivated fluence model was developed to characterize fluence exiting the linear accelerator head. The model was further refined using results from Monte Carlo simulations and schematics of the linear accelerator. The fluence incident on the EPID was converted to a portal dose image through a superposition of Monte Carlo-generated, monoenergetic dose kernels specific to the a-Si EPID. Predictions of clinical IMRT fields with no patient present agreed with measured portal dose images within 3% and 3 mm. The dose kernels were applied ignoring the geometrically divergent nature of incident fluence on the EPID. A computational investigation into this parallel dose kernel assumption determined its validity under clinically relevant situations. Introducing a patient or phantom into the beam required the portal image prediction algorithm to account for patient scatter and attenuation. Primary fluence was calculated by attenuating raylines cast through the patient CT dataset, while scatter fluence was determined through the superposition of pre-calculated scatter fluence kernels. Total dose in the EPID was calculated by convolving the total predicted incident fluence with the EPID-specific dose kernels. The algorithm was tested on water slabs with square fields, agreeing with measurement within 3% and 3 mm. The method was then applied to five prostate and six head-and-neck IMRT treatment courses (˜1900 clinical images). Deviations between the predicted and measured images were quantified. The portal dose image prediction model developed in this thesis work has been shown to be accurate, and it was demonstrated to be able to verify patients' delivered radiation treatments.

Assessing coastal flood risk and sea level rise impacts at New York City area airports

NASA Astrophysics Data System (ADS)

Ohman, K. A.; Kimball, N.; Osler, M.; Eberbach, S.

2014-12-01

Flood risk and sea level rise impacts were assessed for the Port Authority of New York and New Jersey (PANYNJ) at four airports in the New York City area. These airports included John F. Kennedy International, LaGuardia, Newark International, and Teterboro Airports. Quantifying both present day and future flood risk due to climate change and developing flood mitigation alternatives is crucial for the continued operation of these airports. During Hurricane Sandy in October 2012 all four airports were forced to shut down, in part due to coastal flooding. Future climate change and sea level rise effects may result in more frequent shutdowns and disruptions in travel to and from these busy airports. The study examined the effects of the 1%-annual-chance coastal flooding event for present day existing conditions and six different sea level rise scenarios at each airport. Storm surge model outputs from the Federal Emergency Management Agency (FEMA) provided the present day storm surge conditions. 50th and 90thpercentile sea level rise projections from the New York Panel on Climate Change (NPCC) 2013 report were incorporated into storm surge results using linear superposition methods. These projections were evaluated for future years 2025, 2035, and 2055. In addition to the linear superposition approach for storm surge at airports where waves are a potential hazard, one dimensional wave modeling was performed to get the total water level results. Flood hazard and flood depth maps were created based on these results. In addition to assessing overall flooding at each airport, major at-risk infrastructure critical to the continued operation of the airport was identified and a detailed flood vulnerability assessment was performed. This assessment quantified flood impacts in terms of potential critical infrastructure inundation and developed mitigation alternatives to adapt to coastal flooding and future sea level changes. Results from this project are advancing the PANYNJ's understanding of the effects of sea level rise on coastal flooding at the airports and guiding decision-making in the selection of effective adaptation actions. Given the importance of these airports to transportation, this project is advancing security and continuity of national and international commerce well into the 21st century.

Improved pedagogy for linear differential equations by reconsidering how we measure the size of solutions

NASA Astrophysics Data System (ADS)

Tisdell, Christopher C.

2017-11-01

For over 50 years, the learning of teaching of a priori bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to a priori bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving second-order, linear problems with constant co-efficients, we believe it is not pedagogically optimal. Moreover, the Euclidean method becomes pedagogically unwieldy in the proofs involving higher-order cases. The purpose of this work is to propose a simpler pedagogical approach to establish a priori bounds on solutions by considering a different way of measuring the size of a solution to linear problems, which we refer to as the Uber size. The Uber form enables a simplification of pedagogy from the literature and the ideas are accessible to learners who have an understanding of the Fundamental Theorem of Calculus and the exponential function, both usually seen in a first course in calculus. We believe that this work will be of mathematical and pedagogical interest to those who are learning and teaching in the area of differential equations or in any of the numerous disciplines where linear differential equations are used.

On the growth of solutions of a class of higher order linear differential equations with coefficients having the same order

NASA Astrophysics Data System (ADS)

Tu, Jin; Yi, Cai-Feng

2008-04-01

In this paper, the authors investigate the growth of solutions of a class of higher order linear differential equationsf(k)+Ak-1f(k-1)+...+A0f=0 when most coefficients in the above equations have the same order with each other, and obtain some results which improve previous results due to K.H. Kwon [K.H. Kwon, Nonexistence of finite order solutions of certain second order linear differential equations, Kodai Math. J. 19 (1996) 378-387] and ZE-X. Chen [Z.-X. Chen, The growth of solutions of the differential equation f''+e-zf'+Q(z)f=0, Sci. China Ser. A 31 (2001) 775-784 (in Chinese); ZE-X. Chen, On the hyper order of solutions of higher order differential equations, Chinese Ann. Math. Ser. B 24 (2003) 501-508 (in Chinese); Z.-X. Chen, On the growth of solutions of a class of higher order differential equations, Acta Math. Sci. Ser. B 24 (2004) 52-60 (in Chinese); Z.-X. Chen, C.-C. Yang, Quantitative estimations on the zeros and growth of entire solutions of linear differential equations, Complex Var. 42 (2000) 119-133].

On basis set superposition error corrected stabilization energies for large n-body clusters.

PubMed

Walczak, Katarzyna; Friedrich, Joachim; Dolg, Michael

2011-10-07

In this contribution, we propose an approximate basis set superposition error (BSSE) correction scheme for the site-site function counterpoise and for the Valiron-Mayer function counterpoise correction of second order to account for the basis set superposition error in clusters with a large number of subunits. The accuracy of the proposed scheme has been investigated for a water cluster series at the CCSD(T), CCSD, MP2, and self-consistent field levels of theory using Dunning's correlation consistent basis sets. The BSSE corrected stabilization energies for a series of water clusters are presented. A study regarding the possible savings with respect to computational resources has been carried out as well as a monitoring of the basis set dependence of the approximate BSSE corrections. © 2011 American Institute of Physics

Simultaneous classification of Oranges and Apples Using Grover's and Ventura' Algorithms in a Two-qubits System

NASA Astrophysics Data System (ADS)

Singh, Manu Pratap; Radhey, Kishori; Kumar, Sandeep

2017-08-01

In the present paper, simultaneous classification of Orange and Apple has been carried out using both Grover's iterative algorithm (Grover 1996) and Ventura's model (Ventura and Martinez, Inf. Sci. 124, 273-296, 2000) taking different superposition of two- pattern start state containing Orange and Apple both, one- pattern start state containing Apple as search state and another one- pattern start state containing Orange as search state. It has been shown that the exclusion superposition is the most suitable two- pattern search state for simultaneous classification of pattern associated with Apples and Oranges and the superposition of phase-invariance are the best choice as the respective search state based on one -pattern start-states in both Grover's and Ventura's methods of classifications of patterns.

Photonic microwave waveforms generation based on pulse carving and superposition in time-domain

NASA Astrophysics Data System (ADS)

Xia, Yi; Jiang, Yang; Zi, Yuejiao; He, Yutong; Tian, Jing; Zhang, Xiaoyu; Luo, Hao; Dong, Ruyang

2018-05-01

A novel photonic approach for various microwave waveforms generation based on time-domain synthesis is theoretically analyzed and experimentally investigated. In this scheme, two single-drive Mach-Zehnder modulators are used for pulses shaping. After shifting the phase and implementing envelopes superposition of the pulses, desired waveforms can be achieved in time-domain. The theoretic analysis and simulations are presented. In the experimental demonstrations, a triangular waveform, square waveform, and half duty cycle sawtooth (or reversed-sawtooth) waveform are generated successfully. By utilizing time multiplexing technique, a frequency-doubled sawtooth (or reversed-sawtooth) waveform with 100% duty cycle can be obtained. In addition, a fundamental frequency sawtooth (or reversed-sawtooth) waveform with 100% duty cycle can also be achieved by the superposition of square waveform and frequency-doubled sawtooth waveform.

Superposition-model analysis of rare-earth doped BaY2F8

NASA Astrophysics Data System (ADS)

Magnani, N.; Amoretti, G.; Baraldi, A.; Capelletti, R.

The energy level schemes of four rare-earth dopants (Ce3+ , Nd3+ , Dy3+ , and Er3+) in BaY2 F-8 , as determined by optical absorption spectra, were fitted with a single-ion Hamiltonian and analysed within Newman's Superposition Model for the crystal field. A unified picture for the four dopants was obtained, by assuming a distortion of the F- ligand cage around the RE site; within the framework of the Superposition Model, this distortion is found to have a marked anisotropic behaviour for heavy rare earths, while it turns into an isotropic expansion of the nearest-neighbours polyhedron for light rare earths. It is also inferred that the substituting ion may occupy an off-center position with respect to the original Y3+ site in the crystal.

Transient change in the shape of premixed burner flame with the superposition of pulsed dielectric barrier discharge

NASA Astrophysics Data System (ADS)

Zaima, Kazunori; Sasaki, Koichi

2016-08-01

We investigated the transient phenomena in a premixed burner flame with the superposition of a pulsed dielectric barrier discharge (DBD). The length of the flame was shortened by the superposition of DBD, indicating the activation of combustion chemical reactions with the help of the plasma. In addition, we observed the modulation of the top position of the unburned gas region and the formations of local minimums in the axial distribution of the optical emission intensity of OH. These experimental results reveal the oscillation of the rates of combustion chemical reactions as a response to the activation by pulsed DBD. The cycle of the oscillation was 0.18-0.2 ms, which could be understood as the eigenfrequency of the plasma-assisted combustion reaction system.

Coherent inflation for large quantum superpositions of levitated microspheres

NASA Astrophysics Data System (ADS)

Romero-Isart, Oriol

2017-12-01

We show that coherent inflation (CI), namely quantum dynamics generated by inverted conservative potentials acting on the center of mass of a massive object, is an enabling tool to prepare large spatial quantum superpositions in a double-slit experiment. Combined with cryogenic, extreme high vacuum, and low-vibration environments, we argue that it is experimentally feasible to exploit CI to prepare the center of mass of a micrometer-sized object in a spatial quantum superposition comparable to its size. In such a hitherto unexplored parameter regime gravitationally-induced decoherence could be unambiguously falsified. We present a protocol to implement CI in a double-slit experiment by letting a levitated microsphere traverse a static potential landscape. Such a protocol could be experimentally implemented with an all-magnetic scheme using superconducting microspheres.

Optical threshold secret sharing scheme based on basic vector operations and coherence superposition

NASA Astrophysics Data System (ADS)

Deng, Xiaopeng; Wen, Wei; Mi, Xianwu; Long, Xuewen

2015-04-01

We propose, to our knowledge for the first time, a simple optical algorithm for secret image sharing with the (2,n) threshold scheme based on basic vector operations and coherence superposition. The secret image to be shared is firstly divided into n shadow images by use of basic vector operations. In the reconstruction stage, the secret image can be retrieved by recording the intensity of the coherence superposition of any two shadow images. Compared with the published encryption techniques which focus narrowly on information encryption, the proposed method can realize information encryption as well as secret sharing, which further ensures the safety and integrality of the secret information and prevents power from being kept centralized and abused. The feasibility and effectiveness of the proposed method are demonstrated by numerical results.

A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

NASA Technical Reports Server (NTRS)

Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

1992-01-01

The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem.

PubMed

Narayanamoorthy, S; Kalyani, S

2015-01-01

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

Discrete Applied Mathematics

DTIC Science & Technology

1993-05-31

program. In paper [28], we give a brief and elementary proof of a result of Hoffman [1952) about approximate solutions to systems, of linear inequalities...UCLA, Vestvood, CA, February 1993. " Linear Problems: Formulation and Solution," International Linear Algebra Society, Pensacola, FL, May 1993. Denise S...thresAold If there is a number h and a linear k-separator w assigning a real number to each vertex so that for any subset S of vertices, the sum of w

Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration.

PubMed

Xia, Youshen; Sun, Changyin; Zheng, Wei Xing

2012-05-01

There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L1 estimation problems but also needs much less computational time than the related algorithms in solving both linear L1 estimation and image restoration problems.

Towards a viscoelastic model for the unfused midpalatal suture: development and validation using the midsagittal suture in New Zealand white rabbits.

PubMed

Romanyk, D L; Liu, S S; Lipsett, M G; Toogood, R W; Lagravère, M O; Major, P W; Carey, J P

2013-06-21

Maxillary expansion treatment is a commonly used procedure by orthodontists to widen a patient's upper jaw. As this is typically performed in adolescent patients, the midpalatal suture, connective tissue adjoining the two maxilla halves, remains unfused. Studies that have investigated patient response to expansion treatment, generally through finite element analysis, have considered this suture to behave in a linear elastic manner or it was left vacant. The purpose of the study presented here was to develop a model that could represent the midpalatal suture's viscoelastic behavior. Quasilinear viscoelastic, modified superposition, Schapery's, and Burgers modeling approaches were all considered. Raw data from a previously published study using New Zealand White Rabbits was utilized for model parameter estimation and validation. In this study, Sentalloy(®) coil springs at load levels of 0.49N (50g), 0.98N (100g), and 1.96N (200g) were used to widen the midsagittal suture of live rabbits over a period of 6 weeks. Evaluation was based on a models ability to represent experimental data well over all three load sets. Ideally, a single set of model constants could be used to represent data over all loads tested. Upon completion of the analysis it was found that the modified superposition method was able to replicate experimental data within one standard deviation of the means using a single set of constants for all loads. Future work should focus on model improvement as well as prediction of treatment outcomes. Copyright © 2013 Elsevier Ltd. All rights reserved.

Evaluation of bias associated with capture maps derived from nonlinear groundwater flow models

USGS Publications Warehouse

Nadler, Cara; Allander, Kip K.; Pohll, Greg; Morway, Eric D.; Naranjo, Ramon C.; Huntington, Justin

2018-01-01

The impact of groundwater withdrawal on surface water is a concern of water users and water managers, particularly in the arid western United States. Capture maps are useful tools to spatially assess the impact of groundwater pumping on water sources (e.g., streamflow depletion) and are being used more frequently for conjunctive management of surface water and groundwater. Capture maps have been derived using linear groundwater flow models and rely on the principle of superposition to demonstrate the effects of pumping in various locations on resources of interest. However, nonlinear models are often necessary to simulate head-dependent boundary conditions and unconfined aquifers. Capture maps developed using nonlinear models with the principle of superposition may over- or underestimate capture magnitude and spatial extent. This paper presents new methods for generating capture difference maps, which assess spatial effects of model nonlinearity on capture fraction sensitivity to pumping rate, and for calculating the bias associated with capture maps. The sensitivity of capture map bias to selected parameters related to model design and conceptualization for the arid western United States is explored. This study finds that the simulation of stream continuity, pumping rates, stream incision, well proximity to capture sources, aquifer hydraulic conductivity, and groundwater evapotranspiration extinction depth substantially affect capture map bias. Capture difference maps demonstrate that regions with large capture fraction differences are indicative of greater potential capture map bias. Understanding both spatial and temporal bias in capture maps derived from nonlinear groundwater flow models improves their utility and defensibility as conjunctive-use management tools.

Dynamics of the solute-solvent interactions of electronically excited 4-N,N-dimethylaminobenzonitrile (DMABN) and of 3,5,N,N-tetramethyl-4-aminobenzonitrile (TMABN) dissolved in viscous alcohols and in a viscous nitrile

NASA Astrophysics Data System (ADS)

Weisenborn, Petra C. M.; Huizer, A. Herbert; Varma, Cyril A. G. O.

1989-06-01

The time dependence of the fluorescence of solutions of 4-N,N-dimethylaminobenzonitrile (DMABN) and 3,5,N,N-tetramethyl-4-aminobenzonitrile (TMA BN) in neat polar solvents has been investigated, using a 25 ps UV-laser pulse for excitation and a streak camera for detection. Both the compounds DMABN and TMABN exhibit normal fluorescence F N and anomalous fluorescence F A, but all the solutions of TMABN show merely a single band in the fluorescence spectrum, which is a superposition of the bands F N and F A. In the case of DMABN the fluorescence in the region λ < 400 nm, where F N dominates, the fluorescence decays tri-exponentially due to fluorescence from three types of species, namely excited solute-solvent complexes, excited bare solutes and solute-solvent exciplexes. Within the lifetime of these emitting species there is probably no reverse reaction from exciplexes to excited solute-solvent complexes or excited bare solutes. This is in contrast with a previously presented picture, which includes such a reverse reaction. In the case of the solution of DMABN in n-butanol, the fluorescence at λ < 400 nm is bi-exponential. We show that this is due to an accidental degeneracy of two lifetimes. In contrast to a previous conclusion, we find that DMABN exists partially in the form of ground state solute-solvent complexes also in the solution in nitriles. The anomalous fluorescence develops in two phases, in the first one solute-solvent exciplexes are formed and in the second one the dielectric polarization of the solvent around the exciplex builds up. The rate constant for the formation of the anomalously fluorescing species, i.e. solute-solvent exciplexes, bears no relation with the longitudinal relaxation time, as claimed to have been shown previously.

On the absence of reverse running waves in general displacement of lattice vibration in popular books on solid state theory

NASA Astrophysics Data System (ADS)

Xia, Shangda; Lou, Liren

2018-05-01

In this article we point out that there is a deficiency in the presentation of the general solution of harmonic lattice vibration, the omission of half of the allowed running waves, in many popular textbooks published since 1940, e.g. O Madelung’s 1978 Introduction to Solid-State Theory and J Solyom’s 2007 Fundamentals of the Physics of Solids, vol 1. So we provide a revised presentation, which gives a complete general solution and demonstrates clearly that the conventional complex normal coordinate should be a superposition of two coordinates (multiplied by a factor \\sqrt{1/2}) of running waves travelling oppositely along q and -q, not only a coordinate of a unidirectional running wave as many books considered. It is noticed that the book, Quantum Theory of the Solid State: An Introduction, by L Kantorovich, published in 2004, and the review article, ‘Phonons in perfect crystals’ by W Cochran and R A Cowly, published in 1967, for a one-dimensional single-atom chain gave correct (but not normalized) formulae for the general solution of lattice vibration and the normal coordinate. However, both of them stated still that each normal coordinate describes an independent mode of vibration, which in our opinion needs to be further discussed. Moreover, in books such as Fundamentals of the Physics of Solids, vol 1, by J Solyom, and The Physics and Chemistry of Solids, by S R Elliott, published in 2006 and 2007, respectively, the reverse waves were still lost. Hence, we also discuss a few related topics. In quantization of the lattice vibration, the introduction of the conventional two (not one) independent phonon operators in a normal coordinate is closely related to the ‘independence’ of the two constituent waves mentioned above, and we propose a simple propositional relation between the phonon operator and the corresponding running wave coordinate. Moreover, only the coordinate of the superposition wave (not the running wave), as the normal coordinate can give the correct quantization commutation relations. In addition, there is an interference between the direct and reverse running waves in kinetic and potential energies, which also questions the popular term ‘normal mode’ for a running wave mode. Therefore we have made a few suggestions and discuss the terms of relative quantities.

Improving the Yule-Nielsen modified Neugebauer model by dot surface coverages depending on the ink superposition conditions

NASA Astrophysics Data System (ADS)

Hersch, Roger David; Crété, Frédérique

2004-12-01

Dot gain is different when dots are printed alone, printed in superposition with one ink or printed in superposition with two inks. In addition, the dot gain may also differ depending on which solid ink the considered halftone layer is superposed. In a previous research project, we developed a model for computing the effective surface coverage of a dot according to its superposition conditions. In the present contribution, we improve the Yule-Nielsen modified Neugebauer model by integrating into it our effective dot surface coverage computation model. Calibration of the reproduction curves mapping nominal to effective surface coverages in every superposition condition is carried out by fitting effective dot surfaces which minimize the sum of square differences between the measured reflection density spectra and reflection density spectra predicted according to the Yule-Nielsen modified Neugebauer model. In order to predict the reflection spectrum of a patch, its known nominal surface coverage values are converted into effective coverage values by weighting the contributions from different reproduction curves according to the weights of the contributing superposition conditions. We analyze the colorimetric prediction improvement brought by our extended dot surface coverage model for clustered-dot offset prints, thermal transfer prints and ink-jet prints. The color differences induced by the differences between measured reflection spectra and reflection spectra predicted according to the new dot surface estimation model are quantified on 729 different cyan, magenta, yellow patches covering the full color gamut. As a reference, these differences are also computed for the classical Yule-Nielsen modified spectral Neugebauer model incorporating a single halftone reproduction curve for each ink. Taking into account dot surface coverages according to different superposition conditions considerably improves the predictions of the Yule-Nielsen modified Neugebauer model. In the case of offset prints, the mean difference between predictions and measurements expressed in CIE-LAB CIE-94 ΔE94 values is reduced at 100 lpi from 1.54 to 0.90 (accuracy improvement factor: 1.7) and at 150 lpi it is reduced from 1.87 to 1.00 (accuracy improvement factor: 1.8). Similar improvements have been observed for a thermal transfer printer at 600 dpi, at lineatures of 50 and 75 lpi. In the case of an ink-jet printer at 600 dpi, the mean ΔE94 value is reduced at 75 lpi from 3.03 to 0.90 (accuracy improvement factor: 3.4) and at 100 lpi from 3.08 to 0.91 (accuracy improvement factor: 3.4).

Improving the Yule-Nielsen modified Neugebauer model by dot surface coverages depending on the ink superposition conditions

NASA Astrophysics Data System (ADS)

Hersch, Roger David; Crete, Frederique

2005-01-01

Dot gain is different when dots are printed alone, printed in superposition with one ink or printed in superposition with two inks. In addition, the dot gain may also differ depending on which solid ink the considered halftone layer is superposed. In a previous research project, we developed a model for computing the effective surface coverage of a dot according to its superposition conditions. In the present contribution, we improve the Yule-Nielsen modified Neugebauer model by integrating into it our effective dot surface coverage computation model. Calibration of the reproduction curves mapping nominal to effective surface coverages in every superposition condition is carried out by fitting effective dot surfaces which minimize the sum of square differences between the measured reflection density spectra and reflection density spectra predicted according to the Yule-Nielsen modified Neugebauer model. In order to predict the reflection spectrum of a patch, its known nominal surface coverage values are converted into effective coverage values by weighting the contributions from different reproduction curves according to the weights of the contributing superposition conditions. We analyze the colorimetric prediction improvement brought by our extended dot surface coverage model for clustered-dot offset prints, thermal transfer prints and ink-jet prints. The color differences induced by the differences between measured reflection spectra and reflection spectra predicted according to the new dot surface estimation model are quantified on 729 different cyan, magenta, yellow patches covering the full color gamut. As a reference, these differences are also computed for the classical Yule-Nielsen modified spectral Neugebauer model incorporating a single halftone reproduction curve for each ink. Taking into account dot surface coverages according to different superposition conditions considerably improves the predictions of the Yule-Nielsen modified Neugebauer model. In the case of offset prints, the mean difference between predictions and measurements expressed in CIE-LAB CIE-94 ΔE94 values is reduced at 100 lpi from 1.54 to 0.90 (accuracy improvement factor: 1.7) and at 150 lpi it is reduced from 1.87 to 1.00 (accuracy improvement factor: 1.8). Similar improvements have been observed for a thermal transfer printer at 600 dpi, at lineatures of 50 and 75 lpi. In the case of an ink-jet printer at 600 dpi, the mean ΔE94 value is reduced at 75 lpi from 3.03 to 0.90 (accuracy improvement factor: 3.4) and at 100 lpi from 3.08 to 0.91 (accuracy improvement factor: 3.4).

Options for refractive index and viscosity matching to study variable density flows

NASA Astrophysics Data System (ADS)

Clément, Simon A.; Guillemain, Anaïs; McCleney, Amy B.; Bardet, Philippe M.

2018-02-01

Variable density flows are often studied by mixing two miscible aqueous solutions of different densities. To perform optical diagnostics in such environments, the refractive index of the fluids must be matched, which can be achieved by carefully choosing the two solutes and the concentration of the solutions. To separate the effects of buoyancy forces and viscosity variations, it is desirable to match the viscosity of the two solutions in addition to their refractive index. In this manuscript, several pairs of index matched fluids are compared in terms of viscosity matching, monetary cost, and practical use. Two fluid pairs are studied in detail, with two aqueous solutions (binary solutions of water and a salt or alcohol) mixed into a ternary solution. In each case: an aqueous solution of isopropanol mixed with an aqueous solution of sodium chloride (NaCl) and an aqueous solution of glycerol mixed with an aqueous solution of sodium sulfate (Na_2SO_4). The first fluid pair allows reaching high-density differences at low cost, but brings a large difference in dynamic viscosity. The second allows matching dynamic viscosity and refractive index simultaneously, at reasonable cost. For each of these four solutes, the density, kinematic viscosity, and refractive index are measured versus concentration and temperature, as well as wavelength for the refractive index. To investigate non-linear effects when two index-matched, binary solutions are mixed, the ternary solutions formed are also analyzed. Results show that density and refractive index follow a linear variation with concentration. However, the viscosity of the isopropanol and NaCl pair deviates from the linear law and has to be considered. Empirical correlations and their coefficients are given to create index-matched fluids at a chosen temperature and wavelength. Finally, the effectiveness of the refractive index matching is illustrated with particle image velocimetry measurements performed for a buoyant jet in a linearly stratified environment. The creation of the index-matched solutions and linear stratification in a large-scale experimental facility are detailed, as well as the practical challenges to obtain precise refractive index matching.

Java application for the superposition T-matrix code to study the optical properties of cosmic dust aggregates

NASA Astrophysics Data System (ADS)

Halder, P.; Chakraborty, A.; Deb Roy, P.; Das, H. S.

2014-09-01

In this paper, we report the development of a java application for the Superposition T-matrix code, JaSTA (Java Superposition T-matrix App), to study the light scattering properties of aggregate structures. It has been developed using Netbeans 7.1.2, which is a java integrated development environment (IDE). The JaSTA uses double precession superposition codes for multi-sphere clusters in random orientation developed by Mackowski and Mischenko (1996). It consists of a graphical user interface (GUI) in the front hand and a database of related data in the back hand. Both the interactive GUI and database package directly enable a user to model by self-monitoring respective input parameters (namely, wavelength, complex refractive indices, grain size, etc.) to study the related optical properties of cosmic dust (namely, extinction, polarization, etc.) instantly, i.e., with zero computational time. This increases the efficiency of the user. The database of JaSTA is now created for a few sets of input parameters with a plan to create a large database in future. This application also has an option where users can compile and run the scattering code directly for aggregates in GUI environment. The JaSTA aims to provide convenient and quicker data analysis of the optical properties which can be used in different fields like planetary science, atmospheric science, nano science, etc. The current version of this software is developed for the Linux and Windows platform to study the light scattering properties of small aggregates which will be extended for larger aggregates using parallel codes in future. Catalogue identifier: AETB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETB_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.: 571570 No. of bytes in distributed program, including test data, etc.: 120226886 Distribution format: tar.gz Programming language: Java, Fortran95. Computer: Any Windows or Linux systems capable of hosting a java runtime environment, java3D and fortran95 compiler; Developed on 2.40 GHz Intel Core i3. Operating system: Any Windows or Linux systems capable of hosting a java runtime environment, java3D and fortran95 compiler. RAM: Ranging from a few Mbytes to several Gbytes, depending on the input parameters. Classification: 1.3. External routines: jfreechart-1.0.14 [1] (free plotting library for java), j3d-jre-1.5.2 [2] (3D visualization). Nature of problem: Optical properties of cosmic dust aggregates. Solution method: Java application based on Mackowski and Mischenko's Superposition T-Matrix code. Restrictions: The program is designed for single processor systems. Additional comments: The distribution file for this program is over 120 Mbytes and therefore is not delivered directly when Download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: Ranging from few minutes to several hours, depending on the input parameters. References: [1] http://www.jfree.org/index.html [2] https://java3d.java.net/

The role and production of polar/subtropical jet superpositions in two high-impact weather events over North America

NASA Astrophysics Data System (ADS)

Winters, Andrew C.

Careful observational work has demonstrated that the tropopause is typically characterized by a three-step pole-to-equator structure, with each break between steps in the tropopause height associated with a jet stream. While the two jet streams, the polar and subtropical jets, typically occupy different latitude bands, their separation can occasionally vanish, resulting in a vertical superposition of the two jets. A cursory examination of a number of historical and recent high-impact weather events over North America and the North Atlantic indicates that superposed jets can be an important component of their evolution. Consequently, this dissertation examines two recent jet superposition cases, the 18--20 December 2009 Mid-Atlantic Blizzard and the 1--3 May 2010 Nashville Flood, in an effort (1) to determine the specific influence that a superposed jet can have on the development of a high-impact weather event and (2) to illuminate the processes that facilitated the production of a superposition in each case. An examination of these cases from a basic-state variable and PV inversion perspective demonstrates that elements of both the remote and local synoptic environment are important to consider while diagnosing the development of a jet superposition. Specifically, the process of jet superposition begins with the remote production of a cyclonic (anticyclonic) tropopause disturbance at high (low) latitudes. The cyclonic circulation typically originates at polar latitudes, while organized tropical convection can encourage the development of an anticyclonic circulation anomaly within the tropical upper-troposphere. The concurrent advection of both anomalies towards middle latitudes subsequently allows their individual circulations to laterally displace the location of the individual tropopause breaks. Once the two circulation anomalies position the polar and subtropical tropopause breaks in close proximity to one another, elements within the local environment, such as proximate convection or transverse vertical circulations, can work to further deform the tropopause and to aid in the production of the two-step tropopause structure characteristic of a superposed jet. The analysis also demonstrates that the intensified transverse vertical circulation that accompanies a superposed jet serves as the primary mechanism through which it can influence the evolution of a high-impact weather event.

An outflow boundary condition for aeroacoustic computations

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Hagstrom, Thomas

1995-01-01

A formulation of boundary condition for flows with small disturbances is presented. The authors test their methodology in an axisymmetric jet flow calculation, using both the Navier-Stokes and Euler equations. Solutions in the far field are assumed to be oscillatory. If the oscillatory disturbances are small, the growth of the solution variables can be predicted by linear theory. Eigenfunctions of the linear theory are used explicitly in the formulation of the boundary conditions. This guarantees correct solutions at the boundary in the limit where the predictions of linear theory are valid.

The Intelligence of Dual Simplex Method to Solve Linear Fractional Fuzzy Transportation Problem

PubMed Central

Narayanamoorthy, S.; Kalyani, S.

2015-01-01

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example. PMID:25810713

Linear rheology and structure of molecular bottlebrushes with short side chains

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

López-Barrón, Carlos R., E-mail: carlos.r.lopez-barron@exxonmobil.com; Brant, Patrick; Crowther, Donna J.

We investigate the microstructure and linear viscoelasticity of model molecular bottlebrushes (BBs) using rheological and small-angle X-ray and neutron scattering measurements. Our polymers have short atactic polypropylene (aPP) side chains of molecular weight ranging from 119 g/mol to 259 g/mol and narrow molecular weight distribution (M{sub w}/M{sub n} 1.02–1.05). The side chain molecular weights are a small fraction of the entanglement molecular weight of the corresponding linear polymer (M{sub e,aPP}= 7.05 kg/mol), and as such, they are unentangled. The morphology of the aPP BBs is characterized as semiflexible thick chains with small side chain interdigitation. Their dynamic master curves, obtained by time-temperature superposition,more » reveal two sequential relaxation processes corresponding to the segmental relaxation and the relaxation of the BB backbone. Due to the short length of the side chains, their fast relaxation could not be distinguished from the glassy relaxation. The fractional free volume is an increasing function of the side chain length (N{sub SC}). Therefore, the glassy behavior of these polymers as well as their molecular friction and dynamic properties are influenced by their N{sub SC} values. The apparent flow activation energies are a decreasing function of N{sub SC}, and their values explain the differences in zero-shear viscosity measured at different temperatures.« less

Structure parameters in rotating Couette-Poiseuille channel flow

NASA Technical Reports Server (NTRS)

Knightly, George H.; Sather, D.

1986-01-01

It is well-known that a number of steady state problems in fluid mechanics involving systems of nonlinear partial differential equations can be reduced to the problem of solving a single operator equation of the form: v + lambda Av + lambda B(v) = 0, v is the summation of H, lambda is the summation of one-dimensional Euclid space, where H is an appropriate (real or complex) Hilbert space. Here lambda is a typical load parameter, e.g., the Reynolds number, A is a linear operator, and B is a quadratic operator generated by a bilinear form. In this setting many bifurcation and stability results for problems were obtained. A rotating Couette-Poiseuille channel flow was studied, and it showed that, in general, the superposition of a Poiseuille flow on a rotating Couette channel flow is destabilizing.

Creep and creep rupture of laminated graphite/epoxy composites. Ph.D. Thesis. Final Report, 1 Oct. 1979 - 30 Sep. 1980

NASA Technical Reports Server (NTRS)

Dillard, D. A.; Morris, D. H.; Brinson, H. F.

1981-01-01

An incremental numerical procedure based on lamination theory is developed to predict creep and creep rupture of general laminates. Existing unidirectional creep compliance and delayed failure data is used to develop analytical models for lamina response. The compliance model is based on a procedure proposed by Findley which incorporates the power law for creep into a nonlinear constitutive relationship. The matrix octahedral shear stress is assumed to control the stress interaction effect. A modified superposition principle is used to account for the varying stress level effect on the creep strain. The lamina failure model is based on a modification of the Tsai-Hill theory which includes the time dependent creep rupture strength. A linear cumulative damage law is used to monitor the remaining lifetime in each ply.

Assessment of effectiveness of geologic isolation systems. Geologic-simulation model for a hypothetical site in the Columbia Plateau. Volume 2: results

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

Foley, M.G.; Petrie, G.M.; Baldwin, A.J.

1982-06-01

This report contains the input data and computer results for the Geologic Simulation Model. This model is described in detail in the following report: Petrie, G.M., et. al. 1981. Geologic Simulation Model for a Hypothetical Site in the Columbia Plateau, Pacific Northwest Laboratory, Richland, Washington. The Geologic Simulation Model is a quasi-deterministic process-response model which simulates, for a million years into the future, the development of the geologic and hydrologic systems of the ground-water basin containing the Pasco Basin. Effects of natural processes on the ground-water hydrologic system are modeled principally by rate equations. The combined effects and synergistic interactionsmore » of different processes are approximated by linear superposition of their effects during discrete time intervals in a stepwise-integration approach.« less

Thin-film Faraday patterns in three dimensions

NASA Astrophysics Data System (ADS)

Richter, Sebastian; Bestehorn, Michael

2017-04-01

We investigate the long time evolution of a thin fluid layer in three spatial dimensions located on a horizontal planar substrate. The substrate is subjected to time-periodic external vibrations in normal and in tangential direction with respect to the plane surface. The governing partial differential equation system of our model is obtained from the incompressible Navier-Stokes equations considering the limit of a thin fluid geometry and using the long wave lubrication approximation. It includes inertia and viscous friction. Numerical simulations evince the existence of persistent spatially complex surface patterns (periodic and quasiperiodic) for certain superpositions of two vertical excitations and initial conditions. Additional harmonic lateral excitations cause deformations but retain the basic structure of the patterns. Horizontal ratchet-shaped forces lead to a controllable lateral movement of the fluid. A Floquet analysis is used to determine the stability of the linearized system.

Mode 1 crack surface displacements for a round compact specimen subject to a couple and force

NASA Technical Reports Server (NTRS)

Gross, B.

1979-01-01

Mode I displacement coefficients along the crack surface are presented for a radially cracked round compact specimen, treated as a plane elastostatic problem, subjected to two types of loading; a uniform tensile stress and a nominal bending stress distribution across the net section. By superposition the resultant displacement coefficient or the corresponding influence coefficient can be obtained for any practical load location. Load line displacements are presented for A/D ratios ranging from 0.40 to 0.95, where A is the crack length measured from the crack mouth to the crack tip and D is the specimen diameter. Through a linear extrapolation procedure crack mouth displacements are also obtained. Experimental evidence shows that the results are valid over the range of A/D ratios analyzed for a practical pin loaded round compact specimen.

A study of an arbiter function in the structures of a shared bus

NASA Astrophysics Data System (ADS)

Seck, J.-P.

The results of a comparative study of synchronous and asynchronous arbiters for managing user access to a shared bus is presented. The best available method is determined to be modular arbiter structures attached only to the decision module. Linear and circular arbitration strategies are examined for suitability for automatic decision-making. A multiple strategies arbiter scheme is devised, involving the superposition of various strategies of one sequential machine into another. It is then possible to modify the strategy on-line if the current strategy is ineffective. The utilization of a multiple structure of cascading arbiter devices is noted to be effective if response time is not a critical matter. Finally, attention is given to automatic circuit testing and fault detection. An example is furnished in terms of a management system for a shared memory in a multimicroprocessor structure.

Quantum Associative Neural Network with Nonlinear Search Algorithm

NASA Astrophysics Data System (ADS)

Zhou, Rigui; Wang, Huian; Wu, Qian; Shi, Yang

2012-03-01

Based on analysis on properties of quantum linear superposition, to overcome the complexity of existing quantum associative memory which was proposed by Ventura, a new storage method for multiply patterns is proposed in this paper by constructing the quantum array with the binary decision diagrams. Also, the adoption of the nonlinear search algorithm increases the pattern recalling speed of this model which has multiply patterns to O( {log2}^{2^{n -t}} ) = O( n - t ) time complexity, where n is the number of quantum bit and t is the quantum information of the t quantum bit. Results of case analysis show that the associative neural network model proposed in this paper based on quantum learning is much better and optimized than other researchers' counterparts both in terms of avoiding the additional qubits or extraordinary initial operators, storing pattern and improving the recalling speed.

Quantum state engineering using one-dimensional discrete-time quantum walks

NASA Astrophysics Data System (ADS)

Innocenti, Luca; Majury, Helena; Giordani, Taira; Spagnolo, Nicolò; Sciarrino, Fabio; Paternostro, Mauro; Ferraro, Alessandro

2017-12-01

Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin and providing a method to efficiently compute the corresponding set of coin parameters. We assess the feasibility of our proposal by identifying a linear optics experiment based on photonic orbital angular momentum technology.