Three-Body Coulomb Functions in the Hyperspherical Adiabatic Expansion Method
NASA Astrophysics Data System (ADS)
Garrido, E.; Kievsky, A.; Viviani, M.
2016-10-01
In this work we describe a numerical method devised to compute continuum three-body wave functions. The method is implemented using the hyperspherical adiabatic expansion for the three-body wave function imposing a box boundary condition. The continuum energy spectrum results discretized and, for specific quantum number values, all the possible incoming and outgoing channels are simultaneously computed. For a given energy, the hyperradial continuum functions form a matrix whose ij-term refers to specific incoming and outgoing channels. When applied to three-body systems interacting only through the Coulomb potential, this method provides the adiabatic representation of the regular three-body Coulomb wave function. The computation of the irregular Coulomb wave function representation is also discussed. These regular and irregular Coulomb functions can be used to extract the {S} -matrix for those reactions where, together with some short-range potential, the Coulomb interaction is also present. The method is illustrated in the case of the 3→ 3 process of three alpha particles.
Adiabatic expansion of a strongly correlated pure electron plasma
Dubin, D.H.E.; O'Neil, T.M.
1986-02-17
Adiabatic expansion is proposed as a method of increasing the degree of correlation of a magnetically confined pure electron plasma. Quantum mechanical effects and correlation effects make the physics of the expansion quite different from that for a classical ideal gas. The proposed expansion may be useful in a current experimental effort to cool a pure electron plasma to the liquid and solid (crystalline) states.
Adiabatic expansion of a strongly correlated pure electron plasma
NASA Astrophysics Data System (ADS)
Dubin, D. H. E.; Oneil, T. M.
1986-02-01
Adiabatic expansion is proposed as a method of increasing the degree of correlation of a magnetically confined pure electron plasma. Quantum mechanical effects and correlation effects make the physics of the expansion quite different from that for a classical ideal gas. The proposed expansion may be useful in a current experimental effort to cool a pure electron plasma to the liquid and solid (crystalline) states.
Power-driven and adiabatic expansions into vacuum
NASA Astrophysics Data System (ADS)
Farnsworth, A. V., Jr.
1980-08-01
Analytical solutions are obtained for the planar, cylindrical, and spherical expansions into vacuum of matter initially concentrated at a plane, a line, or a point. Both power-driven and adiabatic expansions are considered, where in the power-driven case, the specific power is deposited uniformly in space, but may vary in time according to a power law. These problems are found to be self-similar. The non-self-similar motion of matter during the adiabatic expansion that follows a power pulse of finite duration has also been addressed and a solution has been obtained.
When an Adiabatic Irreversible Expansion or Compression Becomes Reversible
ERIC Educational Resources Information Center
Anacleto, Joaquim; Ferreira, J. M.; Soares, A. A.
2009-01-01
This paper aims to contribute to a better understanding of the concepts of a "reversible process" and "entropy". For this purpose, an adiabatic irreversible expansion or compression is analysed, by considering that an ideal gas is expanded (compressed), from an initial pressure P[subscript i] to a final pressure P[subscript f], by being placed in…
When an adiabatic irreversible expansion or compression becomes reversible
NASA Astrophysics Data System (ADS)
Anacleto, Joaquim; Ferreira, J. M.; Soares, A. A.
2009-05-01
This paper aims to contribute to a better understanding of the concepts of a reversible process and entropy. For this purpose, an adiabatic irreversible expansion or compression is analysed, by considering that an ideal gas is expanded (compressed), from an initial pressure Pi to a final pressure Pf, by being placed in contact with a set of N work reservoirs with pressures decreasing (increasing) in a geometric or arithmetic progression. The gas entropy change ΔS is evaluated and it is clearly shown that ΔS > 0 for any finite N, but as the number of work reservoirs goes to infinity the entropy change goes to zero, i.e. the process becomes reversible. Additionally, this work draws attention to the work reservoir concept, which is virtually ignored in the literature, and to its analogy with the commonly used heat reservoir concept. Finally, it complements and reinforces an earlier study dealing with irreversible cooling or heating so that the synergy created by the two studies is important from both theoretical and educational standpoints.
Superequilibrium ionization during adiabatic expansion of a relaxing gas
NASA Astrophysics Data System (ADS)
Achasov, O. V.; Zhdanok, S. A.; Soloukhin, R. I.; Fomin, N. A.
1980-08-01
A superequilibrium method for the generation of a weakly ionized plasma in a molecular gas is proposed; the method involves the production of a superequilibrium electron density in a thermally excited and vibrationally frozen molecular gas during expansion in supersonic flow. Experimental results are presented for the case of nitrogen. This method has applications in molecular and laser physics, including preionization in a fast-flow gas-discharge laser, and the study of energy losses in gasdynamic lasers.
ERIC Educational Resources Information Center
Moore, William M.
1984-01-01
Describes the procedures and equipment for an experiment on the adiabatic expansion of gases suitable for demonstration and discussion in the physical chemical laboratory. The expansion produced shows how the process can change temperature and still return to a different location on an isotherm. (JN)
Lattice Boltzmann method for adiabatic acoustics.
Li, Yanbing; Shan, Xiaowen
2011-06-13
The lattice Boltzmann method (LBM) has been proved to be a useful tool in many areas of computational fluid dynamics, including computational aero-acoustics (CAA). However, for historical reasons, its applications in CAA have been largely restricted to simulations of isothermal (Newtonian) sound waves. As the recent kinetic theory-based reformulation establishes a theoretical framework in which LBM can be extended to recover the full Navier-Stokes-Fourier (NS) equations and beyond, in this paper, we show that, at least at the low-frequency limit (sound frequency much less than molecular collision frequency), adiabatic sound waves can be accurately simulated by the LBM provided that the lattice and the distribution function ensure adequate recovery of the full NS equations.
Properties of an equilibrium hadron gas subjected to the adiabatic longitudinal expansion
NASA Astrophysics Data System (ADS)
Prorok, Dariusz; Turko, Ludwik
1995-06-01
We consider an ideal gas of massive hadrons in thermal and chemical equilibrium. The gas expands longitudinally in an adiabatic way. This evolution for a baryonless gas reduces to a hydrodynamic expansion. Cooling process is parametrized by the sound velocity. The sound velocity is temperature dependent and is strongly influenced by hadron mass spectrum.
Transient Particle Energies in Shortcuts to Adiabatic Expansions of Harmonic Traps.
Cui, Yang-Yang; Chen, Xi; Muga, J G
2016-05-19
The expansion of a harmonic potential that holds a quantum particle may be realized without any final particle excitation but much faster than adiabatically via "shortcuts to adiabaticity" (STA). While ideally the process time can be reduced to zero, practical limitations and constraints impose minimal finite times for the externally controlled time-dependent frequency protocols. We examine the role of different time-averaged energies (total, kinetic, potential, nonadiabatic) and of the instantaneous power in characterizing or selecting different protocols. Specifically, we prove a virial theorem for STA processes, set minimal energies (or times) for given times (or energies), and discuss their realizability by means of Dirac impulses or otherwise.
Transient Particle Energies in Shortcuts to Adiabatic Expansions of Harmonic Traps.
Cui, Yang-Yang; Chen, Xi; Muga, J G
2016-05-19
The expansion of a harmonic potential that holds a quantum particle may be realized without any final particle excitation but much faster than adiabatically via "shortcuts to adiabaticity" (STA). While ideally the process time can be reduced to zero, practical limitations and constraints impose minimal finite times for the externally controlled time-dependent frequency protocols. We examine the role of different time-averaged energies (total, kinetic, potential, nonadiabatic) and of the instantaneous power in characterizing or selecting different protocols. Specifically, we prove a virial theorem for STA processes, set minimal energies (or times) for given times (or energies), and discuss their realizability by means of Dirac impulses or otherwise. PMID:26237328
Adiabatic molecular-dynamics-simulation-method studies of kinetic friction
NASA Astrophysics Data System (ADS)
Zhang, J.; Sokoloff, J. B.
2005-06-01
An adiabatic molecular-dynamics method is developed and used to study the Muser-Robbins model for dry friction (i.e., nonzero kinetic friction in the slow sliding speed limit). In this model, dry friction between two crystalline surfaces rotated with respect to each other is due to mobile molecules (i.e., dirt particles) adsorbed at the interface. Our adiabatic method allows us to quickly locate interface potential-well minima, which become unstable during sliding of the surfaces. Since dissipation due to friction in the slow sliding speed limit results from mobile molecules dropping out of such unstable wells, our method provides a way to calculate dry friction, which agrees extremely well with results found by conventional molecular dynamics for the same system, but our method is more than a factor of 10 faster.
Colossal Spincaloritronic Cooling by Adiabatic Spin-Entropy Expansion in Nanospintronics
NASA Astrophysics Data System (ADS)
Katayama-Yoshida, Hiroshi; Fukushima, Tetsuya; Dinh, Van An; Sato, Kazunori
2009-03-01
The exchange interactions in DMS are short ranged and can not play an important role for realizing high-TC because the solubility of magnetic impurity is too low to achieve magnetic percolation [1]. We show that spinodal nano-decomposition under layer-by-layer crystal growth condition (2D) leads to characteristic quasi-one dimensional nano-structures (Konbu- Phase) with highly anisotropic shape and high TC (> 1000K) even for low concentrations in DMS [2]. We design a spin-currents- controlled 100 Tera bits/icnh^2, Tera Hz switching, and non- volatile MRAM without Si-CMOS based on Konbu-Phase [3]. In addition to the conventional Peltier effect, we propose a colossal spincaloritronic cooling based on the adiabatic spin- entropy expansion in a Konbu-Phase (Zn,Cr)Te with very high blocking temperature (TB > 1000 K) by spinodal nano- decomposition and by nano-column of Half-Heusler NiMnSi (TC = 1050 K) [4]. [1] K. Sato et al., Phys. Rev. B70, 201202 (2004). [2] H. Katayama-Yoshida et al., Phys. stat. sol. (a) 204 (2007) 15. [3] Japanese Patent: JP3571034, US Patent: US 7,164,180 B2, EU Patent: EP 1548832A1, Taiwan Patent:1262593, Korean Patent: 0557387. [4] H. Katayama-Yoshida et al., Jpn. J. Appl. Phys. 46 (2007) L777.
Nucleon-deuteron scattering using the adiabatic projection method
NASA Astrophysics Data System (ADS)
Elhatisari, Serdar; Lee, Dean; Meißner, Ulf-G.; Rupak, Gautam
2016-06-01
In this paper we discuss the adiabatic projection method, a general framework for scattering and reaction calculations on the lattice. We also introduce several new techniques developed to study nucleus-nucleus scattering and reactions on the lattice. We present technical details of the method for large-scale problems. To estimate the systematic errors of the calculations we consider simple two-particle scattering on the lattice. Then we benchmark the accuracy and efficiency of the numerical methods by applying these to calculate fermion-dimer scattering in lattice effective field theory with and without a long-range Coulomb potential. The fermion-dimer calculations correspond to neutron-deuteron and proton-deuteron scattering in the spin-quartet channel at leading order in the pionless effective field theory.
Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru
2015-12-31
We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.
Kinetic Models for Adiabatic Reversible Expansion of a Monatomic Ideal Gas.
ERIC Educational Resources Information Center
Chang, On-Kok
1983-01-01
A fixed amount of an ideal gas is confined in an adiabatic cylinder and piston device. The relation between temperature and volume in initial/final phases can be derived from the first law of thermodynamics. However, the relation can also be derived based on kinetic models. Several of these models are discussed. (JN)
NASA Astrophysics Data System (ADS)
Zhu, Xiaolei; Yarkony, David R.
2012-05-01
In two previous papers we have introduced a method to generate coupled quasi-diabatic Hamiltonians (Hd) that are capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, two new synergistic features are introduced. Firstly, the functional form of Hd is generalized. Rather than requiring there to be a low energy point of high symmetry to serve as the unique origin, functions centered on points distributed in nuclear coordinate space are used in the polynomials that comprise the matrix elements in Hd. The use of functions with distributed origins, allows reproduction of the ab initio data with lower order expansions, and offers the possibility of describing multichannel dissociation. The fitting algorithm is combined with a three-step procedure in which the domain of Hd is extended from a core set of nuclear configurations to a region of nuclear coordinate space appropriate for nuclear dynamics, with a prescribed accuracy. This significant extension of the domain of definition compared to our original work, which is facilitated by the distributed origin approach, is achieved largely through the use of surface hopping trajectories. The 1,21A states of NH3, which provide an archetypical example of nonadiabatic dynamics, are used to demonstrate the utility of this approach. The representation describes 21 points on the 11A-21A seam of conical intersection and their local topography flawlessly and on the entire domain, the electronic structure data is represented to an accuracy of 77.00 (46.90) cm-1, as measured by the root mean square (mean unsigned) error for energies lower than 50 000 cm-1. This error is a factor of 10 lower than that of the most accurate representation of high quality ab initio data, on a comparable domain, previously reported for this system.
Temperature gradients due to adiabatic plasma expansion in a magnetic nozzle
NASA Astrophysics Data System (ADS)
Sheehan, J. P.; Longmier, B. W.; Bering, E. A.; Olsen, C. S.; Squire, J. P.; Ballenger, M. G.; Carter, M. D.; Cassady, L. D.; Díaz, F. R. Chang; Glover, T. W.; Ilin, A. V.
2014-08-01
A mechanism for ambipolar ion acceleration in a magnetic nozzle is proposed. The plasma is adiabatic (i.e., does not exchange energy with its surroundings) in the diverging section of a magnetic nozzle so any energy lost by the electrons must be transferred to the ions via the electric field. Fluid theory indicates that the change in plasma potential is proportional to the change in average electron energy. These predictions were compared to measurements in the VX-200 experiment which has conditions conducive to ambipolar ion acceleration. A planar Langmuir probe was used to measure the plasma potential, electron density, and electron temperature for a range of mass flow rates and power levels. Axial profiles of those parameters were also measured, showing consistency with the adiabatic ambipolar fluid theory.
Multipole expansion method for supernova neutrino oscillations
Duan, Huaiyu; Shalgar, Shashank E-mail: shashankshalgar@unm.edu
2014-10-01
We demonstrate a multipole expansion method to calculate collective neutrino oscillations in supernovae using the neutrino bulb model. We show that it is much more efficient to solve multi-angle neutrino oscillations in multipole basis than in angle basis. The multipole expansion method also provides interesting insights into multi-angle calculations that were accomplished previously in angle basis.
Isothermal and Adiabatic Measurements.
ERIC Educational Resources Information Center
McNairy, William W.
1996-01-01
Describes the working of the Adiabatic Gas Law Apparatus, a useful tool for measuring the pressure, temperature, and volume of a variety of gases undergoing compressions and expansions. Describes the adaptation of this apparatus to perform isothermal measurements and discusses the theory behind the adiabatic and isothermal processes. (JRH)
Heating and cooling in adiabatic mixing process
Zhou Jing; Zou Xubo; Guo Guangcan; Cai Zi
2010-12-15
We study the effect of interaction on the temperature change in the process of adiabatic mixing of two components of Fermi gases using the real-space Bogoliubov-de Gennes method. We find that in the process of adiabatic mixing, the competition between the adiabatic expansion and the attractive interaction makes it possible to cool or heat the system depending on the strength of the interaction and the initial temperature of the system. The changes of the temperature in a bulk system and in a trapped system are investigated.
Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures
Sevastianov, L. A.; Egorov, A. A.; Sevastyanov, A. L.
2013-02-15
Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell's equations is made to obey 'inclined' boundary conditions at the interfaces between themedia being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of 'entanglement' of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized waveguide Lueneburg lens.
NASA Astrophysics Data System (ADS)
Elhatisari, Serdar; Lee, Dean
2014-12-01
We present lattice Monte Carlo calculations of fermion-dimer scattering in the limit of zero-range interactions using the adiabatic projection method. The adiabatic projection method uses a set of initial cluster states and Euclidean time projection to give a systematically improvable description of the low-lying scattering cluster states in a finite volume. We use Lüscher's finite-volume relations to determine the s -wave, p -wave, and d -wave phase shifts. For comparison, we also compute exact lattice results using Lanczos iteration and continuum results using the Skorniakov-Ter-Martirosian equation. For our Monte Carlo calculations we use a new lattice algorithm called impurity lattice Monte Carlo. This algorithm can be viewed as a hybrid technique which incorporates elements of both worldline and auxiliary-field Monte Carlo simulations.
Development of new hole expansion testing method
NASA Astrophysics Data System (ADS)
Kim, Hyunok; Shang, Jianhui; Beam, Kevin; Samant, Anoop; Hoschouer, Cliff; Dykeman, Jim
2016-08-01
This paper introduces a new hole expansion (HE) testing method that could be more relevant to the edge cracking problem observed in stamping advanced high strength steel (AHSS). The new testing method adopted a large hole diameter of 75 mm compared to the standard hole diameter of 10 mm. An inline monitoring system was developed to visually monitor the hole edge cracking during the test and synchronize the load-displacement data with the recorded video for capturing the initial crack. A new hole expansion testing method was found to be effective in evaluating the edge cracking by considering the effects of material properties and trimming methods. It showed a much larger difference, up to 11%, of the HE ratio between DP980 and TRIP780 compared to the standard HE testing method giving less than a 2% difference.
NASA Astrophysics Data System (ADS)
Geroux, Chris M.; Deupree, Robert G.
2011-04-01
We are developing a three-dimensional radiation hydrodynamics code to simulate the interaction of convection and pulsation in classical variable stars. One key goal is the ability to carry these simulations to full amplitude in order to compare them with observed light and velocity curves. Previous two-dimensional calculations were prevented from doing this because of drift in the radial coordinate system, due to the algorithm defining radial movement of the coordinate system during the pulsation cycle. We remove this difficulty by defining our coordinate system flow algorithm to require that the mass in a spherical shell remains constant throughout the pulsation cycle. We perform adiabatic test calculations to show that large amplitude solutions repeat over more than 150 pulsation periods. We also verify that the computational method conserves the peak kinetic energy per period, as must be true for adiabatic pulsation models.
Geroux, Chris M.; Deupree, Robert G.
2011-04-10
We are developing a three-dimensional radiation hydrodynamics code to simulate the interaction of convection and pulsation in classical variable stars. One key goal is the ability to carry these simulations to full amplitude in order to compare them with observed light and velocity curves. Previous two-dimensional calculations were prevented from doing this because of drift in the radial coordinate system, due to the algorithm defining radial movement of the coordinate system during the pulsation cycle. We remove this difficulty by defining our coordinate system flow algorithm to require that the mass in a spherical shell remains constant throughout the pulsation cycle. We perform adiabatic test calculations to show that large amplitude solutions repeat over more than 150 pulsation periods. We also verify that the computational method conserves the peak kinetic energy per period, as must be true for adiabatic pulsation models.
Liu, Fei
2014-09-01
We present a characteristic function method to calculate the probability density functions of the inclusive work in adiabatic two-level quantum Markovian master equations. These systems are steered by some slowly varying parameters and the dissipations may depend on time. Our theory is based on the interpretation of the quantum jump for the master equations. In addition to the calculation, we also find that the fluctuation properties of the work can be described by the symmetry of the characteristic functions, which is exactly the same as in the case of isolated systems. A periodically driven two-level model is used to demonstrate the method. PMID:25314409
The method of Gaussian weighted trajectories. III. An adiabaticity correction proposal
Bonnet, L.
2008-01-28
The addition of an adiabaticity correction (AC) to the Gaussian weighted trajectory (GWT) method and its normalized version (GWT-N) is suggested. This correction simply consists in omitting vibrationally adiabatic nonreactive trajectories in the calculations of final attributes. For triatomic exchange reactions, these trajectories satisfy the criterion {omega} not much larger than ({Dirac_h}/2{pi}), where {omega} is a vibrational action defined by {omega}={integral}{sup []}-[]dt(pr-p{sub 0}r{sub 0}), r being the reagent diatom bond length, p its conjugate momentum, and r{sub 0} and p{sub 0} the corresponding variables for the unperturbed diatom ({omega}/({Dirac_h}/2{pi}) bears some analogy with the semiclassical elastic scattering phase shift). The resulting GWT-AC and GWT-ACN methods are applied to the recently studied H{sup +}+H{sub 2} and H{sup +}+D{sub 2} reactions and the agreement between their predictions and those of exact quantum scattering calculations is found to be much better than for the initial GWT and GWT-N methods. The GWT-AC method, however, appears to be the most accurate one for the processes considered, in particular, the H{sup +}+D{sub 2} reaction.
Theory of laser-induced adiabat shaping in inertial fusion implosions: The relaxation method
Betti, R.; Anderson, K.; Knauer, J.; Collins, T.J.B.; McCrory, R.L.; McKenty, P.W.; Skupsky, S.
2005-04-15
The theory of the adiabat shaping induced by a strong shock propagating through a relaxed density profile is carried out for inertial confinement fusion (ICF) capsules. The relaxed profile is produced through a laser prepulse, while the adiabat-shaping shock is driven by the foot of the main laser pulse. The theoretical adiabat profiles accurately reproduce the simulation results. ICF capsules with a shaped adiabat are expected to benefit from improved hydrodynamic stability while maintaining the same one-dimensional performances as flat-adiabat shells.
Bischoff, J.L.
1980-01-01
Pressure-volume-temperature relations for water at the depth of the magma chamber at 21°N on the East Pacific Rise suggest that the maximum subsurface temperature of the geothermal fluid is about 420°C. Both the chemistry of the discharging fluid and thermal balance considerations indicate that the effective water/rock ratios in the geothermal system are between 7 and 16. Such low ratios preclude effective metal transport at temperatures below 350°C, but metal solubilization at 400°C and above is effective even at such low ratios. It is proposed that the 420°C fluid ascends essentially adiabatically and in the process expands, cools, and precipitates metal sulfides within the upper few hundred meters of the sea floor and on the sea floor itself.
Alonso, J L; Castro, A; Clemente-Gallardo, J; Echenique, P; Mazo, J J; Polo, V; Rubio, A; Zueco, D
2012-12-14
At non-zero temperature and when a system has low-lying excited electronic states, the ground-state Born-Oppenheimer approximation breaks down and the low-lying electronic states are involved in any chemical process. In this work, we use a temperature-dependent effective potential for the nuclei which can accommodate the influence of an arbitrary number of electronic states in a simple way, while at the same time producing the correct Boltzmann equilibrium distribution for the electronic part. With the help of this effective potential, we show that thermally activated low-lying electronic states can have a significant effect in molecular properties for which electronic excitations are oftentimes ignored. We study the thermal expansion of the Manganese dimer, Mn(2), where we find that the average bond length experiences a change larger than the present experimental accuracy upon the inclusion of the excited states into the picture. We also show that, when these states are taken into account, reaction-rate constants are modified. In particular, we study the opening of the ozone molecule, O(3), and show that in this case the rate is modified as much as a 20% with respect to the ground-state Born-Oppenheimer prediction.
Generalization of the cavity method for adiabatic evolution of Gibbs states
NASA Astrophysics Data System (ADS)
Zdeborová, Lenka; Krzakala, Florent
2010-06-01
Mean-field glassy systems have a complicated energy landscape and an enormous number of different Gibbs states. In this paper, we introduce a generalization of the cavity method in order to describe the adiabatic evolution of these glassy Gibbs states as an external parameter, such as the temperature, is tuned. We give a general derivation of the method and describe in details the solution of the resulting equations for the fully connected p -spin model, the XOR-satisfiability (SAT) problem and the antiferromagnetic Potts glass (coloring problem). As direct results of the states following method we present a study of very slow Monte Carlo annealings, the demonstration of the presence of temperature chaos in these systems and the identification of an easy/hard transition for simulated annealing in constraint optimization problems. We also discuss the relation between our approach and the Franz-Parisi potential, as well as with the reconstruction problem on trees in computer science. A mapping between the states following method and the physics on the Nishimori line is also presented.
Method of assembling a thermal expansion compensator
NASA Technical Reports Server (NTRS)
Determan, William (Inventor); Matejczyk, Daniel Edward (Inventor)
2012-01-01
A thermal expansion compensator is provided and includes a first electrode structure having a first surface, a second electrode structure having a second surface facing the first surface and an elastic element bonded to the first and second surfaces and including a conductive element by which the first and second electrode structures electrically and/or thermally communicate, the conductive element having a length that is not substantially longer than a distance between the first and second surfaces.
Series Expansion of Functions with He's Homotopy Perturbation Method
ERIC Educational Resources Information Center
Khattri, Sanjay Kumar
2012-01-01
Finding a series expansion, such as Taylor series, of functions is an important mathematical concept with many applications. Homotopy perturbation method (HPM) is a new, easy to use and effective tool for solving a variety of mathematical problems. In this study, we present how to apply HPM to obtain a series expansion of functions. Consequently,…
Homentcovschi, Dorel; Miles, Ronald N.
2012-01-01
The paper applies the re-expansion method for analyzing planar discontinuities at the junction of two axi-symmetrical circular waveguides. The normal modes in the two waveguides are expanded at the junction plane into a system of functions accounting for velocity singularities at the corner points. As the new expansion has a high convergence order, only a few terms have to be considered for obtaining the solution of most practical problems. This paper gives the equivalent impedance accounting for nonplanar waves into a plane-wave analysis and also the scattering matrix describing the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both sides of the duct. The last section applies the re-expansion technique to some concentric expansion chambers providing an explicit formula for the transmission loss coefficient. PMID:22352491
Homentcovschi, Dorel; Miles, Ronald N
2012-02-01
The paper applies the re-expansion method for analyzing planar discontinuities at the junction of two axi-symmetrical circular waveguides. The normal modes in the two waveguides are expanded at the junction plane into a system of functions accounting for velocity singularities at the corner points. As the new expansion has a high convergence order, only a few terms have to be considered for obtaining the solution of most practical problems. This paper gives the equivalent impedance accounting for nonplanar waves into a plane-wave analysis and also the scattering matrix describing the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both sides of the duct. The last section applies the re-expansion technique to some concentric expansion chambers providing an explicit formula for the transmission loss coefficient.
Thermal expansion method for lining tantalum alloy tubing with tungsten
NASA Technical Reports Server (NTRS)
Watson, G. K.; Whittenberger, J. D.; Mattson, W. F.
1973-01-01
A differential-thermal expansion method was developed to line T-111 (tantalum - 8 percent tungsten - 2 percent hafnium) tubing with a tungsten diffusion barrier as part of a fuel element fabrication study for a space power nuclear reactor concept. This method uses a steel mandrel, which has a larger thermal expansion than T-111, to force the tungsten against the inside of the T-111 tube. Variables investigated include lining temperature, initial assembly gas size, and tube length. Linear integrity increased with increasing lining temperature and decreasing gap size. The method should have more general applicability where cylinders must be lined with a thin layer of a second material.
Improved fake mode free plane wave expansion method.
Jiang, Bin; Zhou, Wenjun; Chen, Wei; Liu, Anjin; Zheng, Wanhua
2011-08-01
We analyze the origin of the fake modes introduced by the plane wave expansion method with three-dimension (3D) supercell approximation. Through the detailed analysis of the energy distribution of fake modes and real modes, we propose the plane wave expansion-three planar-slab waveguides method to remove the fake modes and obtain the fake mode free band structure of a two-dimensional air hole photonic crystal slab. To the best of our knowledge, this is the first time that such a fake mode free photonic crystal band structure is presented. Our method is also definitely useful in designing other 3D devices.
Shortcuts to adiabaticity in a time-dependent box
Campo, A. del; Boshier, M. G.
2012-01-01
A method is proposed to drive an ultrafast non-adiabatic dynamics of an ultracold gas trapped in a time-dependent box potential. The resulting state is free from spurious excitations associated with the breakdown of adiabaticity, and preserves the quantum correlations of the initial state up to a scaling factor. The process relies on the existence of an adiabatic invariant and the inversion of the dynamical self-similar scaling law dictated by it. Its physical implementation generally requires the use of an auxiliary expulsive potential. The method is extended to a broad family of interacting many-body systems. As illustrative examples we consider the ultrafast expansion of a Tonks-Girardeau gas and of Bose-Einstein condensates in different dimensions, where the method exhibits an excellent robustness against different regimes of interactions and the features of an experimentally realizable box potential. PMID:22970340
Shortcuts to adiabaticity in a time-dependent box.
del Campo, A; Boshier, M G
2012-01-01
A method is proposed to drive an ultrafast non-adiabatic dynamics of an ultracold gas trapped in a time-dependent box potential. The resulting state is free from spurious excitations associated with the breakdown of adiabaticity, and preserves the quantum correlations of the initial state up to a scaling factor. The process relies on the existence of an adiabatic invariant and the inversion of the dynamical self-similar scaling law dictated by it. Its physical implementation generally requires the use of an auxiliary expulsive potential. The method is extended to a broad family of interacting many-body systems. As illustrative examples we consider the ultrafast expansion of a Tonks-Girardeau gas and of Bose-Einstein condensates in different dimensions, where the method exhibits an excellent robustness against different regimes of interactions and the features of an experimentally realizable box potential.
Shortcuts to adiabaticity in a time-dependent box
NASA Astrophysics Data System (ADS)
Del Campo, A.; Boshier, M. G.
2012-09-01
A method is proposed to drive an ultrafast non-adiabatic dynamics of an ultracold gas trapped in a time-dependent box potential. The resulting state is free from spurious excitations associated with the breakdown of adiabaticity, and preserves the quantum correlations of the initial state up to a scaling factor. The process relies on the existence of an adiabatic invariant and the inversion of the dynamical self-similar scaling law dictated by it. Its physical implementation generally requires the use of an auxiliary expulsive potential. The method is extended to a broad family of interacting many-body systems. As illustrative examples we consider the ultrafast expansion of a Tonks-Girardeau gas and of Bose-Einstein condensates in different dimensions, where the method exhibits an excellent robustness against different regimes of interactions and the features of an experimentally realizable box potential.
Bacon, Dave; Flammia, Steven T
2009-09-18
The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation, which is robust to timing errors and many control errors and maintains a constant energy gap throughout the computation above a degenerate ground state space. This construction allows for geometric robustness based upon the control of two independent qubit interactions. Further, our piecewise adiabatic evolution easily relates to the quantum circuit model, enabling the use of standard methods from fault-tolerance theory for establishing thresholds.
Experiences using DAKOTA stochastic expansion methods in computational simulations.
Templeton, Jeremy Alan; Ruthruff, Joseph R.
2012-01-01
Uncertainty quantification (UQ) methods bring rigorous statistical connections to the analysis of computational and experiment data, and provide a basis for probabilistically assessing margins associated with safety and reliability. The DAKOTA toolkit developed at Sandia National Laboratories implements a number of UQ methods, which are being increasingly adopted by modeling and simulation teams to facilitate these analyses. This report disseminates results as to the performance of DAKOTA's stochastic expansion methods for UQ on a representative application. Our results provide a number of insights that may be of interest to future users of these methods, including the behavior of the methods in estimating responses at varying probability levels, and the expansion levels for the methodologies that may be needed to achieve convergence.
Bleiziffer, Patrick Schmidtel, Daniel; Görling, Andreas
2014-11-28
The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N{sub 2}, O{sub 2}, and the polyyne C{sub 10}H{sub 2}) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions.
Density-functional expansion methods: Generalization of the auxiliary basis
Giese, Timothy J.; York, Darrin M.
2011-01-01
The formulation of density-functional expansion methods is extended to treat the second and higher-order terms involving the response density and spin densities with an arbitrary single-center auxiliary basis. The two-center atomic orbital products are represented by the auxiliary functions centered about those two atoms, and the mapping coefficients are determined from a local constrained variational procedure. This two-center variational procedure allows the mapping coefficients to be pretabulated and splined as a function of internuclear separation for efficient look up. The splines of mapping coefficients have a range no longer than that of the overlap integrals, and the auxiliary density appears as a single point-multipole expansion to all nonoverlapping atoms, thus allowing for the trivial implementation of a linear-scaling algorithm. The method is tested using Gaussian multipole expansions, and the effect of angular and radial completeness is explored. Several auxiliary basis sets are parametrized and compared to an auxiliary basis analogous to that used in the self-consistent-charge density-functional tight-binding model, and the method is demonstrated to greatly improve the representation of the density response with respect to a reference expansion model that does not use an auxiliary basis. PMID:21599040
Improved Fermi operator expansion methods for fast electronic structure calculations
NASA Astrophysics Data System (ADS)
Liang, WanZhen; Saravanan, Chandra; Shao, Yihan; Baer, Roi; Bell, Alexis T.; Head-Gordon, Martin
2003-08-01
Linear scaling algorithms based on Fermi operator expansions (FOE) have been considered significantly slower than other alternative approaches in evaluating the density matrix in Kohn-Sham density functional theory, despite their attractive simplicity. In this work, two new improvements to the FOE method are introduced. First, novel fast summation methods are employed to evaluate a matrix polynomial or Chebyshev matrix polynomial with matrix multiplications totalling roughly twice the square root of the degree of the polynomial. Second, six different representations of the Fermi operators are compared to assess the smallest possible degree of polynomial expansion for a given target precision. The optimal choice appears to be the complementary error function. Together, these advances make the FOE method competitive with the best existing alternatives.
Comparison of methods for improving the 1/N expansion
NASA Astrophysics Data System (ADS)
Varshni, Y. P.
1989-08-01
The recently proposed method by Papp [Phys. Rev. A 36, 3550 (1987); 38, 2158 (1988)] for determining the shift parameter in the shifted 1/N expansion method has been applied in three approximations to calculate the eigenenergies for the static screened Coulomb potential (SSCP) and Lennard-Jones 12-6 potential. The results are compared with those obtained by the method of Imbo et al. [Phys. Rev. D 29, 1669 (1984)] and the exact values. For the SSCP, comparison is also made with the results obtained by two methods proposed by Doren and Herschbach [Phys. Rev. A 34, 2654 (1986); 34, 2665 (1986)].
A general moment expansion method for stochastic kinetic models
NASA Astrophysics Data System (ADS)
Ale, Angelique; Kirk, Paul; Stumpf, Michael P. H.
2013-05-01
Moment approximation methods are gaining increasing attention for their use in the approximation of the stochastic kinetics of chemical reaction systems. In this paper we derive a general moment expansion method for any type of propensities and which allows expansion up to any number of moments. For some chemical reaction systems, more than two moments are necessary to describe the dynamic properties of the system, which the linear noise approximation is unable to provide. Moreover, also for systems for which the mean does not have a strong dependence on higher order moments, moment approximation methods give information about higher order moments of the underlying probability distribution. We demonstrate the method using a dimerisation reaction, Michaelis-Menten kinetics and a model of an oscillating p53 system. We show that for the dimerisation reaction and Michaelis-Menten enzyme kinetics system higher order moments have limited influence on the estimation of the mean, while for the p53 system, the solution for the mean can require several moments to converge to the average obtained from many stochastic simulations. We also find that agreement between lower order moments does not guarantee that higher moments will agree. Compared to stochastic simulations, our approach is numerically highly efficient at capturing the behaviour of stochastic systems in terms of the average and higher moments, and we provide expressions for the computational cost for different system sizes and orders of approximation. We show how the moment expansion method can be employed to efficiently quantify parameter sensitivity. Finally we investigate the effects of using too few moments on parameter estimation, and provide guidance on how to estimate if the distribution can be accurately approximated using only a few moments.
Lens array fabrication method with volume expansion property of PDMS
NASA Astrophysics Data System (ADS)
Jang, WonJae; Kim, Junoh; Lee, Muyoung; Lee, Jooho; Bang, Yousung; Won, Yong Hyub
2016-03-01
Conventionally, poly (dimethylsiloxane) lens array is fabricated by replica molding. In this paper, we describe simple method for fabricating lens array with expanding property of PDMS. The PDMS substrate is prepared by spin coating on cleaned glass. After spin coating PDMS, substrate is treated with O2 plasma to promote adhesion between PDMS substrate and photoresist pattern on it. Positive photoresist az-4330 and AZ 430K developer is used for patterning on PDMS. General photolithography process is used to patterning. Then patterned PDMS substrate is dipped to 1- Bromododecane bath. During this process, patterned photoresist work as a barrier and prevent blocked PDMS substrate from reaction with 1-Bromododecane. Unblocked part of PDMS directly react with 1-Bromododecane and results in expanded PDMS volume. The expansion of PDMS is depends on absorbed 1-Bromododecane volume, dipping time and ratio of block to open area. The focal length of lens array is controlled by those PDMS expansion factors. Scale of patterned photoresist determine a diameter of each lens. The expansion occurs symmetrically at center of unblocked PDMS and 1-Bromododecane interface. As a result, the PDMS lens array is achieved by this process.
Degenerate adiabatic perturbation theory: Foundations and applications
NASA Astrophysics Data System (ADS)
Rigolin, Gustavo; Ortiz, Gerardo
2014-08-01
We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010), 10.1103/PhysRevLett.104.170406], and on the formulation of the degenerate adiabatic theorem, along with its necessary and sufficient conditions [given in Phys. Rev. A 85, 062111 (2012), 10.1103/PhysRevA.85.062111]. We start with the adiabatic approximation for degenerate Hamiltonians that paves the way to a clear and rigorous statement of the associated degenerate adiabatic theorem, where the non-Abelian geometric phase (Wilczek-Zee phase) plays a central role to its quantitative formulation. We then describe the degenerate adiabatic perturbation theory, whose zeroth-order term is the degenerate adiabatic approximation, in its full generality. The parameter in the perturbative power-series expansion of the time-dependent wave function is directly associated to the inverse of the time it takes to drive the system from its initial to its final state. With the aid of the degenerate adiabatic perturbation theory we obtain rigorous necessary and sufficient conditions for the validity of the adiabatic theorem of quantum mechanics. Finally, to illustrate the power and wide scope of the methodology, we apply the framework to a degenerate Hamiltonian, whose closed-form time-dependent wave function is derived exactly, and also to other nonexactly solvable Hamiltonians whose solutions are numerically computed.
Shortcuts to adiabaticity in quantum many-body systems: a quantum dynamical microscope
NASA Astrophysics Data System (ADS)
Del Campo, Adolfo
2014-03-01
The evolution of a quantum system induced by a shortcut to adiabaticity mimics the adiabatic dynamics without the requirement of slow driving. Engineering it involves diagonalizing the instantaneous Hamiltonian of the system and results in the need of auxiliary non-local interactions for matter-waves. Here experimentally realizable driving protocols are found for a large class of single-particle, many-body, and non-linear systems without demanding the spectral properties as an input. The method is applied to the expansion of a trapped ultracold gas which spatially scales up the size of the cloud while conserving the quantum correlations of the initial many-body state. This shortcut to adiabatic expansions acts as a quantum dynamical microscope.
On the question of adiabatic invariants
NASA Astrophysics Data System (ADS)
Mitropol'Skii, Iu. A.
Some aspects of the construction of adiabadic invariants for dynamic systems with a single degree of freedom are discussed. Adiabatic invariants are derived using classical principles and the method proposed by Djukic (1981). The discussion covers an adiabatic invariant for a dynamic system with slowly varying parameters; derivation of an expression for an adiabatic invariant by the Djukic method for a second-order equation with a variable mass; and derivation of an expression for the adiabatic invariant for a nearly integrable differential equation.
NASA Astrophysics Data System (ADS)
Sahoo, S.; Saha Ray, S.
2016-04-01
In the present paper, we construct the analytical exact solutions of a nonlinear evolution equation in mathematical physics; namely time fractional modified KdV equation by using (G‧ / G)-expansion method and improved (G‧ / G)-expansion method. As a result, new types of exact analytical solutions are obtained.
A Multipole Expansion Method for Analyzing Lightning Field Changes
NASA Technical Reports Server (NTRS)
Koshak, William J.; Krider, E. Philip; Murphy, Martin J.
1999-01-01
Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q model) or a point dipole (the P model). The Q model has four unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P model has six unknown parameters and describes many intracloud (IC) discharges. In this paper we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a dme-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer-simulated sources and on natural lightning at the NASA Kennedy Space Center and U.S. Air Force Eastern Range.
Smit, Hans Harmen; Meijaard, Erik; van der Laan, Carina; Mantel, Stephan; Budiman, Arif; Verweij, Pita
2013-01-01
Land degradation is a global concern. In tropical areas it primarily concerns the conversion of forest into non-forest lands and the associated losses of environmental services. Defining such degradation is not straightforward hampering effective reduction in degradation and use of already degraded lands for more productive purposes. To facilitate the processes of avoided degradation and land rehabilitation, we have developed a methodology in which we have used international environmental and social sustainability standards to determine the suitability of lands for sustainable agricultural expansion. The method was developed and tested in one of the frontiers of agricultural expansion, West Kalimantan province in Indonesia. The focus was on oil palm expansion, which is considered as a major driver for deforestation in tropical regions globally. The results suggest that substantial changes in current land-use planning are necessary for most new plantations to comply with international sustainability standards. Through visualizing options for sustainable expansion with our methodology, we demonstrate that the link between oil palm expansion and degradation can be broken. Application of the methodology with criteria and thresholds similar to ours could help the Indonesian government and the industry to achieve its pro-growth, pro-job, pro-poor and pro-environment development goals. For sustainable agricultural production, context specific guidance has to be developed in areas suitable for expansion. Our methodology can serve as a template for designing such commodity and country specific tools and deliver such guidance. PMID:24039700
Harmen Smit, Hans; Meijaard, Erik; van der Laan, Carina; Mantel, Stephan; Budiman, Arif; Verweij, Pita
2013-01-01
Land degradation is a global concern. In tropical areas it primarily concerns the conversion of forest into non-forest lands and the associated losses of environmental services. Defining such degradation is not straightforward hampering effective reduction in degradation and use of already degraded lands for more productive purposes. To facilitate the processes of avoided degradation and land rehabilitation, we have developed a methodology in which we have used international environmental and social sustainability standards to determine the suitability of lands for sustainable agricultural expansion. The method was developed and tested in one of the frontiers of agricultural expansion, West Kalimantan province in Indonesia. The focus was on oil palm expansion, which is considered as a major driver for deforestation in tropical regions globally. The results suggest that substantial changes in current land-use planning are necessary for most new plantations to comply with international sustainability standards. Through visualizing options for sustainable expansion with our methodology, we demonstrate that the link between oil palm expansion and degradation can be broken. Application of the methodology with criteria and thresholds similar to ours could help the Indonesian government and the industry to achieve its pro-growth, pro-job, pro-poor and pro-environment development goals. For sustainable agricultural production, context specific guidance has to be developed in areas suitable for expansion. Our methodology can serve as a template for designing such commodity and country specific tools and deliver such guidance.
Adiabatic processes in monatomic gases
NASA Astrophysics Data System (ADS)
Carrera-Patiño, Martin E.
1988-08-01
A kinetic model is used to predict the temperature evolution of a monatomic ideal gas undergoing an adiabatic expansion or compression at a constant finite rate, and it is then generalized to treat real gases. The effects of interatomic forces are considered, using as examples the gas with the square-well potential and the van der Waals gas. The model is integrated into a Carnot cycle operating at a finite rate to compare the efficiency's rate-dependent behavior with the reversible result. Limitations of the model, rate penalties, and their importance are discussed.
Dynamical aspects of an adiabatic piston.
Munakata, T; Ogawa, H
2001-09-01
Dynamical aspects of an adiabatic piston are investigated, based on the mass ratio expansion of the master equation for the piston velocity distribution function. Simple theory for piston motion and relaxation of an ideal gas in a cylinder turns out to reproduce our numerical experiments quantitatively.
Adiabatic reversible compression: a molecular view
NASA Astrophysics Data System (ADS)
Miranda, E. N.
2002-07-01
The adiabatic compression (or expansion) of an ideal gas has been analysed. Using the kinetic theory of gases the usual relation between temperature and volume is obtained, while textbooks follow a thermodynamic approach. In this way we show, once again, the agreement between a macroscopic view (thermodynamics) and a microscopic one (kinetic theory).
Dynamical aspects of an adiabatic piston
NASA Astrophysics Data System (ADS)
Munakata, Toyonori; Ogawa, Hideki
2001-09-01
Dynamical aspects of an adiabatic piston are investigated, based on the mass ratio expansion of the master equation for the piston velocity distribution function. Simple theory for piston motion and relaxation of an ideal gas in a cylinder turns out to reproduce our numerical experiments quantitatively.
Laboratory Measurements of Adiabatic and Isothermal Processes
NASA Astrophysics Data System (ADS)
McNairy, W. W.
1997-04-01
Adiabatic and isothermal measurements on various of gases are made possible by using the Adiabatic Gas Law apparatus made by PASCO Scientific(Much of this work was published by the author in "The Physics Teacher", vol. 34, March 1996, p. 178-80.). By using a computer interface, undergraduates are able to data for monatomic, diatomic and polyatomic gases for both compression and expansion processes. Designed principally to obtain adiabatic data, the apparatus may be easily modified for use in isothermal processes. The various sets of data are imported into a spreadsheet program where fits may be made to the ideal gas law and the adiabatic gas law. Excellent results are obtained for the natural logarithm of pressure versus the natural logarithm of volume for both the isothermal data (expected slope equal to -1 in all cases) and the adiabatic data (slope equal to -1 times the ratio of specific heats for the particular gas). An overview of the lab procedure used at VMI will be presented along with data obtained for several adiabatic and isothermal processes.
Time dependence of adiabatic particle number
NASA Astrophysics Data System (ADS)
Dabrowski, Robert; Dunne, Gerald V.
2016-09-01
We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time-dependent particle number not just at asymptotic early and late times, but also during the perturbation. Naïvely, this is not a well-defined notion for such a nonequilibrium process, as the particle number at intermediate times depends on a basis choice of reference states with respect to which particles and antiparticles are defined, even though the final late-time particle number is independent of this basis choice. The basis choice is associated with a particular truncation of the adiabatic expansion. The adiabatic expansion is divergent, and we show that if this divergent expansion is truncated at its optimal order, a universal time dependence is obtained, confirming a general result of Dingle and Berry. This optimally truncated particle number provides a clear picture of quantum interference effects for perturbations with nontrivial temporal substructure. We illustrate these results using several equivalent definitions of adiabatic particle number: the Bogoliubov, Riccati, spectral function and Schrödinger picture approaches. In each approach, the particle number may be expressed in terms of the tiny deviations between the exact and adiabatic solutions of the Ermakov-Milne equation for the associated time-dependent oscillators.
On adiabatic invariant in generalized Galileon theories
Ema, Yohei; Jinno, Ryusuke; Nakayama, Kazunori; Mukaida, Kyohei E-mail: jinno@hep-th.phys.s.u-tokyo.ac.jp E-mail: kazunori@hep-th.phys.s.u-tokyo.ac.jp
2015-10-01
We consider background dynamics of generalized Galileon theories in the context of inflation, where gravity and inflaton are non-minimally coupled to each other. In the inflaton oscillation regime, the Hubble parameter and energy density oscillate violently in many cases, in contrast to the Einstein gravity with minimally coupled inflaton. However, we find that there is an adiabatic invariant in the inflaton oscillation regime in any generalized Galileon theory. This adiabatic invariant is useful in estimating the expansion law of the universe and also the particle production rate due to the oscillation of the Hubble parameter.
A geometric criterion for adiabatic chaos
Kaper, T.J. ); Kovacic, G. )
1994-03-01
Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.
NASA Technical Reports Server (NTRS)
Hill, P R
1958-01-01
A method of calculating the temperature of thick walls has been developed in which the time series and the response to a unit triangle variation of surface temperature concepts are used, together with essentially standard formulas for transient temperature and heat flow into thick walls. The method can be used without knowledge of the mathematical tools of its development. The method is particularly suitable for determining the wall temperature in one-dimensional thermal problems in aeronautics where there is a continuous variation of the heat-transfer coefficient and adiabatic-wall temperature. The method also offers a convenient means for solving the inverse problem of determining the heat-flow history when temperature history is known.
Wireless adiabatic power transfer
Rangelov, A.A.; Suchowski, H.; Silberberg, Y.; Vitanov, N.V.
2011-03-15
Research Highlights: > Efficient and robust mid-range wireless energy transfer between two coils. > The adiabatic energy transfer is analogous to adiabatic passage in quantum optics. > Wireless energy transfer is insensitive to any resonant constraints. > Wireless energy transfer is insensitive to noise in the neighborhood of the coils. - Abstract: We propose a technique for efficient mid-range wireless power transfer between two coils, by adapting the process of adiabatic passage for a coherently driven two-state quantum system to the realm of wireless energy transfer. The proposed technique is shown to be robust to noise, resonant constraints, and other interferences that exist in the neighborhood of the coils.
Parallelizable adiabatic gate teleportation
NASA Astrophysics Data System (ADS)
Nakago, Kosuke; Hajdušek, Michal; Nakayama, Shojun; Murao, Mio
2015-12-01
To investigate how a temporally ordered gate sequence can be parallelized in adiabatic implementations of quantum computation, we modify adiabatic gate teleportation, a model of quantum computation proposed by Bacon and Flammia [Phys. Rev. Lett. 103, 120504 (2009), 10.1103/PhysRevLett.103.120504], to a form deterministically simulating parallelized gate teleportation, which is achievable only by postselection. We introduce a twisted Heisenberg-type interaction Hamiltonian, a Heisenberg-type spin interaction where the coordinates of the second qubit are twisted according to a unitary gate. We develop parallelizable adiabatic gate teleportation (PAGT) where a sequence of unitary gates is performed in a single step of the adiabatic process. In PAGT, numeric calculations suggest the necessary time for the adiabatic evolution implementing a sequence of L unitary gates increases at most as O (L5) . However, we show that it has the interesting property that it can map the temporal order of gates to the spatial order of interactions specified by the final Hamiltonian. Using this property, we present a controlled-PAGT scheme to manipulate the order of gates by a control qubit. In the controlled-PAGT scheme, two differently ordered sequential unitary gates F G and G F are coherently performed depending on the state of a control qubit by simultaneously applying the twisted Heisenberg-type interaction Hamiltonians implementing unitary gates F and G . We investigate why the twisted Heisenberg-type interaction Hamiltonian allows PAGT. We show that the twisted Heisenberg-type interaction Hamiltonian has an ability to perform a transposed unitary gate by just modifying the space ordering of the final Hamiltonian implementing a unitary gate in adiabatic gate teleportation. The dynamics generated by the time-reversed Hamiltonian represented by the transposed unitary gate enables deterministic simulation of a postselected event of parallelized gate teleportation in adiabatic
Modeling laser beam diffraction and propagation by the mode-expansion method.
Snyder, James J
2007-08-01
In the mode-expansion method for modeling propagation of a diffracted beam, the beam at the aperture can be expanded as a weighted set of orthogonal modes. The parameters of the expansion modes are chosen to maximize the weighting coefficient of the lowest-order mode. As the beam propagates, its field distribution can be reconstructed from the set of weighting coefficients and the Gouy phase of the lowest-order mode. We have developed a simple procedure to implement the mode-expansion method for propagation through an arbitrary ABCD matrix, and we have demonstrated that it is accurate in comparison with direct calculations of diffraction integrals and much faster.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Iwashige, Kengo; Ikeda, Takashi
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
NASA Astrophysics Data System (ADS)
Dobbyn, Abigail J.; Knowles, Peter J.
A number of established techniques for obtaining diabatic electronic states in small molecules are critically compared for the example of the X and B states in the water molecule, which contribute to the two lowest-energy conical intersections. Integration of the coupling matrix elements and analysis of configuration mixing coefficients both produce reliable diabatic states globally. Methods relying on diagonalization of dipole moment and angular momentum operators are shown to fail in large regions of coordinate space. However, the use of transition angular momentum matrix elements involving the A state, which is degenerate with B at the conical intersections, is successful globally, provided that an appropriate choice of coordinates is made. Long range damping of non-adiabatic coupling to give correct asymptotic mixing angles also is investigated.
Analysis for the convergence problem of the plane-wave expansion method for photonic crystals.
Shen, Linfang; He, Sailing
2002-05-01
The convergence feature of two types of plane-wave expansion methods commonly used for photonic crystals is analyzed. It is shown that the reason for the slow convergence of these plane-wave expansion methods is not the slow convergence of the Fourier series for the permittivity profile of the photonic crystal but the inappropriate formulation of the eigenproblem. A new formulation of the eigenproblem is presented to improve the convergence in the one-dimensional case.
Three-Dimensional Simulation of Scalp Soft Tissue Expansion Using Finite Element Method
Guan, Qiu; Du, Xiaochen; Shao, Yan; Lin, Lili; Chen, Shengyong
2014-01-01
Scalp soft tissue expansion is one of the key medical techniques to generate new skin tissue for correcting various abnormalities and defects of skin in plastic surgery. Therefore, it is very important to work out the appropriate approach to evaluate the increase of expanded scalp area and to predict the shape, size, number, and placement of the expander. A novel method using finite element model is proposed to solve large deformation of scalp expansion in this paper. And the procedure to implement the scalp tissue expansion with finite element method is also described in detail. The three-dimensional simulation results show that the proposed method is effective, and the analysis of simulation experiment shows that the volume and area of the expansion scalp can be accurately calculated and the quantity, location, and size of the expander can also be predicted successfully with the proposed model. PMID:25110514
Adiabatic capture and debunching
Ng, K.Y.; /Fermilab
2012-03-01
In the study of beam preparation for the g-2 experiment, adiabatic debunching and adiabatic capture are revisited. The voltage programs for these adiabbatic processes are derived and their properties discussed. Comparison is made with some other form of adiabatic capture program. The muon g-2 experiment at Fermilab calls for intense proton bunches for the creation of muons. A booster batch of 84 bunches is injected into the Recycler Ring, where it is debunched and captured into 4 intense bunches with the 2.5-MHz rf. The experiment requires short bunches with total width less than 100 ns. The transport line from the Recycler to the muon-production target has a low momentum aperture of {approx} {+-}22 MeV. Thus each of the 4 intense proton bunches required to have an emittance less than {approx} 3.46 eVs. The incoming booster bunches have total emittance {approx} 8.4 eVs, or each one with an emittance {approx} 0.1 eVs. However, there is always emittance increase when the 84 booster bunches are debunched. There will be even larger emittance increase during adiabatic capture into the buckets of the 2.5-MHz rf. In addition, the incoming booster bunches may have emittances larger than 0.1 eVs. In this article, we will concentrate on the analysis of the adiabatic capture process with the intention of preserving the beam emittance as much as possible. At this moment, beam preparation experiment is being performed at the Main Injector. Since the Main Injector and the Recycler Ring have roughly the same lattice properties, we are referring to adiabatic capture in the Main Injector instead in our discussions.
Adiabatically implementing quantum gates
Sun, Jie; Lu, Songfeng Liu, Fang
2014-06-14
We show that, through the approach of quantum adiabatic evolution, all of the usual quantum gates can be implemented efficiently, yielding running time of order O(1). This may be considered as a useful alternative to the standard quantum computing approach, which involves quantum gates transforming quantum states during the computing process.
Entanglement and adiabatic quantum computation
NASA Astrophysics Data System (ADS)
Ahrensmeier, D.
2006-06-01
Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a resource is discussed.
Zhao, Xuefeng; Gong, Peng; Qiao, Guofu; Lu, Jie; Lv, Xingjun; Ou, Jinping
2011-01-01
In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring. PMID:22346672
Vibrations of micro-beams actuated by an electric field via Parameter Expansion Method
NASA Astrophysics Data System (ADS)
Sedighi, Hamid M.; Shirazi, Kourosh H.
2013-04-01
This paper presents a new asymptotic procedure to predict the nonlinear vibrational behavior of micro-beams pre-deformed by an electric field. The nonlinear equation of motion includes both even and odd nonlinearities. A powerful analytical method called Parameter Expansion Method (PEM) is employed to obtain the approximated solution and frequency-amplitude relationship. It is demonstrated that the first two terms in series expansions are sufficient to produce an acceptable solution of mentioned system. The obtained results from numerical methods verify the soundness of the analytical procedure. Finally, the influences of basic parameters on pull-in instability and natural frequency are investigated.
NASA Astrophysics Data System (ADS)
Álvarez, Gabriel; Martínez Alonso, Luis; Medina, Elena
2011-07-01
We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach.
"Flypaper technique" a modified expansion method for preparation of postage stamp autografts.
Lee, Su-Shin; Lin, Tsai-Ming; Chen, Yi-Hui; Lin, Sin-Daw; Lai, Chung-Sheng
2005-09-01
The gold standard for management of extensive burn has been early excision, temporary allografting and final autografting. However, "lack of donor skin" is a challenge condition when autografting in the treatment of extensive burns. Designing an efficient and easy to apply expansion method may improve burn care quality and shorten the hospital stay period. From December 1998 to May 2004, we have performed fly paper technique postage stamp skin autografting for eight major burn patients in the Kaohsiung Medical University Hospital. By using a quick cutting plate, chessboard tray and petrolatum gauze, the skin islands can be uniformly located and correctly oriented on gauze. Then, the gauze with skin islands was grafted on to the wound. The wound healing time depends on the size of skin islands and expansion ratio. This method allows true expansion ratio up to nine times. The average wound healing times are 27.2 days for six times expansion and 34 days for nine times expansion. However, the burn scar needs further compression therapy to improve the cosmetic result. In comparison with the mesh technique, the skin islands are independent of each other, any dislodgement of a skin island will not interfere with the surrounding skin squares. When compared with the modified Meek technique, this method also offers rapid wound reepithilization but with lower cost. This flypaper technique is worthy of consideration in dealing with the extensive burns.
Romero-Redondo, C.; Garrido, E.; Barletta, P.; Kievsky, A.; Viviani, M.
2011-02-15
In this work we investigate 1+2 reactions within the framework of the hyperspherical adiabatic expansion method. With this aim two integral relations, derived from the Kohn variational principle, are used. A detailed derivation of these relations is shown. The expressions derived are general, not restricted to relative s partial waves, and with applicability in multichannel reactions. The convergence of the K matrix in terms of the adiabatic potentials is investigated. Together with a simple model case used as a test for the method, we show results for the collision of a {sup 4}He atom on a {sup 4}He{sub 2} dimer (only the elastic channel open), and for collisions involving a {sup 6}Li and two {sup 4}He atoms (two channels open).
Adiabatic topological quantum computing
NASA Astrophysics Data System (ADS)
Cesare, Chris; Landahl, Andrew J.; Bacon, Dave; Flammia, Steven T.; Neels, Alice
2015-07-01
Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.
Adiabatic Hyperspherical Analysis of Realistic Nuclear Potentials
NASA Astrophysics Data System (ADS)
Daily, K. M.; Kievsky, Alejandro; Greene, Chris H.
2015-12-01
Using the hyperspherical adiabatic method with the realistic nuclear potentials Argonne V14, Argonne V18, and Argonne V18 with the Urbana IX three-body potential, we calculate the adiabatic potentials and the triton bound state energies. We find that a discrete variable representation with the slow variable discretization method along the hyperradial degree of freedom results in energies consistent with the literature. However, using a Laguerre basis results in missing energy, even when extrapolated to an infinite number of basis functions and channels. We do not include the isospin T = 3/2 contribution in our analysis.
NASA Astrophysics Data System (ADS)
Ye, Hezhou; Yin, Yanhua; Wang, Jianfeng
2015-08-01
While commercially available computational fluid dynamic packages are employed nowadays to analyze the spraying behavior of the cold spray (CS) system and optimize the nozzle geometry design, using these packages is often prohibitive because of complex computational resource requirements and expensive copyright licenses. This paper proposes a quick and economical method for predicting the performance of the CS system, while asking for minimal computational resource. A one-dimensional adiabatic friction model with the consideration of friction was developed to calculate the critical pressure of nozzles under different expansion ratios and the gas/particle velocity at different spraying conditions. The accuracy of the critical pressure calculation was evidenced by polymeric nozzle destructive tests. The particle velocities achieved from the nozzles with different expansion ratios were measured and compared with the velocity values calculated by the model. The suggested adiabatic friction model is validated by the well-matched values between the calculated results and the experimental data.
Complexity of the Quantum Adiabatic Algorithm
NASA Technical Reports Server (NTRS)
Hen, Itay
2013-01-01
The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorithms.
A novel hybrid Neumann expansion method for stochastic analysis of mistuned bladed discs
NASA Astrophysics Data System (ADS)
Yuan, Jie; Allegri, Giuliano; Scarpa, Fabrizio; Patsias, Sophoclis; Rajasekaran, Ramesh
2016-05-01
The paper presents a novel hybrid method to enhance the computational efficiency of matrix inversions during the stochastic analysis of mistuned bladed disc systems. The method is based on the use of stochastic Neumann expansion in the frequency domain, coupled with a matrix factorization in the neighbourhood of the resonant frequencies. The number of the expansion terms is used as an indicator to select the matrix inversion technique to be used, without introducing any additional computational cost. The proposed method is validated using two case studies, where the dynamics an aero-engine bladed disc is modelled first using a lumped parameter approach and then with high-fidelity finite element analysis. The frequency responses of the blades are evaluated according to different mistuning patterns via stiffness or mass perturbations under the excitation provided by the engine orders. Results from standard matrix factorization methods are used to benchmark the responses obtained from the proposed hybrid method. Unlike classic Neumann expansion methods, the new technique can effectively update the inversion of an uncertain matrix with no convergence problems during Monte Carlo simulations. The novel hybrid method is more computationally efficient than standard techniques, with no accuracy loss.
Bazzani, A.; Turchetti, G.; Benedetti, C.; Rambaldi, S.; Servizi, G.
2005-06-08
In a high intensity circular accelerator the synchrotron dynamics introduces a slow modulation in the betatronic tune due to the space-charge tune depression. When the transverse motion is non-linear due to the presence of multipolar effects, resonance islands move in the phase space and change their amplitude. This effect introduces the trapping and detrapping phenomenon and a slow diffusion in the phase space. We apply the neo-adiabatic theory to describe this diffusion mechanism that can contribute to halo formation.
An In Vitro Intact Globe Expansion Method for Evaluation of Cross-linking Treatments
Mattson, Matthew S.; Huynh, Joyce; Wiseman, Meredith; Coassin, Marco; Kornfield, Julia A.; Schwartz, Daniel M.
2010-01-01
Purpose. To measure the tissue mechanical response to elevated intraocular pressure (IOP) using intact globe expansion of rabbit eyes. This method examined rabbit kit (2–3 weeks old) eyes as a model for weakened tissue and evaluated riboflavin/UVA and glyceraldehyde cross-linking treatments. Methods. The ocular shape of enucleated eyes was photographed during a 24-hour period while a controlled IOP was imposed (either low IOP = 22 mm Hg or high IOP = 85 mm Hg). Untreated controls consisted of kit eyes tested at both low- and high IOP and adult eyes tested at high IOP. Treated kit eyes (dextran controls, riboflavin/UVA treatment of the cornea, and glyceraldehyde treatment of the entire globe) were tested at high IOP. Results. Low IOP elicited negligible creep of the sclera and very gradual creep of the cornea. In contrast, high IOP induced up to an 8% strain in the sclera and a 15% strain in the cornea of rabbit kit eyes. The expansion of adult eyes was less than one third that of kit eyes at the same, high IOP. Riboflavin/UVA treatment of corneas reduced expansion compared with that in both dextran-treated and untreated control corneas. Glyceraldehyde treatment prevented expansion of the cornea and sclera. Conclusions. The intact globe expansion method (GEM) imposes a loading geometry comparable to in vivo conditions and can quantify changes in mechanical stability as a function of testing conditions (e.g., IOP, tissue maturation, and therapeutic cross-linking) with small sample sizes and small variability. Rabbit kit eyes provide a model of weak tissue suitable for screening treatments that strengthen the cornea and sclera. PMID:20071684
Fast Quasi-Adiabatic Gas Cooling: An Experiment Revisited
ERIC Educational Resources Information Center
Oss, S.; Gratton, L. M.; Calza, G.; Lopez-Arias, T.
2012-01-01
The well-known experiment of the rapid expansion and cooling of the air contained in a bottle is performed with a rapidly responsive, yet very cheap thermometer. The adiabatic, low temperature limit is approached quite closely and measured with our apparatus. A straightforward theoretical model for this process is also presented and discussed.…
Ultrasonic elastic modes in solid bars: an application of the plane wave expansion method.
Manzanares-Martinez, Betsabe; Ramos-Mendieta, Felipe; Baltazar, Arturo
2010-06-01
Ultrasonic elastic modes in solid bars are investigated theoretically and experimentally using the plane wave expansion method to calculate the dispersion curves k=k(omega) for longitudinal, torsional, and flexural waves. The plane wave extension method allows to consider rods of circular and square cross sections. The technique, which has received attention in the study of photonic and phononic crystals, is adapted in order to identify the various types of modes. Results are compared with predictions from semi-analytical models. The numerical approximation is validated with the experimental determination of the time-frequency dispersion curves. The technique based on the plane wave expansion method presented here could be a numerical alternative used to determine the wave propagation and modal vibration with high precision in structures like bars and cylinders. Practical applications of this study could include the inspection of long-span engineering systems with bar or cylinder like characteristics.
Expanded-mode semiconductor laser with tapered-rib adiabatic-following fiber coupler
Vawter, G.A.; Smith, R.E.; Hou, H.; Wendt, J.R.
1997-02-01
A new diode laser using a Tapered-Rib Adiabatic-Following Fiber Coupler to achieve 2D mode expansion and narrow, symmetric far-field emission without epitaxial regrowth or sharply-defined tips on tapered waveguides is presented.
Adiabatic Mass Parameters for Spontaneous Fission
Baran, A.; Sheikh, J. A.; Nazarewicz, Witold
2009-01-01
The collective mass tensor derived from the adiabatic time-dependent Hartree-Fock-Bogoliubov theory, perturbative cranking approximation, and the Gaussian overlap approximation to the generator-coordinate method is discussed. Illustrative calculations are carried out for ^{252}Fm using the nuclear density functional theory with Skyrme interaction SkM* and seniority pairing.
Non-adiabatic dark fluid cosmology
Hipólito-Ricaldi, W.S.; Velten, H.E.S.; Zimdahl, W. E-mail: velten@cce.ufes.br
2009-06-01
We model the dark sector of the cosmic substratum by a viscous fluid with an equation of state p = −ζΘ, where Θ is the fluid-expansion scalar and ζ is the coefficient of bulk viscosity for which we assume a dependence ζ∝ρ{sup ν} on the energy density ρ. The homogeneous and isotropic background dynamics coincides with that of a generalized Chaplygin gas with equation of state p = −A/ρ{sup α}. The perturbation dynamics of the viscous model, however, is intrinsically non-adiabatic and qualitatively different from the Chaplygin-gas case. In particular, it avoids short-scale instabilities and/or oscillations which apparently have ruled out unified models of the Chaplygin-gas type. We calculate the matter power spectrum and demonstrate that the non-adiabatic model is compatible with the data from the 2dFGRS and the SDSS surveys. A χ{sup 2}-analysis shows, that for certain parameter combinations the viscous-dark-fluid (VDF) model is well competitive with the ΛCDM model. These results indicate that non-adiabatic unified models can be seen as potential contenders for a General-Relativity-based description of the cosmic substratum.
Bleiziffer, Patrick Krug, Marcel; Görling, Andreas
2015-06-28
A self-consistent Kohn-Sham method based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem, employing the frequency-dependent exact exchange kernel f{sub x} is presented. The resulting SC-exact-exchange-only (EXX)-ACFD method leads to even more accurate correlation potentials than those obtained within the direct random phase approximation (dRPA). In contrast to dRPA methods, not only the Coulomb kernel but also the exact exchange kernel f{sub x} is taken into account in the EXX-ACFD correlation which results in a method that, unlike dRPA methods, is free of self-correlations, i.e., a method that treats exactly all one-electron systems, like, e.g., the hydrogen atom. The self-consistent evaluation of EXX-ACFD total energies improves the accuracy compared to EXX-ACFD total energies evaluated non-self-consistently with EXX or dRPA orbitals and eigenvalues. Reaction energies of a set of small molecules, for which highly accurate experimental reference data are available, are calculated and compared to quantum chemistry methods like Møller-Plesset perturbation theory of second order (MP2) or coupled cluster methods [CCSD, coupled cluster singles, doubles, and perturbative triples (CCSD(T))]. Moreover, we compare our methods to other ACFD variants like dRPA combined with perturbative corrections such as the second order screened exchange corrections or a renormalized singles correction. Similarly, the performance of our EXX-ACFD methods is investigated for the non-covalently bonded dimers of the S22 reference set and for potential energy curves of noble gas, water, and benzene dimers. The computational effort of the SC-EXX-ACFD method exhibits the same scaling of N{sup 5} with respect to the system size N as the non-self-consistent evaluation of only the EXX-ACFD correlation energy; however, the prefactor increases significantly. Reaction energies from the SC-EXX-ACFD method deviate quite little from EXX-ACFD energies obtained non
Adiabat Shaping of ICF Capsules Using Ramped Pressure Profiles
NASA Astrophysics Data System (ADS)
Anderson, K.; Betti, R.; Collins, T. J. B.; Marinak, M. M.; Haan, S. W.
2002-11-01
Target design of direct-drive ICF capsules has historically involved a compromise between high 1-D (clean) yield and capsule stability. Low-adiabat fuel is desirable to achieve high compression and, hence, high yield. A higher adiabat at the ablation front reduces the growth rate of the Raleigh--Taylor instability due to higher ablation velocity. An optimal target design will take advantage of both by shaping the adiabat of the capsule to allow for high adiabat in the material that is to be ablated and low adiabat in the remaining fuel. We present here a method of adiabat shaping using a low-intensity prepulse followed by laser shutoff before beginning the main drive pulse. This creates a decaying shock with a ramped pressure profile behind it. Since the prepulse is low intensity, the adiabat is not strongly affected by the prepulse. The main shock is then launched up this ramped pressure profile to set the adiabat. Because the main shock sees an increasing pressure profile, the effective strength of the shock decreases as it propagates through the shell, thus creating a smooth adiabat profile from high outer-shell adiabat to low inner-shell adiabat. Results of simulations using 1-D LILAC and 2-D DRACO (LLE), as well as 1-D and 2-D HYDRA (LLNL), are presented. This work was supported by the U.S. DOE Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC03-92SF19460 and by the University of California LLNL under contract No. W-7405-Eng-48.
Huberts, W; Donders, W P; Delhaas, T; van de Vosse, F N
2014-12-01
Patient-specific modeling requires model personalization, which can be achieved in an efficient manner by parameter fixing and parameter prioritization. An efficient variance-based method is using generalized polynomial chaos expansion (gPCE), but it has not been applied in the context of model personalization, nor has it ever been compared with standard variance-based methods for models with many parameters. In this work, we apply the gPCE method to a previously reported pulse wave propagation model and compare the conclusions for model personalization with that of a reference analysis performed with Saltelli's efficient Monte Carlo method. We furthermore differentiate two approaches for obtaining the expansion coefficients: one based on spectral projection (gPCE-P) and one based on least squares regression (gPCE-R). It was found that in general the gPCE yields similar conclusions as the reference analysis but at much lower cost, as long as the polynomial metamodel does not contain unnecessary high order terms. Furthermore, the gPCE-R approach generally yielded better results than gPCE-P. The weak performance of the gPCE-P can be attributed to the assessment of the expansion coefficients using the Smolyak algorithm, which might be hampered by the high number of model parameters and/or by possible non-smoothness in the output space. PMID:25377937
LETTERS AND COMMENTS: Adiabatic process reversibility: microscopic and macroscopic views
NASA Astrophysics Data System (ADS)
Anacleto, Joaquim; Pereira, Mário G.
2009-05-01
The reversibility of adiabatic processes was recently addressed by two publications. In the first (Miranda 2008 Eur. J. Phys. 29 937-43), an equation was derived relating the initial and final volumes and temperatures for adiabatic expansions of an ideal gas, using a microscopic approach. In that relation the parameter r accounts for the process reversibility, ranging between 0 and 1, which corresponds to the free and reversible expansion, respectively. In the second (Anacleto and Pereira 2009 Eur. J. Phys. 30 177-83), the authors have shown that thermodynamics can effectively and efficiently be used to obtain the general law for adiabatic processes carried out by an ideal gas, including compressions, for which r \\ge 1. The present work integrates and extends the aforementioned studies, providing thus further insights into the analysis of the adiabatic process. It is shown that Miranda's work is wholly valid for compressions. In addition, it is demonstrated that the adiabatic reversibility coefficient given in terms of the piston velocity and the root mean square velocity of the gas particles is equivalent to the macroscopic description, given just by the quotient between surroundings and system pressure values.
NASA Astrophysics Data System (ADS)
Kovalchuk, Valery I.
2014-11-01
In this paper, a method has been developed to solve three-particle Faddeev equations in the configuration space making use of a series expansion in hyperspherical harmonics. The following parameters of the bound state of triton and helium-3 nuclei have been calculated: the binding energies, the weights of symmetric and mixed-symmetry components of the wave function, the magnetic moments, and the charge radii.
Some Remarks on the Riccati Equation Expansion Method for Variable Separation of Nonlinear Models
NASA Astrophysics Data System (ADS)
Zhang, Yu-Peng; Dai, Chao-Qing
2015-10-01
Based on the Riccati equation expansion method, 11 kinds of variable separation solutions with different forms of (2+1)-dimensional modified Korteweg-de Vries equation are obtained. The following two remarks on the Riccati equation expansion method for variable separation are made: (i) a remark on the equivalence of different solutions constructed by the Riccati equation expansion method. From analysis, we find that these seemly independent solutions with different forms actually depend on each other, and they can transform from one to another via some relations. We should avoid arbitrarily asserting so-called "new" solutions; (ii) a remark on the construction of localised excitation based on variable separation solutions. For two or multi-component systems, we must be careful with excitation structures constructed by all components for the same model lest the appearance of some un-physical structures. We hope that these results are helpful to deeply study exact solutions of nonlinear models in physical, engineering and biophysical contexts.
NASA Technical Reports Server (NTRS)
Parrott, T. L.
1973-01-01
An improved method for the design of expansion-chamber mufflers is described and applied to the task of reducing exhaust noise generated by a helicopter. The method is an improvement of standard transmission-line theory in that it accounts for the effect of the mean exhaust-gas flow on the acoustic-transmission properties of a muffler system, including the termination boundary condition. The method has been computerized, and the computer program includes an optimization procedure that adjusts muffler component lengths to achieve a minimum specified desired transmission loss over a specified frequency range. A printout of the program is included together with a user-oriented description.
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
NASA Astrophysics Data System (ADS)
Lu, Wangtao; Qian, Jianliang; Burridge, Robert
2016-05-01
In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation can be viewed as an evolution equation in one of the spatial directions. With such applications in mind, starting from Babich's expansion, we develop a new high-order asymptotic method, which we dub the fast Huygens sweeping method, for solving point-source Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of this method is that we develop a new Eulerian approach to compute the asymptotics, i.e. the traveltime function and amplitude coefficients that arise in Babich's expansion, yielding a locally valid solution, which is accurate close enough to the source. The second novelty is that we utilize the Huygens-Kirchhoff integral to integrate many locally valid wavefields to construct globally valid wavefields. This automatically treats caustics and yields uniformly accurate solutions both near the source and remote from it. The third novelty is that the butterfly algorithm is adapted to accelerate the Huygens-Kirchhoff summation, achieving nearly optimal complexity O (Nlog N), where N is the number of mesh points; the complexity prefactor depends on the desired accuracy and is independent of the frequency. To reduce the storage of the resulting tables of asymptotics in Babich's expansion, we use the multivariable Chebyshev series expansion to compress each table by encoding the information into a small number of coefficients. The new method enjoys the following desired features. First, it precomputes the asymptotics in Babich's expansion, such as traveltime and amplitudes. Second, it takes care of caustics automatically. Third, it can compute the point-source Helmholtz solution for many different sources at many frequencies simultaneously. Fourth, for a specified number of points per wavelength, it can construct the wavefield in nearly optimal complexity in terms
NASA Astrophysics Data System (ADS)
De Micheli, Enrico; Viano, Giovanni Alberto
2013-04-01
We present a simple and fast algorithm for the computation of the Gegenbauer transform, which is known to be very useful in the development of spectral methods for the numerical solution of ordinary and partial differential equations of physical interest. We prove that the coefficients of the expansion of a function f(x) in Gegenbauer (also known as ultraspherical) polynomials coincide with the Fourier coefficients of a suitable integral transform of the function f(x). This allows to compute N Gegenbauer coefficients in O(Nlog2N) operations by means of a single Fast Fourier Transform of the integral transform of f(x). We also show that the inverse Gegenbauer transform is expressible as the Abel-type transform of a suitable Fourier series. This fact produces a novel algorithm for the fast evaluation of Gegenbauer expansions.
An Improved (G'/G)-expansion Method for Solving Nonlinear PDEs in Mathematical Physics
NASA Astrophysics Data System (ADS)
Zayed, Elsayed M. E.; Al-Joudi, Shorog
2010-09-01
In the present article, we construct the traveling wave solutions of the (1+1)-dimensional coupled Hirota-Satsuma-KdV equations and the (1+1)-dimensional variant coupled Boussinesq system of equations by using an improved (G'/G)-expansion method, where G satisfies the second order linear ordinary differential equation. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.
An Improved ((G'/G))-expansion Method for Solving Nonlinear PDEs in Mathematical Physics
Zayed, Elsayed M. E.; Al-Joudi, Shorog
2010-09-30
In the present article, we construct the traveling wave solutions of the (1+1)-dimensional coupled Hirota-Satsuma-KdV equations and the (1+1)-dimensional variant coupled Boussinesq system of equations by using an improved ((G'/G))-expansion method, where G satisfies the second order linear ordinary differential equation. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.
Adiabatic principles in atom-diatom collisional energy transfer
Hovingh, W.J.
1993-01-01
This work describes the application of numerical methods to the solution of the time dependent Schroedinger equation for non-reactive atom-diatom collisions in which only one of the degrees of freedom has been removed. The basic method involves expanding the wave function in a basis set in two of the diatomic coordinates in a body-fixed frame (with respect to the triatomic complex) and defining the coefficients in that expansion as functions on a grid in the collision coordinate. The wave function is then propagated in time using a split operator method. The bulk of this work is devoted to the application of this formalism to the study of internal rotational predissociation in NeHF, in which quasibound states of the triatom predissociate through the transfer of energy from rotation of the diatom into translational energy in the atom-diatom separation coordinate. The author analyzes the computed time dependent wave functions to calculate the lifetimes for several quasibound states; these are in agreement with time independent quantum calculations using the same potential. Moreover, the time dependent behavior of the wave functions themselves sheds light on the dynamics of the predissociation processes. Finally, the partial cross sections of the products in those processes is determined with multiple exit channels. These show strong selectivity in the orbital angular momentum of the outgoing fragments, which the author explains with an adiabatic channel interpretation of the wave function's dynamics. The author also suggests that the same formalism might profitably be used to investigate the quantum dynamics of [open quotes]quasiresonant vibration-rotation transfer[close quotes], in which remarkably strong propensity rules in certain inelastic atom-diatom collision arise from classical adiabatic invariance theory.
Non-adiabatic effects in near-adiabatic mixed-field orientation and alignment
NASA Astrophysics Data System (ADS)
Maan, Anjali; Ahlawat, Dharamvir Singh; Prasad, Vinod
2016-11-01
We present a theoretical study of the impact of a pair of moderate electric fields tilted an angle with respect to one another on a molecule. As a prototype, we consider a molecule with large rotational constant (with corresponding small rotational period) and moderate dipole moment. Within rigid-rotor approximation, the time-dependent Schrodinger equation is solved using fourth-order Runge-Kutta method. We have analysed that lower rotational states are significantly influenced by variation in pulse durations, the tilt angle between the fields and also on the electric field strengths. We also suggest a control scheme of how the rotational dynamics, orientation and alignment of a molecule can be enhanced by a combination of near-adiabatic pulses in comparision to non-adiabatic or adiabatic pulses.
Eigenfunction-expansion method for solving the quantum-wire problem: Formulation
NASA Astrophysics Data System (ADS)
Baraff, G. A.; Gershoni, D.
1991-02-01
We present a method of formulating the multiband-envelope-function equations for a quantum structure whose internal interfaces are perpendicular planes. The method can be used for quantum wells, quantum wires, or quantum dots (one-, two-, or three-dimensional confinement of the electronic wave function), as well as for periodic repetitions (superlattices) of these elementary structures. The technique used is expansion of the multiband envelope functions in a Fourier series for each of the coordinates x, y, and z. Special attention is paid to formulating interface-matching conditions that impose Hermiticity on the resulting systems of equations. This demand leads to the usual condition that the normal component of the current must be continuous across each internal interface. The method we have devised is similar to the one used by Altarelli for the quantum-well problem in that it leads to a secular equation that is solved by diagonalizing an energy-independent matrix. It differs in that here, the envelope functions are expanded in smooth continuous functions using the same expansion coefficients in all regions of the structure. Using this method, one can now calculate the optical absorption, its frequency, and polarization dependence, with the same amount of detail that has previously been possible only for confinement in one dimension, namely, in the quantum well and one-dimensional superlattice.
Axial expansion methods for solution of the multi-dimensional neutron diffusion equation
Beaklini Filho, J.F.
1984-01-01
The feasibility and practical implementation of axial expansion methods for the solution of the multi-dimensional multigroup neutron diffusion (MGD) equations is investigated. The theoretical examination which is applicable to the general MGD equations in arbitrary geometry includes the derivation of a new weak (reduced) form of the MGD equations by expanding the axial component of the neutron flux in a series of known trial functions and utilizing the Galerkin weighting. A general two-group albedo boundary condition is included in the weak form as a natural boundary condition. The application of different types of trial functions is presented.
NASA Astrophysics Data System (ADS)
Huang, Qing; Wang, Li-Zhen; Zuo, Su-Li
2016-02-01
In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada-Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed. Supported by the National Natural Science Foundation of China under Grant Nos. 11101332, 11201371, 11371293 and the Natural Science Foundation of Shaanxi Province under Grant No. 2015JM1037
Rapid maxillary expansion effects: An alternative assessment method by means of cone-beam tomography
Melgaço, Camilo Aquino; Columbano, José; Jurach, Estela Maris; Nojima, Matilde da Cunha Gonçalves; Sant'Anna, Eduardo Franzotti; Nojima, Lincoln Issamu
2014-01-01
INTRODUCTION: This study aims to develop a method to assess the changes in palatal and lingual cross-sectional areas in patients submitted to rapid maxillary expansion (RME). METHODS: The sample comprised 31 Class I malocclusion individuals submitted to RME and divided into two groups treated with Haas (17 patients) and Hyrax (14 patients) expanders. Cone-beam computed tomography scans were acquired at T0 (before expansion ) and T1 (six months after screw stabilization). Maxillary and mandibular cross-sectional areas were assessed at first permanent molars and first premolars regions and compared at T0 and T1. Mandibular occlusal area was also analyzed. RESULTS: Maxillary cross-sectional areas increased in 56.18 mm2 and 44.32 mm2 for the posterior and anterior regions. These values were smaller for the mandible, representing augmentation of 40.32 mm2 and 39.91 mm2 for posterior and anterior sections. No differences were found when comparing both expanders. Mandibular occlusal area increased 43.99mm2 and mandibular incisors proclined. Increments of 1.74 mm and 1.7 mm occurred in mandibular intermolar and interpremolar distances. These same distances presented increments of 5.5 mm and 5.57 mm for the maxillary arch. CONCLUSION: Occlusal and cross-sectional areas increased significantly after RME. The method described seems to be reliable and precise to assess intraoral area changes. PMID:25715721
Adiabatic rotation, quantum search, and preparation of superposition states
NASA Astrophysics Data System (ADS)
Siu, M. Stewart
2007-06-01
We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied “straight line” adiabatic evolution. In ways that complement recent results, we show how to efficiently prepare three types of states: Kitaev’s toric code state, the cluster state of the measurement-based computation model, and the history state used in the adiabatic simulation of a quantum circuit. We also show that the method, when adapted for quantum search, provides quadratic speedup as other optimal methods do with the advantages that the problem Hamiltonian is time independent and that the energy gap above the ground state is strictly nondecreasing with time. Likewise the method can be used for optimization as an alternative to the standard adiabatic algorithm.
Method for fabricating an ultra-low expansion mask blank having a crystalline silicon layer
Cardinale, Gregory F.
2002-01-01
A method for fabricating masks for extreme ultraviolet lithography (EUVL) using Ultra-Low Expansion (ULE) substrates and crystalline silicon. ULE substrates are required for the necessary thermal management in EUVL mask blanks, and defect detection and classification have been obtained using crystalline silicon substrate materials. Thus, this method provides the advantages for both the ULE substrate and the crystalline silicon in an Extreme Ultra-Violet (EUV) mask blank. The method is carried out by bonding a crystalline silicon wafer or member to a ULE wafer or substrate and thinning the silicon to produce a 5-10 .mu.m thick crystalline silicon layer on the surface of the ULE substrate. The thinning of the crystalline silicon may be carried out, for example, by chemical mechanical polishing and if necessary or desired, oxidizing the silicon followed by etching to the desired thickness of the silicon.
A spectral element method for fluid dynamics - Laminar flow in a channel expansion
NASA Technical Reports Server (NTRS)
Patera, A. T.
1984-01-01
A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.
Time-domain incident-field extrapolation technique based on the singularity-expansion method
Klaasen, J.J.
1991-05-01
In this report, a method presented to extrapolate measurements from Nuclear Electromagnetic Pulse (NEMP) assessments directly in the time domain. This method is based on a time-domain extrapolation function which is obtained from the Singularity Expansion Method representation of the measured incident field of the NEMP simulator. Once the time-domain extrapolation function is determined, the responses recorded during an assessment can be extrapolated simply by convolving them with the time domain extrapolation function. It is found that to obtain useful extrapolated responses, the incident field measurements needs to be made minimum phase; otherwise unbounded results can be obtained. Results obtained with this technique are presented, using data from actual assessments.
Borgia, Alessandro; Zheng, Wenwei; Buholzer, Karin; Borgia, Madeleine B; Schüler, Anja; Hofmann, Hagen; Soranno, Andrea; Nettels, Daniel; Gast, Klaus; Grishaev, Alexander; Best, Robert B; Schuler, Benjamin
2016-09-14
There has been a long-standing controversy regarding the effect of chemical denaturants on the dimensions of unfolded and intrinsically disordered proteins: A wide range of experimental techniques suggest that polypeptide chains expand with increasing denaturant concentration, but several studies using small-angle X-ray scattering (SAXS) have reported no such increase of the radius of gyration (Rg). This inconsistency challenges our current understanding of the mechanism of chemical denaturants, which are widely employed to investigate protein folding and stability. Here, we use a combination of single-molecule Förster resonance energy transfer (FRET), SAXS, dynamic light scattering (DLS), and two-focus fluorescence correlation spectroscopy (2f-FCS) to characterize the denaturant dependence of the unfolded state of the spectrin domain R17 and the intrinsically disordered protein ACTR in two different denaturants. Standard analysis of the primary data clearly indicates an expansion of the unfolded state with increasing denaturant concentration irrespective of the protein, denaturant, or experimental method used. This is the first case in which SAXS and FRET have yielded even qualitatively consistent results regarding expansion in denaturant when applied to the same proteins. To more directly illustrate this self-consistency, we used both SAXS and FRET data in a Bayesian procedure to refine structural ensembles representative of the observed unfolded state. This analysis demonstrates that both of these experimental probes are compatible with a common ensemble of protein configurations for each denaturant concentration. Furthermore, the resulting ensembles reproduce the trend of increasing hydrodynamic radius with denaturant concentration obtained by 2f-FCS and DLS. We were thus able to reconcile the results from all four experimental techniques quantitatively, to obtain a comprehensive structural picture of denaturant-induced unfolded state expansion, and to
The use of many-body expansions and geometry optimizations in fragment-based methods.
Fedorov, Dmitri G; Asada, Naoya; Nakanishi, Isao; Kitaura, Kazuo
2014-09-16
Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a
SU-E-J-221: A Novel Expansion Method for MRI Based Target Delineation in Prostate Radiotherapy
Ruiz, B; Feng, Y; Shores, R; Fung, C
2015-06-15
Purpose: To compare a novel bladder/rectum carveout expansion method on MRI delineated prostate to standard CT and expansion based methods for maintaining prostate coverage while providing superior bladder and rectal sparing. Methods: Ten prostate cases were planned to include four trials: MRI vs CT delineated prostate/proximal seminal vesicles, and each image modality compared to both standard expansions (8mm 3D expansion and 5mm posterior, i.e. ∼8mm) and carveout method expansions (5mm 3D expansion, 4mm posterior for GTV-CTV excluding expansion into bladder/rectum followed by additional 5mm 3D expansion to PTV, i.e. ∼1cm). All trials were planned to total dose 7920 cGy via IMRT. Evaluation and comparison was made using the following criteria: QUANTEC constraints for bladder/rectum including analysis of low dose regions, changes in PTV volume, total control points, and maximum hot spot. Results: ∼8mm MRI expansion consistently produced the most optimal plan with lowest total control points and best bladder/rectum sparing. However, this scheme had the smallest prostate (average 22.9% reduction) and subsequent PTV volume, consistent with prior literature. ∼1cm MRI had an average PTV volume comparable to ∼8mm CT at 3.79% difference. Bladder QUANTEC constraints were on average less for the ∼1cm MRI as compared to the ∼8mm CT and observed as statistically significant with 2.64% reduction in V65. Rectal constraints appeared to follow the same trend. Case-by-case analysis showed variation in rectal V30 with MRI delineated prostate being most favorable regardless of expansion type. ∼1cm MRI and ∼8mm CT had comparable plan quality. Conclusion: MRI delineated prostate with standard expansions had the smallest PTV leading to margins that may be too tight. Bladder/rectum carveout expansion method on MRI delineated prostate was found to be superior to standard CT based methods in terms of bladder and rectal sparing while maintaining prostate coverage
Edee, Kofi; Guizal, Brahim
2013-04-01
In this paper we present an extension of the modal method by Gegenbauer expansion (MMGE) [J. Opt. Soc. Am. A28, 2006 (2011)], [Progress Electromagn. Res.133, 17 (2013)] to the study of nonperiodic problems. The nonperiodicity is introduced through the perfectly matched layers (PMLs) concept, which can be introduced in an equivalent way either by a change of coordinates or by the use of a uniaxial anisotropic medium. These PMLs can generate strong irregularities of the electromagnetic fields that can significantly alter the convergence and stability of the numerical scheme. This is the case, e.g., for the famous Fourier modal method, especially when using complex stretching coordinates. In this work, it will be shown that the MMGE equipped with PMLs is a robust approach because of its natural immunity against spurious modes. PMID:23595322
Pole positions and residues from pion photoproduction using the Laurent-Pietarinen expansion method
NASA Astrophysics Data System (ADS)
Švarc, Alfred; Hadžimehmedović, Mirza; Osmanović, Hedim; Stahov, Jugoslav; Tiator, Lothar; Workman, Ron L.
2014-06-01
We applied a new approach to determine the pole positions and residues from pion photoproduction multipoles. The method is based on a Laurent expansion of the partial-wave T matrices, with a Pietarinen series representing the regular part of energy-dependent and single-energy photoproduction solutions. The method is applied to multipole fits generated by the MAID and George Washington University SAID (GWU-SAID) groups. We show that the number and properties of poles extracted from photoproduction data correspond very well to results from πN elastic data and values cited by the Particle Data Group (PDG). The photoproduction residues provide new information for the electromagnetic current at the pole position, which are independent of background parametrizations, which is not the case for the Breit-Wigner representation. Finally, we present the photodecay amplitudes from the current MAID and SAID solutions at the pole for all four-star nucleon resonances below W =2 GeV.
Calculation of Coherent Synchrotron Radiation Impedance Using the Mode Expansion Method
Stupakov, G.V.; Kotelnikov, I.A.; /Novosibirsk, IYF
2009-12-09
We study an impedance due to coherent synchrotron radiation (CSR) generated by a short bunch of charged particles passing through a dipole magnet of finite length in a vacuum chamber of a given cross section. In our method we decompose the electromagnetic field of the beam over the eigenmodes of the toroidal chamber and derive a system of equations for the expansion coefficients in the series. The general method is further specialized for a toroidal vacuum chamber of a rectangular cross section where the eigenmodes can be computed analytically. We also develop a computer code that calculates the CSR impedance for a toroid of rectangular cross section. Numerical results obtained with the code are presented in the paper.
An operator expansion method for computing nonlinear surface waves on a ferrofluid jet
NASA Astrophysics Data System (ADS)
Guyenne, Philippe; Părău, Emilian I.
2016-09-01
We present a new numerical method to simulate the time evolution of axisymmetric nonlinear waves on the surface of a ferrofluid jet. It is based on the reduction of this problem to a lower-dimensional computation involving surface variables alone. To do so, we describe the associated Dirichlet-Neumann operator in terms of a Taylor series expansion where each term can be efficiently computed by a pseudo-spectral scheme using the fast Fourier transform. We show detailed numerical tests on the convergence of this operator and, to illustrate the performance of our method, we simulate the long-time propagation and pairwise collisions of axisymmetric solitary waves. Both depression and elevation waves are examined by varying the magnetic field. Comparisons with weakly nonlinear predictions are also provided.
Zhang, Yongliang; Chen, Yu; Li, David Day-Uei
2016-06-27
Fast deconvolution is an essential step to calibrate instrument responses in big fluorescence lifetime imaging microscopy (FLIM) image analysis. This paper examined a computationally effective least squares deconvolution method based on Laguerre expansion (LSD-LE), recently developed for clinical diagnosis applications, and proposed new criteria for selecting Laguerre basis functions (LBFs) without considering the mutual orthonormalities between LBFs. Compared with the previously reported LSD-LE, the improved LSD-LE allows to use a higher laser repetition rate, reducing the acquisition time per measurement. Moreover, we extended it, for the first time, to analyze bi-exponential fluorescence decays for more general FLIM-FRET applications. The proposed method was tested on both synthesized bi-exponential and realistic FLIM data for studying the endocytosis of gold nanorods in Hek293 cells. Compared with the previously reported constrained LSD-LE, it shows promising results. PMID:27410552
Quantum Adiabatic Algorithms and Large Spin Tunnelling
NASA Technical Reports Server (NTRS)
Boulatov, A.; Smelyanskiy, V. N.
2003-01-01
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.
Nishimoto, Yoshio
2015-09-01
We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well. PMID:26342360
Nishimoto, Yoshio
2015-09-07
We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.
Quantum adiabatic evolution with energy degeneracy levels
NASA Astrophysics Data System (ADS)
Zhang, Qi
2016-01-01
A classical-kind phase-space formalism is developed to address the tiny intrinsic dynamical deviation from what is predicted by Wilczek-Zee theorem during quantum adiabatic evolution on degeneracy levels. In this formalism, the Hilbert space and the aggregate of degenerate eigenstates become the classical-kind phase space and a high-dimensional subspace in the phase space, respectively. Compared with the previous analogous study by a different method, the current result is qualitatively different in that the first-order deviation derived here is always perpendicular to the degeneracy subspace. A tripod-scheme Hamiltonian with two degenerate dark states is employed to illustrate the adiabatic deviation with degeneracy levels.
Adiabatic quantum optimization for associative memory recall
Seddiqi, Hadayat; Humble, Travis S.
2014-12-22
Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO). Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are stored in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.
Adiabatic quantum optimization for associative memory recall
Seddiqi, Hadayat; Humble, Travis S.
2014-12-22
Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO). Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are storedmore » in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.« less
Stirling engine with one adiabatic cylinder
NASA Astrophysics Data System (ADS)
West, C. D.
1982-03-01
It is shown that integration around the P-V loop of a Stirling-like cycle with an adiabatic expansion or compression space is possible through careful application of the ideal gas laws. The result is a set of closed-form solutions or the work output, work input, and efficiency for ideal gases. Previous analyses yielded closed-form solutions only for machines in which all spaces behave isothermally, or that have other limitations that simplify the arithmetic but omit important aspects of real machines. The results of this analysis, although still far removed from the exact behavior of real, practical engines, yield important insights into the effects observed in computer models and experimental machines. These results are especially illuminating for machines intended to operate with fairly small temperature differences. Heat pumps and low-technology solar-powered engines might be included in this category.
Fast quasi-adiabatic gas cooling: an experiment revisited
NASA Astrophysics Data System (ADS)
Oss, S.; Gratton, L. M.; Calzà, G.; López-Arias, T.
2012-09-01
The well-known experiment of the rapid expansion and cooling of the air contained in a bottle is performed with a rapidly responsive, yet very cheap thermometer. The adiabatic, low temperature limit is approached quite closely and measured with our apparatus. A straightforward theoretical model for this process is also presented and discussed. Both the experimental setup and the associated theoretical interpretation of the cooling phenomenon are suited for a standard general physics course at undergraduate level.
Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings.
Edee, Kofi
2011-10-01
A first approach of a modal method by Gegenbauer polynomial expansion (MMGE1) is presented for a plane wave diffraction by a lamellar grating. Modal methods are among the most popular methods that are used to solve the problem of lamellar gratings. They consist in describing the electromagnetic field in terms of eigenfunctions and eigenvalues of an operator. In the particular case of the Fourier modal method (FMM), the eigenfunctions are approximated by a finite Fourier sum, and this approximation can lead to a poor convergence of the FMM. The Wilbraham-Gibbs phenomenon may be one of the reasons for this poor convergence. Thus, it is interesting to investigate other basis functions that may represent the fields more accurately. The approach proposed in this paper consists in subdividing the pattern in homogeneous layers, according to the periodicity axis. The field is expanded, in each layer, on the basis of Gegenbauer's polynomials. Boundary conditions are rigorously written between adjacent layers; thus, an eigenvalue equation is obtained. The approach presented in this paper proves to describe the fields accurately. Finally, it is demonstrated that the results obtained with the MMGE1 are more accurate than several existing modal methods, such as the classical and the parametric FMM.
Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings.
Edee, Kofi
2011-10-01
A first approach of a modal method by Gegenbauer polynomial expansion (MMGE1) is presented for a plane wave diffraction by a lamellar grating. Modal methods are among the most popular methods that are used to solve the problem of lamellar gratings. They consist in describing the electromagnetic field in terms of eigenfunctions and eigenvalues of an operator. In the particular case of the Fourier modal method (FMM), the eigenfunctions are approximated by a finite Fourier sum, and this approximation can lead to a poor convergence of the FMM. The Wilbraham-Gibbs phenomenon may be one of the reasons for this poor convergence. Thus, it is interesting to investigate other basis functions that may represent the fields more accurately. The approach proposed in this paper consists in subdividing the pattern in homogeneous layers, according to the periodicity axis. The field is expanded, in each layer, on the basis of Gegenbauer's polynomials. Boundary conditions are rigorously written between adjacent layers; thus, an eigenvalue equation is obtained. The approach presented in this paper proves to describe the fields accurately. Finally, it is demonstrated that the results obtained with the MMGE1 are more accurate than several existing modal methods, such as the classical and the parametric FMM. PMID:21979505
Olsen, Jeppe
2014-07-21
A novel algorithm is introduced for the transformation of wave functions between the bases of Slater determinants (SD) and configuration state functions (CSF) in the genealogical coupling scheme. By modifying the expansion coefficients as each electron is spin-coupled, rather than performing a single many-electron transformation, the large transformation matrix that plagues previous approaches is avoided and the required number of operations is drastically reduced. As an example of the efficiency of the algorithm, the transformation for a configuration with 30 unpaired electrons and singlet spin is discussed. For this case, the 10 × 10{sup 6} coefficients in the CSF basis is obtained from the 150 × 10{sup 6} coefficients in the SD basis in 1 min, which should be compared with the seven years that the previously employed method is estimated to require.
Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.
Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko
2014-04-01
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials.
Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.
Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko
2014-04-01
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials. PMID:24827360
Orr, Leigh-Ann; Mulholland, Anthony J; O'Leary, Richard L; Hayward, Gordon
2008-12-01
Periodic composite ultrasonic transducers offer many advantages but the periodic pillar architecture can give rise to unwanted modes of vibration which interfere with the piston like motion of the fundamental thickness mode. In this paper, viscoelastic loss is incorporated into a three-dimensional plane wave expansion model (PWE) of these transducers. A comparison with experimental and finite element data is conducted and a design to damp out these lateral modes is investigated. Scaling and regularisation techniques are introduced to the PWE method to reduce ill-conditioning in the large matrices which can arise. The identification of the modes of vibration is aided by examining profiles of the displacements, electrical potential and Poynting vector. The dispersive behaviour of a 2-2 composite transducer with high shear attenuation in the passive phase is examined. The model shows that the use of a high shear attenuation filler material improves the frequency band gap surrounding the fundamental thickness mode.
Error analysis of the quadratic nodal expansion method in slab geometry
Penland, R.C.; Turinsky, P.J.; Azmy, Y.Y.
1994-10-01
As part of an effort to develop an adaptive mesh refinement strategy for use in state-of-the-art nodal diffusion codes, the authors derive error bounds on the solution variables of the quadratic Nodal Expansion Method (NEM) in slab geometry. Closure of the system is obtained through flux discontinuity relationships and boundary conditions. In order to verify the analysis presented, the authors compare the quadratic NEM to the analytic solution of a test problem. The test problem for this investigation is a one-dimensional slab [0,20cm] with L{sup 2} = 6.495cm{sup 2} and D = 0.1429cm. The slab has a unit neutron source distributed uniformly throughout and zero flux boundary conditions. The analytic solution to this problem is used to compute the node-average fluxes over a variety of meshes, and these are used to compute the NEM maximum error on each mesh.
NASA Astrophysics Data System (ADS)
Tang, Chen; Zhang, Junjiang; Sun, Chen; Su, Yonggang; Su, Kai Leung
2015-05-01
Nuclear graphite has been widely used as moderating and reflecting materials. However, due to severe neutron irradiation under high temperature, nuclear graphite is prone to deteriorate, resulting in massive microscopic flaws and even cracks under large stress in the later period of its service life. It is indispensable, therefore, to understand the fracture behavior of nuclear graphite to provide reference to structural integrity and safety analysis of nuclear graphite members in reactors. In this paper, we investigated the fracture expansion in nuclear graphite based on PDE image processing methods. We used the second-order oriented partial differential equations filtering model (SOOPDE) to denoise speckle noise, then used the oriented gradient vector fields for to obtain skeletons. The full-field displacement of fractured nuclear graphite and the location of the crack tip were lastly measured under various loading conditions.
Introducing the Pietarinen expansion method into the single-channel pole extraction problem
NASA Astrophysics Data System (ADS)
Švarc, Alfred; Hadžimehmedović, Mirza; Osmanović, Hedim; Stahov, Jugoslav; Tiator, Lothar; Workman, Ron L.
2013-09-01
We present a new approach to quantifying pole parameters of single-channel processes based on a Laurent expansion of partial-wave T matrices in the vicinity of the real axis. Instead of using the conventional power-series description of the nonsingular part of the Laurent expansion, we represent this part by a convergent series of Pietarinen functions. As the analytic structure of the nonsingular part is usually very well known (physical cuts with branch points at inelastic thresholds, and unphysical cuts in the negative energy plane), we find that one Pietarinen series per cut represents the analytic structure fairly reliably. The number of terms in each Pietarinen series is determined by the quality of the fit. The method is tested in two ways: on a toy model constructed from two known poles, various background terms, and two physical cuts, and on several sets of realistic πN elastic energy-dependent partial-wave amplitudes (GWU/SAID [Arndt , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.74.045205 74, 045205 (2006); Workman , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.86.035202 86, 035202 (2012)], and Dubna-Mainz-Taipei [Chen , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.76.035206 76, 035206 (2007); Tiator , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.82.055203 82, 055203 (2010)]). We show that the method is robust and confident using up to three Pietarinen series, and is particularly convenient in fits to amplitudes, such as single-energy solutions, coming more directly from experiment: cases where the analytic structure of the regular part is a priori unknown.
Comparing regression methods for the two-stage clonal expansion model of carcinogenesis.
Kaiser, J C; Heidenreich, W F
2004-11-15
In the statistical analysis of cohort data with risk estimation models, both Poisson and individual likelihood regressions are widely used methods of parameter estimation. In this paper, their performance has been tested with the biologically motivated two-stage clonal expansion (TSCE) model of carcinogenesis. To exclude inevitable uncertainties of existing data, cohorts with simple individual exposure history have been created by Monte Carlo simulation. To generate some similar properties of atomic bomb survivors and radon-exposed mine workers, both acute and protracted exposure patterns have been generated. Then the capacity of the two regression methods has been compared to retrieve a priori known model parameters from the simulated cohort data. For simple models with smooth hazard functions, the parameter estimates from both methods come close to their true values. However, for models with strongly discontinuous functions which are generated by the cell mutation process of transformation, the Poisson regression method fails to produce reliable estimates. This behaviour is explained by the construction of class averages during data stratification. Thereby, some indispensable information on the individual exposure history was destroyed. It could not be repaired by countermeasures such as the refinement of Poisson classes or a more adequate choice of Poisson groups. Although this choice might still exist we were unable to discover it. In contrast to this, the individual likelihood regression technique was found to work reliably for all considered versions of the TSCE model. PMID:15490436
Lesage, Jonathan C; Bond, Jill V; Sinclair, Anthony N
2014-09-01
The problem of elastic wave propagation in an infinite bar of arbitrary cross section is studied via a generalized version of the Fourier expansion collocation method. In the current formulation, the exact three dimensional solution to Navier's equation in cylindrical coordinates is used to obtain the boundary traction vector as a periodic, piecewise continuous/differentiable function of the angular coordinate. Traction free conditions are then met by setting the Fourier coefficients of the boundary traction vector to zero without approximating the bounding surface by multi-sided polygons as in the method presented by Nagaya. The method is derived for a general cross section with no axial planes of symmetry. Using the general formulation it is shown that the symmetric and asymmetric modes decouple for cross sections having one axial plane of symmetry. An efficient algorithm for computing dispersion curves based on the current method is presented and used to obtain the fundamental longitudinal and flexural wave speeds for a bar of elliptical cross section. The results are compared to those obtained by previous researchers using exact and approximate treatments.
Adiabatic computation: A toy model
NASA Astrophysics Data System (ADS)
Ribeiro, Pedro; Mosseri, Rémy
2006-10-01
We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter s and the α parameter, which emulates many-variable constraints in the classical computational problem. The proposed model presents, in the s-α plane, a line of first-order quantum phase transition that ends at a second-order point. The relation between computation complexity and the occurrence of quantum phase transitions is discussed. We analyze the behavior of the ground and first excited states near the quantum phase transition, the gap, and the entanglement content of the ground state.
Adiabatic computation: A toy model
Ribeiro, Pedro; Mosseri, Remy
2006-10-15
We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter s and the {alpha} parameter, which emulates many-variable constraints in the classical computational problem. The proposed model presents, in the s-{alpha} plane, a line of first-order quantum phase transition that ends at a second-order point. The relation between computation complexity and the occurrence of quantum phase transitions is discussed. We analyze the behavior of the ground and first excited states near the quantum phase transition, the gap, and the entanglement content of the ground state.
Adiabatic evolution of plasma equilibrium
Grad, H.; Hu, P. N.; Stevens, D. C.
1975-01-01
A new theory of plasma equilibrium is introduced in which adiabatic constraints are specified. This leads to a mathematically nonstandard structure, as compared to the usual equilibrium theory, in which prescription of pressure and current profiles leads to an elliptic partial differential equation. Topologically complex configurations require further generalization of the concept of adiabaticity to allow irreversible mixing of plasma and magnetic flux among islands. Matching conditions across a boundary layer at the separatrix are obtained from appropriate conservation laws. Applications are made to configurations with planned islands (as in Doublet) and accidental islands (as in Tokamaks). Two-dimensional, axially symmetric, helically symmetric, and closed line equilibria are included. PMID:16578729
Sever, Martin; Krč, Janez; Čampa, Andrej; Topič, Marko
2015-11-30
Finite element method is coupled with Huygens' expansion to determine light intensity distribution of scattered light in solar cells and other optoelectronic devices. The rigorous foundation of the modelling enables calculation of the light intensity distribution at a chosen distance and surface of observation in chosen material in reflection or in transmission for given wavelength of the incident light. The calculation of scattering or anti-reflection properties is not limited to a single textured interface, but can be done above more complex structures with several scattering interfaces or even with particles involved. Both scattering at periodic and at random textures can be efficiently handled with the modelling approach. A procedure for minimisation of the effect of small-area sample, which is considered in the finite element method calculation, is proposed and implemented into the modelling. Angular distribution function, total transmission and total reflection of the scattering interface or structure can be determined using the model. Furthermore, a method for calculation of the haze parameter of reflected or transmitted light is proposed. The modelling approach is applied to periodic and random nano-textured samples for photovoltaic applications, showing good agreement with measured data. PMID:26698803
Plane wave expansion method used to engineer photonic crystal sensors with high efficiency.
Antos, Roman; Vozda, Vojtech; Veis, Martin
2014-02-10
A photonic crystal waveguide (PhC-WG) was reported to be usable as an optical sensor highly sensitive to various material parameters, which can be detected via changes in transmission through the PhC-WG caused by small changes of the refractive index of the medium filling its holes. To monitor these changes accurately, a precise optical model is required, for which the plane wave expansion (PWE) method is convenient. We here demonstrate the revision of the PWE method by employing the complex Fourier factorization approach, which enables the calculation of dispersion diagrams with fast convergence, i.e., with high precision in relatively short time. The PhC-WG is proposed as a line defect in a hexagonal array of cylindrical holes periodically arranged in bulk silicon, filled with a variable medium. The method of monitoring the refractive index changes is based on observing cutoff wavelengths in the PhC-WG dispersion diagrams. The PWE results are also compared with finite-difference time-domain calculations of transmittance carried out on a PhC-WG with finite dimensions. PMID:24663549
Sever, Martin; Krč, Janez; Čampa, Andrej; Topič, Marko
2015-11-30
Finite element method is coupled with Huygens' expansion to determine light intensity distribution of scattered light in solar cells and other optoelectronic devices. The rigorous foundation of the modelling enables calculation of the light intensity distribution at a chosen distance and surface of observation in chosen material in reflection or in transmission for given wavelength of the incident light. The calculation of scattering or anti-reflection properties is not limited to a single textured interface, but can be done above more complex structures with several scattering interfaces or even with particles involved. Both scattering at periodic and at random textures can be efficiently handled with the modelling approach. A procedure for minimisation of the effect of small-area sample, which is considered in the finite element method calculation, is proposed and implemented into the modelling. Angular distribution function, total transmission and total reflection of the scattering interface or structure can be determined using the model. Furthermore, a method for calculation of the haze parameter of reflected or transmitted light is proposed. The modelling approach is applied to periodic and random nano-textured samples for photovoltaic applications, showing good agreement with measured data.
Plane wave expansion method used to engineer photonic crystal sensors with high efficiency.
Antos, Roman; Vozda, Vojtech; Veis, Martin
2014-02-10
A photonic crystal waveguide (PhC-WG) was reported to be usable as an optical sensor highly sensitive to various material parameters, which can be detected via changes in transmission through the PhC-WG caused by small changes of the refractive index of the medium filling its holes. To monitor these changes accurately, a precise optical model is required, for which the plane wave expansion (PWE) method is convenient. We here demonstrate the revision of the PWE method by employing the complex Fourier factorization approach, which enables the calculation of dispersion diagrams with fast convergence, i.e., with high precision in relatively short time. The PhC-WG is proposed as a line defect in a hexagonal array of cylindrical holes periodically arranged in bulk silicon, filled with a variable medium. The method of monitoring the refractive index changes is based on observing cutoff wavelengths in the PhC-WG dispersion diagrams. The PWE results are also compared with finite-difference time-domain calculations of transmittance carried out on a PhC-WG with finite dimensions.
He, Yuejing; Chen, Xuanyang
2014-01-01
Compared with coupled-mode theory (CMT), which is widely used for studies involving optical fiber Bragg gratings (FBGs), the proposed investigation scheme is visualized, diagrammatic, and simple. This method combines the finite element method (FEM) and eigenmode expansion method (EEM). The function of the FEM is to calculate all guided modes that match the boundary conditions of optical fiber waveguides. Moreover, the FEM is used for implementing power propagation for HE11 in optical fiber devices. How the periodic characteristic of FBG causes this novel scheme to be substantially superior to CMT is explained in detail. Regarding current numerical calculation techniques, the scheme proposed in this paper is the only method capable of the 3D design and analysis of large periodic components. Additionally, unlike CMT, in which deviations exist between the designed wavelength λD and the maximal reflection wavelength λmax, the proposed method performs rapid scans of the periods of optical FBG. Therefore, once the operating wavelength is set for the component design, the maximal reflection wavelength of the final products can be accurately limited to that of the original design, such as λ = 1550 nm. Furthermore, a comparison between the period scan plot and the optical spectra plot for FBG indicated an inverse relationship between the periods and wavelengths. Consequently, this property can be used to predict the final FBG spectra before implementing time-consuming calculations. By employing this novel investigation scheme involving a rigorous design procedure, the graphical and simple calculation method reduces the studying time and professional expertise required for researching and applying optical FBG. PMID:24949643
Use of advanced particle methods in modeling space propulsion and its supersonic expansions
NASA Astrophysics Data System (ADS)
Borner, Arnaud
This research discusses the use of advanced kinetic particle methods such as Molecular Dynamics (MD) and direct simulation Monte Carlo (DSMC) to model space propulsion systems such as electrospray thrusters and their supersonic expansions. MD simulations are performed to model an electrospray thruster for the ionic liquid (IL) EMIM--BF4 using coarse-grained (CG) potentials. The model is initially featuring a constant electric field applied in the longitudinal direction. Two coarse-grained potentials are compared, and the effective-force CG (EFCG) potential is found to predict the formation of the Taylor cone, the cone-jet, and other extrusion modes for similar electric fields and mass flow rates observed in experiments of a IL fed capillary-tip-extractor system better than the simple CG potential. Later, one-dimensional and fully transient three-dimensional electric fields, the latter solving Poisson's equation to take into account the electric field due to space charge at each timestep, are computed by coupling the MD model to a Poisson solver. It is found that the inhomogeneous electric field as well as that of the IL space-charge improve agreement between modeling and experiment. The boundary conditions (BCs) are found to have a substantial impact on the potential and electric field, and the tip BC is introduced and compared to the two previous BCs, named plate and needle, showing good improvement by reducing unrealistically high radial electric fields generated in the vicinity of the capillary tip. The influence of the different boundary condition models on charged species currents as a function of the mass flow rate is studied, and it is found that a constant electric field model gives similar agreement to the more rigorous and computationally expensive tip boundary condition at lower flow rates. However, at higher mass flow rates the MD simulations with the constant electric field produces extruded particles with higher Coulomb energy per ion, consistent with
NASA Astrophysics Data System (ADS)
Zhou, S.; Solana, J. R.
2014-12-01
In this paper, it is shown that the numerical differentiation method in performing the coupling parameter series expansion [S. Zhou, J. Chem. Phys. 125, 144518 (2006); AIP Adv. 1, 040703 (2011)] excels at calculating the coefficients ai of hard sphere high temperature series expansion (HS-HTSE) of the free energy. Both canonical ensemble and isothermal-isobaric ensemble Monte Carlo simulations for fluid interacting through a hard sphere attractive Yukawa (HSAY) potential with extremely short ranges and at very low temperatures are performed, and the resulting two sets of data of thermodynamic properties are in excellent agreement with each other, and well qualified to be used for assessing convergence of the HS-HTSE for the HSAY fluid. Results of valuation are that (i) by referring to the results of a hard sphere square well fluid [S. Zhou, J. Chem. Phys. 139, 124111 (2013)], it is found that existence of partial sum limit of the high temperature series expansion series and consistency between the limit value and the true solution depend on both the potential shapes and temperatures considered. (ii) For the extremely short range HSAY potential, the HS-HTSE coefficients ai falls rapidly with the order i, and the HS-HTSE converges from fourth order; however, it does not converge exactly to the true solution at reduced temperatures lower than 0.5, wherein difference between the partial sum limit of the HS-HTSE series and the simulation result tends to become more evident. Something worth mentioning is that before the convergence order is reached, the preceding truncation is always improved by the succeeding one, and the fourth- and higher-order truncations give the most dependable and qualitatively always correct thermodynamic results for the HSAY fluid even at low reduced temperatures to 0.25.
Zhou, S; Solana, J R
2014-12-28
In this paper, it is shown that the numerical differentiation method in performing the coupling parameter series expansion [S. Zhou, J. Chem. Phys. 125, 144518 (2006); AIP Adv. 1, 040703 (2011)] excels at calculating the coefficients ai of hard sphere high temperature series expansion (HS-HTSE) of the free energy. Both canonical ensemble and isothermal-isobaric ensemble Monte Carlo simulations for fluid interacting through a hard sphere attractive Yukawa (HSAY) potential with extremely short ranges and at very low temperatures are performed, and the resulting two sets of data of thermodynamic properties are in excellent agreement with each other, and well qualified to be used for assessing convergence of the HS-HTSE for the HSAY fluid. Results of valuation are that (i) by referring to the results of a hard sphere square well fluid [S. Zhou, J. Chem. Phys. 139, 124111 (2013)], it is found that existence of partial sum limit of the high temperature series expansion series and consistency between the limit value and the true solution depend on both the potential shapes and temperatures considered. (ii) For the extremely short range HSAY potential, the HS-HTSE coefficients ai falls rapidly with the order i, and the HS-HTSE converges from fourth order; however, it does not converge exactly to the true solution at reduced temperatures lower than 0.5, wherein difference between the partial sum limit of the HS-HTSE series and the simulation result tends to become more evident. Something worth mentioning is that before the convergence order is reached, the preceding truncation is always improved by the succeeding one, and the fourth- and higher-order truncations give the most dependable and qualitatively always correct thermodynamic results for the HSAY fluid even at low reduced temperatures to 0.25.
Zhou, S.; Solana, J. R.
2014-12-28
In this paper, it is shown that the numerical differentiation method in performing the coupling parameter series expansion [S. Zhou, J. Chem. Phys. 125, 144518 (2006); AIP Adv. 1, 040703 (2011)] excels at calculating the coefficients a{sub i} of hard sphere high temperature series expansion (HS-HTSE) of the free energy. Both canonical ensemble and isothermal-isobaric ensemble Monte Carlo simulations for fluid interacting through a hard sphere attractive Yukawa (HSAY) potential with extremely short ranges and at very low temperatures are performed, and the resulting two sets of data of thermodynamic properties are in excellent agreement with each other, and well qualified to be used for assessing convergence of the HS-HTSE for the HSAY fluid. Results of valuation are that (i) by referring to the results of a hard sphere square well fluid [S. Zhou, J. Chem. Phys. 139, 124111 (2013)], it is found that existence of partial sum limit of the high temperature series expansion series and consistency between the limit value and the true solution depend on both the potential shapes and temperatures considered. (ii) For the extremely short range HSAY potential, the HS-HTSE coefficients a{sub i} falls rapidly with the order i, and the HS-HTSE converges from fourth order; however, it does not converge exactly to the true solution at reduced temperatures lower than 0.5, wherein difference between the partial sum limit of the HS-HTSE series and the simulation result tends to become more evident. Something worth mentioning is that before the convergence order is reached, the preceding truncation is always improved by the succeeding one, and the fourth- and higher-order truncations give the most dependable and qualitatively always correct thermodynamic results for the HSAY fluid even at low reduced temperatures to 0.25.
Elementary examples of adiabatic invariance
NASA Astrophysics Data System (ADS)
Crawford, Frank S.
1990-04-01
Simple classical one-dimensional systems subject to adiabatic (gradual) perturbations are examined. The first examples are well known: the adiabatic invariance of the product Eτ of energy E and period τ for the simple pendulum and for the simple harmonic oscillator. Next, the adiabatic invariants of the vertical bouncer are found—a ball bouncing elastically from the floor of a rising elevator having slowly varying velocity and acceleration. These examples lead to consideration of adiabatic invariance for one-dimensional systems with potentials of the form V=axn, with a=a(t) slowly varying in time. Then, the horizontal bouncer is considered—a mass sliding on a smooth floor, bouncing back and forth between two impenetrable walls, one of which is slowly moving. This example is generalized to a particle in a bound state of a general potential with one slowly moving ``turning point.'' Finally, circular motion of a charged particle in a magnetic field slowly varying in time under three different configurations is considered: (a) a free particle in a uniform field; (b) a free particle in a nonuniform ``betatron'' field; and (c) a particle constrained to a circular orbit in a uniform field.
Pressure Oscillations in Adiabatic Compression
ERIC Educational Resources Information Center
Stout, Roland
2011-01-01
After finding Moloney and McGarvey's modified adiabatic compression apparatus, I decided to insert this experiment into my physical chemistry laboratory at the last minute, replacing a problematic experiment. With insufficient time to build the apparatus, we placed a bottle between two thick textbooks and compressed it with a third textbook forced…
Numerical divergence effects of equivalence theory in the nodal expansion method
Zika, M.R.; Downar, T.J. )
1993-11-01
Accurate solutions of the advanced nodal equations require the use of discontinuity factors (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. During the last several years, nodal equivalence theory (NET) has successfully been implemented for the Cartesian geometry and has received widespread acceptance in the light water reactor industry. The extension of NET to other reactor types has had limited success. Recent efforts to implement NET within the framework of the nodal expansion method have successfully been applied to the fast breeder reactor. However, attempts to apply the same methods to thermal reactors such as the Modular High-Temperature Gas Reactor (MHTGR) have led to numerical divergence problems that can be attributed directly to the magnitude of the DFs. In the work performed here, it was found that the numerical problems occur in the inner and upscatter iterations of the solution algorithm. These iterations use a Gauss-Seidel iterative technique that is always convergent for problems with unity DFs. However, for an MHTGR model that requires large DFs, both the inner and upscatter iterations were divergent. Initial investigations into methods for bounding the DFs have proven unsatisfactory as a means of remedying the convergence problems. Although the DFs could be bounded to yield a convergent solution, several cases were encountered where the resulting flux solution was less accurate than the solution without DFs. For the specific case of problems without upscattering, an alternate numerical method for the inner iteration, an LU decomposition, was identified and shown to be feasible.
NASA Astrophysics Data System (ADS)
Wu, Kun; Zhang, Feng; Min, Jinzhong; Yu, Qiu-Run; Wang, Xin-Yue; Ma, Leiming
2016-09-01
The adding method, which could calculate the infrared radiative transfer (IRT) in inhomogeneous atmosphere with multiple layers, has been applied to δ -four-stream discrete-ordinates method (DOM). This scheme is referred as δ -4DDA. However, there is a lack of application for adding method of δ -four-stream spherical harmonic expansion approximation (SHM) to solve infrared radiative transfer through multiple layers. In this paper, the adding method for δ -four-stream SHM (δ -4SDA) will be obtained and the accuracy of it will be evaluated as well. The result of δ -4SDA in an idealized medium with homogeneous optical property is significantly more accurate than that of the adding method for δ -two-stream DOM (δ -2DDA). The relative errors of δ -2DDA can be over 15% in thin optical depths for downward emissivity, while errors of δ -4SDA are bounded by 2%. However, the result of δ -4SDA is slightly less accurate than that of δ -4DDA. In a radiation model with realistic atmospheric profile considering gaseous transmission, the accuracy for heating rate of δ -4SDA is significantly superior than that of δ -2DDA, especially for the cloudy sky. The accuracy for heating rate of δ -4SDA is slightly less accurate than that of δ -4DDA under water cloud conditions, while it is superior than that of δ -4DDA in ice cloud cases. Beside, the computational efficiency of δ -4SDA is higher than that of δ -4DDA.
Improved generalized F-expansion method for the time fractional modified KdV(fmKdV) equation
NASA Astrophysics Data System (ADS)
Sonmezoglu, Abdullah
2016-06-01
In this article, an improved generalized F-expansion method is used for solving the time fractional modified KdV(fmKdV) equation. Using this approach new Jacobi elliptic function solutions are obtained. This method can be suitable for solving other nonlinear fractional differential equations.
Transitionless driving on adiabatic search algorithm
Oh, Sangchul; Kais, Sabre
2014-12-14
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.
Systematic synthesis of CCCCTA-based T-T filters using NAM expansion method
NASA Astrophysics Data System (ADS)
Li, Yongan; Cao, Rui
2016-06-01
In the light of nullor-mirror models for current-controlled current conveyor trans-conductance amplifier (CCCCTA), initiating the admittance matrices of the Tow-Thomas (T-T) filter, three different types of the T-T filter are synthesised by means of the nodal admittance matrix (NAM) expansion method. The type A filter, which employ one CCCCTA, one grounded resistor and two grounded capacitors, has eight different forms, the type B filter, which employ one CCCCTA, two grounded capacitors and a second-generation current-controlled conveyor (CCCII) or an second-generation inverting current-controlled conveyor (ICCCII) or an operational trans-conductance amplifier (OTA), has 64 different forms and the type C filter employing one CCCCTA and two grounded capacitors has eight different forms. In all, 80 voltage-mode/current-mode T-T filter circuits are obtained. Because of using canonic number components, the circuits are highly desirable from the viewpoint of IC fabrication and their parameters can be electronically tuned through tuning bias currents of CCCCTAs. The hand analysis and computer simulation results have been provided to support the synthesis method.
Failure of geometric electromagnetism in the adiabatic vector Kepler problem
Anglin, J.R.; Schmiedmayer, J.
2004-02-01
The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wire's magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher-order postadiabatic corrections make the orbits precess, but recent analysis of this 'vector Kepler problem' has shown that the effective Hamiltonian incorporating a postadiabatic scalar potential ('geometric electromagnetism') fails to predict the precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the postadiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a 1/r{sup 3} singularity which is an artifact of the adiabatic approximation.
Quantum back-reaction from non-adiabatic changes
NASA Astrophysics Data System (ADS)
Asplund, Curtis; Berenstein, David
2011-04-01
Motivated by the problem of thermalization in QFTs and the dual non-equilibrium BH dynamics, we examine a generic and non-trivial aspect of these phenomena, non-adiabatic changes, in a highly simplified setting. We consider a harmonic oscillator whose frequency depends on a second quantum variable x. Beginning with a classical analysis, we show how the system can be described by an improved adiabatic expansion with a velocity dependent force for x. We find an instability at a critical velocity beyond which the adiabatic (Born-Oppenheimer) approximation breaks down. We extend this calculation to the fully quantum system and to field theory and describe how to study fermions with similar techniques. Finally, we set up a model with an abrupt change in the oscillator whose quantum mechanics can be solved exactly so that one can study the effects of back-reaction of a fully non-adiabatic change in a controlled setting. We comment on applications of these general results to the physics of D-branes, inflation, and BHs in AdS/CFT.
Studies in Chaotic adiabatic dynamics
Jarzynski, C.
1994-01-01
Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the {open_quotes}goodness{close_quotes} of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees).
NASA Astrophysics Data System (ADS)
Bitter, Christopher; Mulligan, Gordon F.; Dall'Erba, Sandy
2007-04-01
Hedonic house price models typically impose a constant price structure on housing characteristics throughout an entire market area. However, there is increasing evidence that the marginal prices of many important attributes vary over space, especially within large markets. In this paper, we compare two approaches to examine spatial heterogeneity in housing attribute prices within the Tucson, Arizona housing market: the spatial expansion method and geographically weighted regression (GWR). Our results provide strong evidence that the marginal price of key housing characteristics varies over space. GWR outperforms the spatial expansion method in terms of explanatory power and predictive accuracy.
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
Zamstein, Noa; Tannor, David J.
2012-12-14
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schroedinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)]. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
From Free Expansion to Abrupt Compression of an Ideal Gas
ERIC Educational Resources Information Center
Anacleto, Joaquim; Pereira, Mario G.
2009-01-01
Using macroscopic thermodynamics, the general law for adiabatic processes carried out by an ideal gas was studied. It was shown that the process reversibility is characterized by the adiabatic reversibility coefficient r, in the range 0 [less than or equal] r [less than or equal] 1 for expansions and r [greater than or equal] 1 for compressions.…
Linear 3 and 5-step methods using Taylor series expansion for solving special 3rd order ODEs
NASA Astrophysics Data System (ADS)
Rajabi, Marzieh; Ismail, Fudziah; Senu, Norazak
2016-06-01
Some new linear 3 and 5-step methods for solving special third order ordinary differential equations directly are constructed using Taylor's series expansion. A set of test problems are solved using the new method and the results are compared when the problem is reduced to a system of first order ordinary differential equations and then using the existing Runge-Kutta method. The numerical results have clearly shown the advantage and competency of the new methods.
Shortcut to Adiabatic Passage in Two- and Three-Level Atoms
Chen Xi; Lizuain, I.; Muga, J. G.; Ruschhaupt, A.; Guery-Odelin, D.
2010-09-17
We propose a method to speed up adiabatic passage techniques in two-level and three-level atoms extending to the short-time domain their robustness with respect to parameter variations. It supplements or substitutes the standard laser beam setups with auxiliary pulses that steer the system along the adiabatic path. Compared to other strategies, such as composite pulses or the original adiabatic techniques, it provides a fast and robust approach to population control.
Uncovering compounds by synergy of cluster expansion and high-throughput methods.
Levy, Ohad; Hart, Gus L W; Curtarolo, Stefano
2010-04-01
Predicting from first-principles calculations whether mixed metallic elements phase-separate or form ordered structures is a major challenge of current materials research. It can be partially addressed in cases where experiments suggest the underlying lattice is conserved, using cluster expansion (CE) and a variety of exhaustive evaluation or genetic search algorithms. Evolutionary algorithms have been recently introduced to search for stable off-lattice structures at fixed mixture compositions. The general off-lattice problem is still unsolved. We present an integrated approach of CE and high-throughput ab initio calculations (HT) applicable to the full range of compositions in binary systems where the constituent elements or the intermediate ordered structures have different lattice types. The HT method replaces the search algorithms by direct calculation of a moderate number of naturally occurring prototypes representing all crystal systems and guides CE calculations of derivative structures. This synergy achieves the precision of the CE and the guiding strengths of the HT. Its application to poorly characterized binary Hf systems, believed to be phase-separating, defines three classes of alloys where CE and HT complement each other to uncover new ordered structures.
Shortcut to adiabaticity in spinor condensates
NASA Astrophysics Data System (ADS)
Sala, Arnau; Núñez, David López; Martorell, Joan; De Sarlo, Luigi; Zibold, Tilman; Gerbier, Fabrice; Polls, Artur; Juliá-Díaz, Bruno
2016-10-01
We devise a method to shortcut the adiabatic evolution of a spin-1 Bose gas with an external magnetic field as the control parameter. An initial many-body state with almost all bosons populating the Zeeman sublevel m =0 is evolved to a final state very close to a macroscopic spin-singlet condensate, a fragmented state with three macroscopically occupied Zeeman states. The shortcut protocol, obtained by an approximate mapping to a harmonic oscillator Hamiltonian, is compared to linear and exponential variations of the control parameter. We find a dramatic speedup of the dynamics when using the shortcut protocol.
On adiabatic perturbations in the ekpyrotic scenario
Linde, A.; Mukhanov, V.; Vikman, A. E-mail: Viatcheslav.Mukhanov@physik.uni-muenchen.de
2010-02-01
In a recent paper, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in Khoury are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario.
Cavity-state preparation using adiabatic transfer
NASA Astrophysics Data System (ADS)
Larson, Jonas; Andersson, Erika
2005-05-01
We show how to prepare a variety of cavity field states for multiple cavities. The state preparation technique used is related to the method of stimulated adiabatic Raman passage. The cavity modes are coupled by atoms, making it possible to transfer an arbitrary cavity field state from one cavity to another and also to prepare nontrivial cavity field states. In particular, we show how to prepare entangled states of two or more cavities, such as an Einstein-Podolsky-Rosen state and a W state, as well as various entangled superpositions of coherent states in different cavities, including Schrödinger cat states. The theoretical considerations are supported by numerical simulations.
An adiabatic demagnetization refrigerator for infrared bolometers
NASA Technical Reports Server (NTRS)
Britt, R. D.; Richards, P. L.
1981-01-01
Adiabatic demagnetization refrigerators have been built and installed in small portable liquid helium cryostats to test the feasibility of this method of cooling infrared bolometric detectors to temperatures below 0.3 K. Performance has been achieved which suggests that bolometer temperatures of 0.2 K can be maintained for periods of approximately 60 hours. Applications to sensitive infrared detection from ground-based telescopes and space satellites are discussed. Design data are given which permit the evaluation of refrigerator performance for a variety of design parameters.
Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas
Rohringer, W.; Fischer, D.; Steiner, F.; Mazets, I. E.; Schmiedmayer, J.; Trupke, M.
2015-01-01
We present experimental evidence for scale invariant behaviour of the excitation spectrum in phase-fluctuating quasi-1d Bose gases after a rapid change of the external trapping potential. Probing density correlations in free expansion, we find that the temperature of an initial thermal state scales with the spatial extension of the cloud as predicted by a model based on adiabatic rescaling of initial eigenmodes with conserved quasiparticle occupation numbers. Based on this result, we demonstrate that shortcuts to adiabaticity for the rapid expansion or compression of the gas do not induce additional heating. PMID:25867640
Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas
NASA Astrophysics Data System (ADS)
Rohringer, W.; Fischer, D.; Steiner, F.; Mazets, I. E.; Schmiedmayer, J.; Trupke, M.
2015-04-01
We present experimental evidence for scale invariant behaviour of the excitation spectrum in phase-fluctuating quasi-1d Bose gases after a rapid change of the external trapping potential. Probing density correlations in free expansion, we find that the temperature of an initial thermal state scales with the spatial extension of the cloud as predicted by a model based on adiabatic rescaling of initial eigenmodes with conserved quasiparticle occupation numbers. Based on this result, we demonstrate that shortcuts to adiabaticity for the rapid expansion or compression of the gas do not induce additional heating.
Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas.
Rohringer, W; Fischer, D; Steiner, F; Mazets, I E; Schmiedmayer, J; Trupke, M
2015-04-13
We present experimental evidence for scale invariant behaviour of the excitation spectrum in phase-fluctuating quasi-1d Bose gases after a rapid change of the external trapping potential. Probing density correlations in free expansion, we find that the temperature of an initial thermal state scales with the spatial extension of the cloud as predicted by a model based on adiabatic rescaling of initial eigenmodes with conserved quasiparticle occupation numbers. Based on this result, we demonstrate that shortcuts to adiabaticity for the rapid expansion or compression of the gas do not induce additional heating.
Design of a photonic lattice using shortcuts to adiabaticity
NASA Astrophysics Data System (ADS)
Stefanatos, Dionisis
2014-08-01
In this article we use the method of shortcuts to adiabaticity to design a photonic lattice (array of waveguides) which can drive the input light to a controlled location at the output. The output position in the array is determined by functions of the propagation distance along the waveguides, which modulate the lattice characteristics (index of refraction, and first- and second-neighbor couplings). The proposed coupler is expected to possess the robustness properties of the design method, coming from its adiabatic nature, and also to have a smaller footprint than purely adiabatic couplers. The present work provides a very interesting example where methods from quantum control can be exploited to design lattices with desired input-output properties.
Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space
NASA Astrophysics Data System (ADS)
An, Shuoming; Lv, Dingshun; Del Campo, Adolfo; Kim, Kihwan
2016-09-01
The application of adiabatic protocols in quantum technologies is severely limited by environmental sources of noise and decoherence. Shortcuts to adiabaticity by counterdiabatic driving constitute a powerful alternative that speed up time-evolution while mimicking adiabatic dynamics. Here we report the experimental implementation of counterdiabatic driving in a continuous variable system, a shortcut to the adiabatic transport of a trapped ion in phase space. The resulting dynamics is equivalent to a `fast-motion video' of the adiabatic trajectory. The robustness of this protocol is shown to surpass that of competing schemes based on classical local controls and Fourier optimization methods. Our results demonstrate that shortcuts to adiabaticity provide a robust speedup of quantum protocols of wide applicability in quantum technologies.
Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space
An, Shuoming; Lv, Dingshun; del Campo, Adolfo; Kim, Kihwan
2016-01-01
The application of adiabatic protocols in quantum technologies is severely limited by environmental sources of noise and decoherence. Shortcuts to adiabaticity by counterdiabatic driving constitute a powerful alternative that speed up time-evolution while mimicking adiabatic dynamics. Here we report the experimental implementation of counterdiabatic driving in a continuous variable system, a shortcut to the adiabatic transport of a trapped ion in phase space. The resulting dynamics is equivalent to a ‘fast-motion video' of the adiabatic trajectory. The robustness of this protocol is shown to surpass that of competing schemes based on classical local controls and Fourier optimization methods. Our results demonstrate that shortcuts to adiabaticity provide a robust speedup of quantum protocols of wide applicability in quantum technologies. PMID:27669897
Favorite, J.A.
1999-09-01
In previous work, exponential convergence of Monte Carlo solutions using the reduced source method with Legendre expansion has been achieved only in one-dimensional rod and slab geometries. In this paper, the method is applied to three-dimensional (right parallelepiped) problems, with resulting evidence suggesting success. As implemented in this paper, the method approximates an angular integral of the flux with a discrete-ordinates numerical quadrature. It is possible that this approximation introduces an inconsistency that must be addressed.
NASA Astrophysics Data System (ADS)
Pandir, Yusuf; Duzgun, Hasan Huseyin
2016-06-01
In this study, we investigate some new analytical solutions to the fractional Sine-Gordon equation by using the new version of generalized F-expansion method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, new analytical solutions were obtained in terms Jacobi elliptic functions.
Adiabatic Quantum Programming: Minor Embedding With Hard Faults
Klymko, Christine F; Sullivan, Blair D; Humble, Travis S
2013-01-01
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into the hardware or logical fabric. An essential programming step is the embedding of problem-specific information into the logical fabric to define the quantum computational transformation. We present algorithms for embedding arbitrary instances of the adiabatic quantum optimization algorithm into a square lattice of specialized unit cells. Our methods are shown to be extensible in fabric growth, linear in time, and quadratic in logical footprint. In addition, we provide methods for accommodating hard faults in the logical fabric without invoking approximations to the original problem. These hard fault-tolerant embedding algorithms are expected to prove useful for benchmarking the adiabatic quantum optimization algorithm on existing quantum logical hardware. We illustrate this versatility through numerical studies of embeddabilty versus hard fault rates in square lattices of complete bipartite unit cells.
Apparatus and method for measuring the expansion properties of a cement composition
Spangle, Lloyd B.
1983-01-01
An apparatus is disclosed which is useful for measuring the expansion properties of semi-solid materials which expand to a solid phase, upon curing, such as cement compositions. The apparatus includes a sleeve, preferably cylindrical, which has a vertical slit on one side, to allow the sleeve to expand. Mounted on the outside of the sleeve are several sets of pins, consisting of two pins each. The two pins in each set are located on opposite sides of the slit. In the test procedure, the sleeve is filled with wet cement, which is then cured to a solid. As the cement cures it causes the sleeve to expand. The actual expansion of the sleeve represents an expansion factor for the cement. This factor is calculated by measuring the distance across the pins of each set, when the sleeve is empty, and again after the cured cement expands the sleeve.
Jackson, T. S.; Read, N.
2010-02-15
Continuing the program begun by the authors in a previous paper, we develop an exact low-density expansion for the random minimum spanning tree (MST) on a finite graph and use it to develop a continuum perturbation expansion for the MST on critical percolation clusters in space dimension d. The perturbation expansion is proved to be renormalizable in d=6 dimensions. We consider the fractal dimension D{sub p} of paths on the latter MST; our previous results lead us to predict that D{sub p}=2 for d>d{sub c}=6. Using a renormalization-group approach, we confirm the result for d>6 and calculate D{sub p} to first order in epsilon=6-d for d<6 using the connection with critical percolation, with the result D{sub p}=2-epsilon/7+O(epsilon{sup 2}).
Asymptotic analysis of stationary adiabatic premixed flames in porous inert media
Pereira, Fernando M.; Oliveira, Amir A.M.; Fachini, Fernando F.
2009-01-15
The structure of adiabatic premixed flames within porous inert media is investigated using the asymptotic expansion method. For this, the flame structure is divided into three characteristic length scales. The two innermost length scales, the gas-phase diffusion length scale and the reaction length scale, are the same scales defined in the classical premixed flame structure analysis. The outermost length scale, the solid-phase diffusion length scale, is related to the heat conduction in the porous matrix. The differences among these three characteristic length-scales result in large temperature differences between the phases and justify the application of asymptotic expansions to determine an approximate (analytical) solution. Since the main focus of this work is the examination of the processes in the outer and the first inner regions, the simplest kinetic mechanism of one global step is adopted to represent the fuel and oxygen consumption. Then, the description of the reaction zone is obtained using the large activation energy asymptotic method. The description of the problem of the order of the gas-phase length scale is obtained using the boundary layer expansion. This work evaluates the influence of the equivalence ratio, the ratio of the solid to the gas thermal conductivities, the porosity of the medium and the fuel Lewis number on such flames. A parameter that universalizes the flame properties is then identified and discussed. (author)
Asymptotic analysis of stationary adiabatic premixed flames in porous inert media
Pereira, Fernando M.; Oliveira, Amir A.M.; Fachini, Fernando F.
2008-11-15
The structure of adiabatic premixed flames within porous inert media is investigated using the asymptotic expansion method. For this, the flame structure is divided into three characteristic length scales. The two innermost length scales, the gas-phase diffusion length scale and the reaction length scale, are the same scales defined in the classical premixed flame structure analysis. The outermost length scale, the solid-phase diffusion length scale, is related to the heat conduction in the porous matrix. The differences among these three characteristic length-scales result in large temperature differences between the phases and justify the application of asymptotic expansions to determine an approximate (analytical) solution. Since the main focus of this work is the examination of the processes in the outer and the first inner regions, the simplest kinetic mechanism of one global step is adopted to represent the fuel and oxygen consumption. Then, the description of the reaction zone is obtained using the large activation energy asymptotic method. The description of the problem of the order of the gas-phase length scale is obtained using the boundary layer expansion. This work evaluates the influence of the equivalence ratio, the ratio of the solid to the gas thermal conductivities, the porosity of the medium and the fuel Lewis number on such flames. A parameter that universalizes the flame properties is then identified and discussed. (author)
NASA Astrophysics Data System (ADS)
Li, Dafa
2016-05-01
The adiabatic theorem was proposed about 90 years ago and has played an important role in quantum physics. The quantitative adiabatic condition constructed from eigenstates and eigenvalues of a Hamiltonian is a traditional tool to estimate adiabaticity and has proven to be the necessary and sufficient condition for adiabaticity. However, recently the condition has become a controversial subject. In this paper, we list some expressions to estimate the validity of the adiabatic approximation. We show that the quantitative adiabatic condition is invalid for the adiabatic approximation via the Euclidean distance between the adiabatic state and the evolution state. Furthermore, we deduce general necessary and sufficient conditions for the validity of the adiabatic approximation by different definitions.
Nishimura, Shin
2015-12-15
The spherical coordinates expressions of the Rosenbluth potentials are applied to the field particle portion in the linearized Coulomb collision operator. The Sonine (generalized Laguerre) polynomial expansion formulas for this operator allowing general field particles' velocity distributions are derived. An important application area of these formulas is the study of flows of thermalized particles in NBI-heated or burning plasmas since the energy space structure of the fast ions' slowing down velocity distribution cannot be expressed by usual orthogonal polynomial expansions, and since the Galilean invariant property and the momentum conservation of the collision must be distinguished there.
Homentcovschi, Dorel; Miles, Ronald N.
2010-01-01
The paper gives a new method for analyzing planar discontinuities in rectangular waveguides. The method consists of a re-expansion of the normal modes in the two ducts at the junction plane into a system of functions accounting for the velocity singularities at the corner points. As the new expansion has an exponential convergence, only a few terms have to be considered for obtaining the solution of most practical problems. To see how the method works some closed form solutions, obtained by the conformal mapping method, are used to discuss the convergence of the re-expanded series when the number of retained terms increases. The equivalent impedance accounting for nonplanar waves into a plane-wave analysis is determined. Finally, the paper yields the scattering matrix which describes the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both parts of the duct. PMID:20707432
Homentcovschi, Dorel; Miles, Ronald N
2010-08-01
The paper gives a new method for analyzing planar discontinuities in rectangular waveguides. The method consists of a re-expansion of the normal modes in the two ducts at the junction plane into a system of functions accounting for the velocity singularities at the corner points. As the new expansion has an exponential convergence, only a few terms have to be considered for obtaining the solution of most practical problems. To see how the method works some closed form solutions, obtained by the conformal mapping method, are used to discuss the convergence of the re-expanded series when the number of retained terms increases. The equivalent impedance accounting for nonplanar waves into a plane-wave analysis is determined. Finally, the paper yields the scattering matrix which describes the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both parts of the duct.
NASA Astrophysics Data System (ADS)
Bobrov, V. B.
2014-03-01
In the framework of the adiabatic approximation for a subsystem of nuclei with the average distance between them significantly exceeding the dimensions of the initial atom, we consider a nonrelativistic Coulomb system consisting of electrons and nuclei of one type for the temperature range where we can restrict ourself to using the ground state to describe the electron subsystem. We show that the equilibrium properties of such a system are equivalent to the thermodynamic properties of the one-component system of initial atoms interacting between themselves via a short-range potential that is the effective potential of the nucleus-nucleus interaction. In the framework of the applicability of Boltzmann statistics, we present quantum group expansions for the thermodynamic properties of a chemically reacting rarified gas that correspond to the method of initial atoms.
Effect of the Heat Pipe Adiabatic Region.
Brahim, Taoufik; Jemni, Abdelmajid
2014-04-01
The main motivation of conducting this work is to present a rigorous analysis and investigation of the potential effect of the heat pipe adiabatic region on the flow and heat transfer performance of a heat pipe under varying evaporator and condenser conditions. A two-dimensional steady-state model for a cylindrical heat pipe coupling, for both regions, is presented, where the flow of the fluid in the porous structure is described by Darcy-Brinkman-Forchheimer model which accounts for the boundary and inertial effects. The model is solved numerically by using the finite volumes method, and a fortran code was developed to solve the system of equations obtained. The results show that a phase change can occur in the adiabatic region due to temperature gradient created in the porous structure as the heat input increases and the heat pipe boundary conditions change. A recirculation zone may be created at the condenser end section. The effect of the heat transfer rate on the vapor radial velocities and the performance of the heat pipe are discussed. PMID:24895467
Gravitational Chern-Simons and the adiabatic limit
NASA Astrophysics Data System (ADS)
McLellan, Brendan
2010-12-01
We compute the gravitational Chern-Simons term explicitly for an adiabatic family of metrics using standard methods in general relativity. We use the fact that our base three-manifold is a quasiregular K-contact manifold heavily in this computation. Our key observation is that this geometric assumption corresponds exactly to a Kaluza-Klein Ansatz for the metric tensor on our three-manifold, which allows us to translate our problem into the language of general relativity. Similar computations have been performed by Guralnik et al. [Ann. Phys. 308, 222 (2008)], although not in the adiabatic context.
Classical nuclear motion coupled to electronic non-adiabatic transitions
Agostini, Federica; Abedi, Ali; Gross, E. K. U.
2014-12-07
Based on the exact factorization of the electron-nuclear wave function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Gravitational Chern-Simons and the adiabatic limit
McLellan, Brendan
2010-12-15
We compute the gravitational Chern-Simons term explicitly for an adiabatic family of metrics using standard methods in general relativity. We use the fact that our base three-manifold is a quasiregular K-contact manifold heavily in this computation. Our key observation is that this geometric assumption corresponds exactly to a Kaluza-Klein Ansatz for the metric tensor on our three-manifold, which allows us to translate our problem into the language of general relativity. Similar computations have been performed by Guralnik et al.[Ann. Phys. 308, 222 (2008)], although not in the adiabatic context.
Global adiabaticity and non-Gaussianity consistency condition
NASA Astrophysics Data System (ADS)
Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao
2016-10-01
In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, Rc, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of Rc holds only after the perturbation has reached the adiabatic limit where the constant mode of Rc dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, δPnad ≡ δP - cw2 δρ where cw2 = P ˙ / ρ ˙ , usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufficient condition for the conservation of Rc on super-horizon scales. In this paper, we consider models that satisfy δPnad = 0 on all scales, which we call global adiabaticity (GA), which is guaranteed if cw2 = cs2, where cs is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll (USR) inflation in which cw2 = cs2 = 1. In order to generalize USR we develop a method to find the Lagrangian of GA K-inflation models from the behavior of background quantities as functions of the scale factor. Applying this method we show that there indeed exists a wide class of GA models with cw2 = cs2, which allows Rc to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition.
Accelerated expansion through interaction
Zimdahl, Winfried
2009-05-01
Interactions between dark matter and dark energy with a given equation of state are known to modify the cosmic dynamics. On the other hand, the strength of these interactions is subject to strong observational constraints. Here we discuss a model in which the transition from decelerated to accelerated expansion of the Universe arises as a pure interaction phenomenon. Various cosmological scenarios that describe a present stage of accelerated expansion, like the {lambda}CDM model or a (generalized) Chaplygin gas, follow as special cases for different interaction rates. This unifying view on the homogeneous and isotropic background level is accompanied by a non-adiabatic perturbation dynamics which can be seen as a consequence of a fluctuating interaction rate.
Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio
2014-10-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.
F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation
Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah
2014-01-01
F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327
F-expansion method and new exact solutions of the Schrödinger-KdV equation.
Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah
2014-01-01
F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327
Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio
2014-01-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530
Adiabatic Wankel type rotary engine
NASA Technical Reports Server (NTRS)
Kamo, R.; Badgley, P.; Doup, D.
1988-01-01
This SBIR Phase program accomplished the objective of advancing the technology of the Wankel type rotary engine for aircraft applications through the use of adiabatic engine technology. Based on the results of this program, technology is in place to provide a rotor and side and intermediate housings with thermal barrier coatings. A detailed cycle analysis of the NASA 1007R Direct Injection Stratified Charge (DISC) rotary engine was performed which concluded that applying thermal barrier coatings to the rotor should be successful and that it was unlikely that the rotor housing could be successfully run with thermal barrier coatings as the thermal stresses were extensive.
Adiabatic preparation of Floquet condensates
NASA Astrophysics Data System (ADS)
Heinisch, Christoph; Holthaus, Martin
2016-10-01
We argue that a Bose-Einstein condensate can be transformed into a Floquet condensate, that is, into a periodically time-dependent many-particle state possessing the coherence properties of a mesoscopically occupied single-particle Floquet state. Our reasoning is based on the observation that the denseness of the many-body system's quasienergy spectrum does not necessarily obstruct effectively adiabatic transport. Employing the idealized model of a driven bosonic Josephson junction, we demonstrate that only a small amount of Floquet entropy is generated when a driving force with judiciously chosen frequency and maximum amplitude is turned on smoothly.
Lukić, Sergio; Hey, Jody
2012-01-01
We present an implementation of a recently introduced method for estimating the allele-frequency spectrum under the diffusion approximation. For single-nucleotide polymorphism (SNP) frequency data from multiple populations, the method computes numerical solutions to the allele-frequency spectrum (AFS) under a complex model that includes population splitting events, migration, population expansion, and admixture. The solution to the diffusion partial differential equation (PDE) that mimics the evolutionary process is found by means of truncated polynomial expansions. In the absence of gene flow, our computation of frequency spectra yields exact results. The results are compared to those that use a finite-difference method and to forward diffusion simulations. In general, all the methods yield comparable results, although the polynomial-based approach is the most accurate in the weak-migration limit. Also, the economical use of memory attained by the polynomial expansions makes the study of models with four populations possible for the first time. The method was applied to a four-population model of the human expansion out of Africa and the peopling of the Americas, using the Environmental Genome Project (EGP) SNP database. Although our confidence intervals largely overlapped previous analyses of these data, some were significantly different. In particular, estimates of migration among African, European, and Asian populations were considerably lower than those in a previous study and the estimated time of migration out of Africa was earlier. The estimated time of founding of a human population outside of Africa was 52,000 years (95% confidence interval: 36,000–80,800 years). PMID:22865734
Pessi, Jenni; Lassila, Ilkka; Meriläinen, Antti; Räikkönen, Heikki; Hæggström, Edward; Yliruusi, Jouko
2016-08-01
We introduce a robust, stable, and reproducible method to produce nanoparticles based on expansion of supercritical solutions using carbon dioxide as a solvent. The method, controlled expansion of supercritical solution (CESS), uses controlled mass transfer, flow, pressure reduction, and particle collection in dry ice. CESS offers control over the crystallization process as the pressure in the system is reduced according to a specific profile. Particle formation takes place before the exit nozzle, and condensation is the main mechanism for postnucleation particle growth. A 2-step gradient pressure reduction is used to prevent Mach disk formation and particle growth by coagulation. Controlled particle growth keeps the production process stable. With CESS, we produced piroxicam nanoparticles, 60 mg/h, featuring narrow size distribution (176 ± 53 nm). PMID:27368121
NASA Technical Reports Server (NTRS)
Savin, Raymond C
1955-01-01
The generalized shock-expansion method is applied to obtain solutions to the flow field about pointed bodies of revolution at high supersonic airspeeds and small angles of attack. Simple explicit expressions are obtained for the surface Mach numbers and surface pressures in the special case of slender bodies. In the case of inclined cones, algebraic solutions are obtained defining the entire flow field. Experimental pressure-distribution data for cones and ogives at Mach numbers from 3 to 5 are included. (author)
Adiabatic quantum computing with phase modulated laser pulses
Goswami, Debabrata
2005-01-01
Implementation of quantum logical gates for multilevel systems is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language. PMID:17195865
Adiabatic frequency conversion with a sign flip in the coupling
NASA Astrophysics Data System (ADS)
Hristova, H. S.; Rangelov, A. A.; Montemezzani, G.; Vitanov, N. V.
2016-09-01
Adiabatic frequency conversion is a method recently developed in nonlinear optics [H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, Phys. Rev. A 78, 063821 (2008), 10.1103/PhysRevA.78.063821], using ideas from the technique of rapid adiabatic passage (RAP) via a level crossing in quantum physics. In this method, the coupling coefficients are constant and the phase mismatch is chirped adiabatically. In this work, we propose another method for adiabatic frequency conversion, in which the phase mismatch is constant and the coupling is a pulse-shaped function with a sign flip (i.e., a phase step of π ) at its maximum. Compared to the RAP method, our technique has comparable efficiency but it is simpler to implement for it only needs two bulk crystals with opposite χ(2 ) nonlinearity. Moreover, because our technique requires constant nonzero frequency mismatch and has zero conversion efficiency on exact frequency matching, it can be used as a frequency filter.
Adiabatic frequency conversion of ultrafast pulses
NASA Astrophysics Data System (ADS)
Suchowski, H.; Bruner, B. D.; Ganany-Padowicz, A.; Juwiler, I.; Arie, A.; Silberberg, Y.
2011-12-01
A new method for efficient, broadband sum and difference frequency generation of ultrafast pulses is demonstrated. The principles of the method follow from an analogy between frequency conversion and coherent optical excitation of a two-level system. For conversion of ultrafast pulses, the concepts of adiabatic conversion are developed further in order to account for dispersion and group velocity mismatch. The scheme was implemented using aperiodically poled nonlinear crystals and a single step nonlinear mixing process, leading to conversion of near-IR (˜790 nm) ultrafast pulses into the blue (˜450 nm) and mid-IR (˜3.15 μm) spectral regions. Conversion bandwidths up to 15 THz FWHM and efficiencies up to 50% are reported.
Spectral expansion method in problems of laser-beam propagation in the turbulent atmosphere.
Aksenov, V P; Mironov, V L
1978-11-01
A mixed spectral expansion over elementary spherical and plane waves is suggested for use as an approximate solution of the stochastic wave equation describing propagation of optical waves in a turbulent medium. In this case, the complex amplitude of an elementary plane wave is calculated as a solution of a shortened equation, considering only the phase fluctuations of this wave. It is shown that such an approximate solution uniformly approximates statistical moments of the field (up to the fourth order, inclusive) under arbitrary conditions of wave propagationin a turbulent medium and conditions of wave diffraction on the transmitting aperture.
Heim, J.R.
1993-02-23
The invention provides a high magnetic field coil. The invention provides a preloaded compressive force to the coil maintain the integrity of the coil. The compressive force is obtained by reinforcing the coil with two materials of different thermal expansion rates and then heating the coil to 700 C to obtain the desired compression. The embodiment of the invention uses Nb[sub 3]Sn as the conducting wire, since Nb[sub 3]Sn must be heated to 700 C to cause a reaction which makes Nb[sub 3]Sn superconducting.
Heim, Joseph R.
1993-01-01
The invention provides a high magnetic field coil. The invention provides a preloaded compressive force to the coil maintain the integrity of the coil. The compressive force is obtained by reinforcing the coil with two materials of different thermal expansion rates and then heating the coil to 700.degree. C. to obtain the desired compression. The embodiment of the invention uses Nb.sub.3 Sn as the conducting wire, since Nb.sub.3 Sn must be heated to 700.degree. C. to cause a reaction which makes Nb.sub.3 Sn superconducting.
NASA Astrophysics Data System (ADS)
Nishimura, S.; Sugama, H.; Maaßberg, H.; Beidler, C. D.; Murakami, S.; Nakamura, Y.; Hirooka, S.
2010-08-01
The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maaßberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
Nishimura, S.; Sugama, H.; Maassberg, H.; Beidler, C. D.; Murakami, S.; Nakamura, Y.; Hirooka, S.
2010-08-15
The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maassberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
NASA Astrophysics Data System (ADS)
Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao
2016-04-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid δPnad, another is for a general matter field δPc,nad, and the last one is valid only on superhorizon scales. The first two definitions coincide if cs2 = cw2 where cs is the propagation speed of the perturbation, while cw2 = P ˙ / ρ ˙ . Assuming the adiabaticity in the general sense, δPc,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δPnad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs ≠cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δPnad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which cw =cs, where δPnad = δPc,nad = 0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure the conservation of Rc or ζ.
All-coupling polaron optical response: Analytic approaches beyond the adiabatic approximation
NASA Astrophysics Data System (ADS)
Klimin, S. N.; Tempere, J.; Devreese, J. T.
2016-09-01
In the present work, the problem of an all-coupling analytic description for the optical conductivity of the Fröhlich polaron is treated, with the goal being to bridge the gap in the validity range that exists between two complementary methods: on the one hand, the memory-function formalism and, on the other hand, the strong-coupling expansion based on the Franck-Condon picture for the polaron response. At intermediate coupling, both methods were found to fail as they do not reproduce diagrammatic quantum Monte Carlo results. To resolve this, we modify the memory-function formalism with respect to the Feynman-Hellwarth-Iddings-Platzman approach in order to take into account a nonquadratic interaction in a model system for the polaron. The strong-coupling expansion is extended beyond the adiabatic approximation by including in the treatment nonadiabatic transitions between excited polaron states. The polaron optical conductivity that we obtain at T =0 by combining the two extended methods agrees well, both qualitatively and quantitatively, with the diagrammatic quantum Monte Carlo results in the whole available range of the electron-phonon coupling strength.
Geometric Adiabatic Transport in Quantum Hall States.
Klevtsov, S; Wiegmann, P
2015-08-21
We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic deformations of geometry and represents the effect of the gravitational anomaly. We also present the method of computing the transport coefficients for quantum Hall states. PMID:26340197
Geometric Adiabatic Transport in Quantum Hall States.
Klevtsov, S; Wiegmann, P
2015-08-21
We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic deformations of geometry and represents the effect of the gravitational anomaly. We also present the method of computing the transport coefficients for quantum Hall states.
Naher, Hasibun; Abdullah, Farah Aini; Akbar, M Ali
2013-01-01
The generalized and improved (G'/G)-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions are found in hyperbolic, trigonometric and rational function form involving more parameters and some of our constructed solutions are identical with results obtained by other authors if certain parameters take special values and some are new. The numerical results described in the figures were obtained with the aid of commercial software Maple. PMID:23741355
NASA Astrophysics Data System (ADS)
Kumar, Hitender; Chand, Fakir
2013-03-01
The (2+1)-dimensional Maccari and nonlinear Schrödinger equations are reduced to a nonlinear ordinary differential equation (ODE) by using a simple transformation, various solutions of the nonlinear ODE are obtained by using extended F-expansion and projective Ricatti equation methods. With the aid of solutions of the nonlinear ODE more explicit traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions are found out. It is shown that these methods provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
Expansion dynamics of laser produced plasma
Doggett, B.; Lunney, J. G.
2011-05-01
We consider the applicability of the isentropic, adiabatic gas dynamical model of plume expansion for laser ablation in vacuum. We show that the model can be applied to ionized plumes and estimate the upper electron temperature limit on the applicability of the isentropic approximation. The model predictions are compared with Langmuir ion probe measurements and deposition profiles obtained for excimer laser ablation of silver.
On a Nonlinear Model in Adiabatic Evolutions
NASA Astrophysics Data System (ADS)
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
Quantum and classical dynamics in adiabatic computation
NASA Astrophysics Data System (ADS)
Crowley, P. J. D.; Äńurić, T.; Vinci, W.; Warburton, P. A.; Green, A. G.
2014-10-01
Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimization algorithms and quantum adiabatic optimization. This perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing—though inconclusive—results.
Assemblies and methods for mitigating effects of reactor pressure vessel expansion
Challberg, Roy C.; Gou, Perng-Fei; Chu, Cherk Lam; Oliver, Robert P.
1999-01-01
Support assemblies for allowing RPV radial expansion while simultaneously limiting horizontal, vertical, and azimuthal movement of the RPV within a nuclear reactor are described. In one embodiment, the support assembly includes a support block and a guide block. The support block includes a first portion and a second portion, and the first portion is rigidly coupled to the RPV adjacent the first portion. The guide block is rigidly coupled to a reactor pressure vessel support structure and includes a channel sized to receive the second portion of the support block. The second portion of the support block is positioned in the guide block channel to movably couple the guide block to the support block.
Assemblies and methods for mitigating effects of reactor pressure vessel expansion
Challberg, R.C.; Gou, P.F.; Chu, C.L.; Oliver, R.P.
1999-07-27
Support assemblies for allowing RPV radial expansion while simultaneously limiting horizontal, vertical, and azimuthal movement of the RPV within a nuclear reactor are described. In one embodiment, the support assembly includes a support block and a guide block. The support block includes a first portion and a second portion, and the first portion is rigidly coupled to the RPV adjacent the first portion. The guide block is rigidly coupled to a reactor pressure vessel support structure and includes a channel sized to receive the second portion of the support block. The second portion of the support block is positioned in the guide block channel to movably couple the guide block to the support block. 6 figs.
An Expansion of the Trait-State-Occasion Model: Accounting for Shared Method Variance
ERIC Educational Resources Information Center
LaGrange, Beth; Cole, David A.
2008-01-01
This article examines 4 approaches for explaining shared method variance, each applied to a longitudinal trait-state-occasion (TSO) model. Many approaches have been developed to account for shared method variance in multitrait-multimethod (MTMM) data. Some of these MTMM approaches (correlated method, orthogonal method, correlated method minus one,…
Hayami, Masao; Seino, Junji; Nakai, Hiromi
2014-07-30
An algorithm of the accompanying coordinate expansion and recurrence relation (ACE-RR), which is used for the rapid evaluation of the electron repulsion integral (ERI), has been extended to the general-contraction (GC) scheme. The present algorithm, denoted by GC-ACE-RR, is designed for molecular calculations including heavy elements, whose orbitals consist of many primitive functions with and without higher angular momentum such as d- and f-orbitals. The performance of GC-ACE-RR was assessed for (ss|ss)-, (pp|pp)-, (dd|dd)-, and (ff|ff)-type ERIs in terms of contraction length and the number of GC orbitals. The present algorithm was found to reduce the central processing unit time compared with the ACE-RR algorithm, especially for higher angular momentum and highly contracted orbitals. Compared with HONDOPLUS and GAMESS program packages, GC-ACE-RR computations for ERIs of three-dimensional gold clusters Aun (n = 1, 2, …, 10, 15, 20, and 25) are more than 10 times faster. PMID:24889356
Assessing the Jeans Anisotropic Multi-Gaussian Expansion method with the Illustris simulation
NASA Astrophysics Data System (ADS)
Li, Hongyu; Li, Ran; Mao, Shude; Xu, Dandan; Long, R. J.; Emsellem, Eric
2016-02-01
We assess the effectiveness of the Jeans Anisotropic Multi-Gaussian Expansion (JAM) technique with a state-of-the-art cosmological hydrodynamic simulation, the Illustris project. We perform JAM modelling on 1413 simulated galaxies with stellar mass M* > 1010 M⊙, and construct an axisymmetric dynamical model for each galaxy. Combined with a Markov chain Monte Carlo simulation, we recover the projected root-mean-square velocity (Vrms) field of the stellar component, and investigate constraints on the stellar mass-to-light ratio, M*/L, and the fraction of dark matter fDM within 2.5 effective radii (Re). We find that the enclosed total mass within 2.5 Re is well constrained to within 10 per cent. However, there is a degeneracy between the dark matter and stellar components with correspondingly larger individual errors. The 1σ scatter in the recovered M*/L is 30-40 per cent of the true value. The accuracy of the recovery of M*/L depends on the triaxial shape of a galaxy. There is no significant bias for oblate galaxies, while for prolate galaxies the JAM-recovered stellar mass is on average 18 per cent higher than the input values. We also find that higher image resolutions alleviate the dark matter and stellar mass degeneracy and yield systematically better parameter recovery.
Edee, K; Plumey, J P
2015-03-01
The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwell's equations, and the boundary conditions complement this undersized system. In the current work, contrary to this previous version of the MMGE, boundary conditions are incorporated into the definition of a new basis of polynomial functions, which are adapted to the boundary value problem of interest. Results are successfully compared for both metallic and dielectric structures to those obtained from the modal method based on Fourier expansion (MMFE) and MMFE with adaptative spatial resolution.
Edee, K; Plumey, J P
2015-03-01
The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwell's equations, and the boundary conditions complement this undersized system. In the current work, contrary to this previous version of the MMGE, boundary conditions are incorporated into the definition of a new basis of polynomial functions, which are adapted to the boundary value problem of interest. Results are successfully compared for both metallic and dielectric structures to those obtained from the modal method based on Fourier expansion (MMFE) and MMFE with adaptative spatial resolution. PMID:26366651
NASA Astrophysics Data System (ADS)
Roy, Ajit K.
An analytical method capable of predicting the in-plane (hoop) and interlaminar (radial) components of effective coefficients of thermal expansion (CTE) of laminated orthotropic rings is presented. This method is based on the linear theory of elasticity assuming the plane-stress condition in the (r, theta) plane of the ring and is applicable to any aspect ratio of the ring. A comparative study of the effective CTE for thin rings indicates that although 2D lamination theory can predict the in-plane CTE quite accurately, it overpredicts the values of the interlaminar CTE by a large amount. As an example, for a thin ring made with T300/5208 laminates, the 2D theory predicts an interlaminar CTE that is 29 percent higher than that predicted by the present method.
The study on the methods of ellipsoid expansion in high-speed railway in high elevation area
NASA Astrophysics Data System (ADS)
Yang, Zhi; Wen, HongYan; Nie, GuangYu; Gao, Hong
2015-12-01
With the development of high-speed railway in recent years, the previous precision of control surveying and the methods of data processing will not meet the requirement of high-speed railway any longer. In view of the characteristics of precision is much higher in large-scale precise construction and the superiority of precision in reform of large-scale engineering control networks, in this paper, using the algorithm of ellipsoid expansion to deal with overrun coordinate projection distortion in high-speed railway, then compares with common calculation method of surveying, we get a conclusion that this method can get minimum projection and it accord with the requirement of high-precision control surveying.
Antos, Roman; Veis, Martin
2010-12-20
We demonstrate an enhancement of the plane wave expansion method treating two-dimensional photonic crystals by applying Fourier factorization with generally elliptic polarization bases. By studying three examples of periodically arranged cylindrical elements, we compare our approach to the classical Ho method in which the permittivity function is simply expanded without changing coordinates, and to the normal vector method using a normal-tangential polarization transform. The compared calculations clearly show that our approach yields the best convergence properties owing to the complete continuity of our distribution of polarization bases. The presented methodology enables us to study more general systems such as periodic elements with an arbitrary cross-section or devices such as photonic crystal waveguides. PMID:21197026
Antos, Roman; Veis, Martin
2010-12-20
We demonstrate an enhancement of the plane wave expansion method treating two-dimensional photonic crystals by applying Fourier factorization with generally elliptic polarization bases. By studying three examples of periodically arranged cylindrical elements, we compare our approach to the classical Ho method in which the permittivity function is simply expanded without changing coordinates, and to the normal vector method using a normal-tangential polarization transform. The compared calculations clearly show that our approach yields the best convergence properties owing to the complete continuity of our distribution of polarization bases. The presented methodology enables us to study more general systems such as periodic elements with an arbitrary cross-section or devices such as photonic crystal waveguides.
Recent developments in trapping and manipulation of atoms with adiabatic potentials
NASA Astrophysics Data System (ADS)
Garraway, Barry M.; Perrin, Hélène
2016-09-01
A combination of static and oscillating magnetic fields can be used to ‘dress’ atoms with radio-frequency (RF), or microwave, radiation. The spatial variation of these fields can be used to create an enormous variety of traps for ultra-cold atoms and quantum gases. This article reviews the type and character of these adiabatic traps and the applications which include atom interferometry and the study of low-dimensional quantum systems. We introduce the main concepts of magnetic traps leading to adiabatic dressed traps. The concept of adiabaticity is discussed in the context of the Landau-Zener model. The first bubble trap experiment is reviewed together with the method used for loading it. Experiments based on atom chips show the production of double wells and ring traps. Dressed atom traps can be evaporatively cooled with an additional RF field, and a weak RF field can be used to probe the spectroscopy of the adiabatic potentials. Several approaches to ring traps formed from adiabatic potentials are discussed, including those based on atom chips, time-averaged adiabatic potentials and induction methods. Several proposals for adiabatic lattices with dressed atoms are also reviewed.
Energy Expansion for the Period of Anharmonic Oscillators by the Method of Lindstedt-Poincare
ERIC Educational Resources Information Center
Fernandez, Francisco M.
2004-01-01
A simple, straightforward and efficient method is proposed for the calculation of the period of anharmonic oscillators as an energy series. The approach is based on perturbation theory and the method of Lindstedt-Poincare.
Yu, Huimin; Zhao, Xiuhua; Zu, Yuangang; Zhang, Xinjuan; Zu, Baishi; Zhang, Xiaonan
2012-01-01
The particle sizes of pharmaceutical substances are important for their bioavailability. Bioavailability can be improved by reducing the particle size of the drug. In this study, artemisinin was micronized by the rapid expansion of supercritical solutions (RESS). The particle size of the unprocessed white needle-like artemisinin particles was 30 to 1200 μm. The optimum micronization conditions are determined as follows: extraction temperature of 62 °C, extraction pressure of 25 MPa, precipitation temperature 45 °C and nozzle diameter of 1000 μm. Under the optimum conditions, micronized artemisinin with a (mean particle size) MPS of 550 nm is obtained. By analysis of variance (ANOVA), extraction temperature and pressure have significant effects on the MPS of the micronized artemisinin. The particle size of micronized artemisinin decreased with increasing extraction temperature and pressure. Moreover, the SEM, LC-MS, FTIR, DSC and XRD allowed the comparison between the crystalline initial state and the micronization particles obtained after the RESS process. The results showed that RESS process has not induced degradation of artemisinin and that processed artemisinin particles have lower crystallinity and melting point. The bulk density of artemisinin was determined before and after RESS process and the obtained results showed that it passes from an initial density of 0.554 to 0.128 g·cm−3 after the processing. The decrease in bulk density of the micronized powder can increase the liquidity of drug particles when they are applied for medicinal preparations. These results suggest micronized powder of artemisinin can be of great potential in drug delivery systems. PMID:22606030
Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving
NASA Astrophysics Data System (ADS)
Deffner, Sebastian; Jarzynski, Christopher; del Campo, Adolfo
2014-04-01
A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final state that would result from an adiabatic, infinitely slow process. A powerful technique to engineer such shortcuts relies on the use of auxiliary counterdiabatic fields. Determining the explicit form of the required fields has generally proven to be complicated. We present explicit counterdiabatic driving protocols for scale-invariant dynamical processes, which describe, for instance, expansion and transport. To this end, we use the formalism of generating functions and unify previous approaches independently developed in classical and quantum studies. The resulting framework is applied to the design of shortcuts to adiabaticity for a large class of classical and quantum, single-particle, nonlinear, and many-body systems.
The signal in total-body plethysmography: errors due to adiabatic-isothermic difference.
Chaui-Berlinck, J G; Bicudo, J E
1998-09-01
Total-body plethysmography is a technique often employed in comparative physiology studies because it avoids excessive handling of the animals. The pressure signal obtained is generated by an increase in internal energy of the gas phase of the system. Currently, this increase in internal energy is ascribed to heating (and water vapour saturation) of the inspired gas. The standard equation for computing tidal-volume implies that only temperature and saturation differences can be responsible for generating the ventilation signal. In this study, we were able to demonstrate that the difference between the external process of the thoracic expansion, which is adiabatic, and the internal process of it, which is isothermic, is an important factor of internal energy change in the total-body plethysmography method. In other words, organic tissues transfer heat to the entering gas but also to the present gas, in a way that keeps internal expansion an isothermic process. This extra amount of energy was never taken into account before. Therefore, experiments using such a technique to measure tidal-volume should be done using isothermic chambers. Moreover, due to uncertainties of the complementary measurements (ambient and lung temperatures, ambient water vapour saturation) needed to compute tidal-volume using total-body plethysmography, a minimal temperature difference about 15 degrees C between body and ambient should exist to keep uncertainties in tidal-volume values below 5%. However, this limit is not absolute, because it varies as a function of humidity and degree of uncertainty of the complementary measurements.
Rodrigo, J.L.; Carrasco, P.; Alamo, J. )
1989-05-01
Previous disagreement about the thermal expansion of the rhombohedral compound, NZP-type, NaTi/sub 2/(PO/sub 4/)/sub 3/ is clarified. It is shown that thermal stresses affect the thermal expansion, but they relax after some time of storage. Its anisotropic thermal expansion, has been calculate from high temperature X-ray diffraction, and it is linear in the range from room temperature up to 800{sup 0}C. The predictability of thermal expansion and the tailoring of the composition of NZP ceramics require checking whether the thermal effect on the rotations and distortions of the atomic polyhedra in this structure is the responsible for the high anisotropy in the thermal expansion. This effect has been determined experimentally by solving the chemical structure at five different temperatures, applying the Rietveld method to deconvolute the powder X-ray diffraction profiles.
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In most cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo.
White, Alexander J; Gorshkov, Vyacheslav N; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-01
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In most cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems. PMID:26156473
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficientmore » as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.« less
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.
COMET-PE: an incident fluence response expansion transport method for radiotherapy calculations
NASA Astrophysics Data System (ADS)
Hayward, Robert M.; Rahnema, Farzad
2013-05-01
Accurate dose calculation is a central component of radiotherapy treatment planning. A new method of dose calculation has been developed based on transport theory and validated by comparison to Monte Carlo methods. The coarse mesh transport method has been extended to allow coupled photon-electron transport in 3D. The method combines stochastic pre-computation with a deterministic solver to achieve high accuracy and precision. To enhance the method for radiotherapy calculations, a new angular basis was derived, and an analytical source treatment was developed. Validation was performed by comparison to DOSXYZnrc using a heterogeneous interface phantom composed of water, aluminum, and lung. Calculations of both kinetic energy released per unit mass and dose were compared. Good agreement was found with a maximum error and root mean square relative error of less than 1.5% for all cases. The results show that the new method achieves an accuracy comparable to Monte Carlo.
Simulation of periodically focused, adiabatic thermal beams
Chen, C.; Akylas, T. R.; Barton, T. J.; Field, D. M.; Lang, K. M.; Mok, R. V.
2012-12-21
Self-consistent particle-in-cell simulations are performed to verify earlier theoretical predictions of adiabatic thermal beams in a periodic solenoidal magnetic focusing field [K.R. Samokhvalova, J. Zhou and C. Chen, Phys. Plasma 14, 103102 (2007); J. Zhou, K.R. Samokhvalova and C. Chen, Phys. Plasma 15, 023102 (2008)]. In particular, results are obtained for adiabatic thermal beams that do not rotate in the Larmor frame. For such beams, the theoretical predictions of the rms beam envelope, the conservations of the rms thermal emittances, the adiabatic equation of state, and the Debye length are verified in the simulations. Furthermore, the adiabatic thermal beam is found be stable in the parameter regime where the simulations are performed.
Adiabatic Motion of Fault Tolerant Qubits
NASA Astrophysics Data System (ADS)
Drummond, David Edward
This work proposes and analyzes the adiabatic motion of fault tolerant qubits in two systems as candidates for the building blocks of a quantum computer. The first proposal examines a pair of electron spins in double quantum dots, finding that the leading source of decoherence, hyperfine dephasing, can be suppressed by adiabatic rotation of the dots in real space. The additional spin-orbit effects introduced by this motion are analyzed, simulated, and found to result in an infidelity below the error-correction threshold. The second proposal examines topological qubits formed by Majorana zero modes theorized to exist at the ends of semiconductor nanowires coupled to conventional superconductors. A model is developed to design adiabatic movements of the Majorana bound states to produce entangled qubits. Analysis and simulations indicate that these adiabatic operations can also be used to demonstrate entanglement experimentally by testing Bell's theorem.
General conditions for quantum adiabatic evolution
Comparat, Daniel
2009-07-15
Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution [H({epsilon}t),{epsilon}{yields}0], are insufficient to describe an evolution driven by the Hamiltonian H(t) itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian H(t). As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions)
Adiabatic Quantum Search in Open Systems
NASA Astrophysics Data System (ADS)
Wild, Dominik S.; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y.; Lukin, Mikhail D.
2016-10-01
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Experimental demonstration of composite adiabatic passage
NASA Astrophysics Data System (ADS)
Schraft, Daniel; Halfmann, Thomas; Genov, Genko T.; Vitanov, Nikolay V.
2013-12-01
We report an experimental demonstration of composite adiabatic passage (CAP) for robust and efficient manipulation of two-level systems. The technique represents a altered version of rapid adiabatic passage (RAP), driven by composite sequences of radiation pulses with appropriately chosen phases. We implement CAP with radio-frequency pulses to invert (i.e., to rephase) optically prepared spin coherences in a Pr3+:Y2SiO5 crystal. We perform systematic investigations of the efficiency of CAP and compare the results with conventional π pulses and RAP. The data clearly demonstrate the superior features of CAP with regard to robustness and efficiency, even under conditions of weakly fulfilled adiabaticity. The experimental demonstration of composite sequences to support adiabatic passage is of significant relevance whenever a high efficiency or robustness of coherent excitation processes need to be maintained, e.g., as required in quantum information technology.
Adiabatic limits on Riemannian Heisenberg manifolds
Yakovlev, A A
2008-02-28
An asymptotic formula is obtained for the distribution function of the spectrum of the Laplace operator, in the adiabatic limit for the foliation defined by the orbits of an invariant flow on a compact Riemannian Heisenberg manifold. Bibliography: 21 titles.
Adiabatic invariance of oscillons/I -balls
NASA Astrophysics Data System (ADS)
Kawasaki, Masahiro; Takahashi, Fuminobu; Takeda, Naoyuki
2015-11-01
Real scalar fields are known to fragment into spatially localized and long-lived solitons called oscillons or I -balls. We prove the adiabatic invariance of the oscillons/I -balls for a potential that allows periodic motion even in the presence of non-negligible spatial gradient energy. We show that such a potential is uniquely determined to be the quadratic one with a logarithmic correction, for which the oscillons/I -balls are absolutely stable. For slightly different forms of the scalar potential dominated by the quadratic one, the oscillons/I -balls are only quasistable, because the adiabatic charge is only approximately conserved. We check the conservation of the adiabatic charge of the I -balls in numerical simulation by slowly varying the coefficient of logarithmic corrections. This unambiguously shows that the longevity of oscillons/I -balls is due to the adiabatic invariance.
Atom cooling by nonadiabatic expansion
Chen Xi; Muga, J. G.; Campo, A. del; Ruschhaupt, A.
2009-12-15
Motivated by the recent discovery that a reflecting wall moving with a square-root-in-time trajectory behaves as a universal stopper of classical particles regardless of their initial velocities, we compare linear-in-time and square-root-in-time expansions of a box to achieve efficient atom cooling. For the quantum single-atom wave functions studied the square-root-in-time expansion presents important advantages: asymptotically it leads to zero average energy whereas any linear-in-time (constant box-wall velocity) expansion leaves a nonzero residual energy, except in the limit of an infinitely slow expansion. For finite final times and box lengths we set a number of bounds and cooling principles which again confirm the superior performance of the square-root-in-time expansion, even more clearly for increasing excitation of the initial state. Breakdown of adiabaticity is generally fatal for cooling with the linear expansion but not so with the square-root-in-time expansion.
Adiabatic Demagnetization Cooler For Far Infrared Detector
NASA Astrophysics Data System (ADS)
Sato, Akio; Yazawa, Takashi; Yamamoto, Junya
1988-11-01
An small adiabatic demagnetization cooler for an astronomical far infrared detector has been built. Single crystals of manganese ammonium sulphate and chromium potassium alum, were prepared as magnetic substances. The superconducting magnet was indirectly cooled and operated by small current up to 13.3 A, the maximum field being 3.5 T. As a preliminary step, adiabatic demagnetization to zero field was implemented. The lowest temperature obtained was 0.5 K, for 5.0 K initial temperature.
Shi, Shouyuan; Chen, Caihua; Prather, Dennis W
2004-09-01
We present a new algorithm for calculation of the band structure of photonic crystal slabs. This algorithm combines the plane-wave expansion method with perfectly matched layers for the termination of the computational region in the direction out of the plane. In addition, the effective-medium tensor is applied to improve convergence. A general complex eigenvalue problem is then obtained. Two criteria are presented to distinguish the guided modes from the PML modes. As such, this scheme can accurately determine the band structure both above and below the light cone. The convergence of the algorithm presented has been studied. The results obtained by using this algorithm have been compared with those obtained by the finite-difference time-domain method and found to agree very well.
Symmetry of the Adiabatic Condition in the Piston Problem
ERIC Educational Resources Information Center
Anacleto, Joaquim; Ferreira, J. M.
2011-01-01
This study addresses a controversial issue in the adiabatic piston problem, namely that of the piston being adiabatic when it is fixed but no longer so when it can move freely. It is shown that this apparent contradiction arises from the usual definition of adiabatic condition. The issue is addressed here by requiring the adiabatic condition to be…
Hierarchical theory of quantum adiabatic evolution
NASA Astrophysics Data System (ADS)
Zhang, Qi; Gong, Jiangbin; Wu, Biao
2014-12-01
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau-Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.
NASA Astrophysics Data System (ADS)
Chang, Zhe; Lin, Hai-Nan
2015-01-01
Type Ia supernovae (SNe Ia) are often used as the standard candles to probe the anisotropic expansion of the Universe. In this paper, we make a comprehensive comparison between the hemisphere comparison (HC) method and dipole-fitting (DF) method in searching for the cosmological preferred direction using the Union2 data set, a compilation of 557 well-calibrated SNe Ia. We find that the directions of the faintest SNe Ia derived from these two methods are approximately opposite. Monte Carlo simulations show that the results of the HC method strongly depend on the distribution of the data points in the sky. The coincidence that the HC method and DF method give two completely opposite directions may be due to the extremely non-uniform distribution of the Union2 data set.
He, Yue-Jing; Hung, Wei-Chih; Lai, Zhe-Ping
2016-01-01
In this study, a numerical simulation method was employed to investigate and analyze superstructure fiber Bragg gratings (SFBGs) with five duty cycles (50%, 33.33%, 14.28%, 12.5%, and 10%). This study focuses on demonstrating the relevance between design period and spectral characteristics of SFBGs (in the form of graphics) for SFBGs of all duty cycles. Compared with complicated and hard-to-learn conventional coupled-mode theory, the result of the present study may assist beginner and expert designers in understanding the basic application aspects, optical characteristics, and design techniques of SFBGs, thereby indirectly lowering the physical concepts and mathematical skills required for entering the design field. To effectively improve the accuracy of overall computational performance and numerical calculations and to shorten the gap between simulation results and actual production, this study integrated a perfectly matched layer (PML), perfectly reflecting boundary (PRB), object meshing method (OMM), and boundary meshing method (BMM) into the finite element method (FEM) and eigenmode expansion method (EEM). The integrated method enables designers to easily and flexibly design optical fiber communication systems that conform to the specific spectral characteristic by using the simulation data in this paper, which includes bandwidth, number of channels, and band gap size. PMID:26861322
He, Yue-Jing; Hung, Wei-Chih; Lai, Zhe-Ping
2016-01-01
In this study, a numerical simulation method was employed to investigate and analyze superstructure fiber Bragg gratings (SFBGs) with five duty cycles (50%, 33.33%, 14.28%, 12.5%, and 10%). This study focuses on demonstrating the relevance between design period and spectral characteristics of SFBGs (in the form of graphics) for SFBGs of all duty cycles. Compared with complicated and hard-to-learn conventional coupled-mode theory, the result of the present study may assist beginner and expert designers in understanding the basic application aspects, optical characteristics, and design techniques of SFBGs, thereby indirectly lowering the physical concepts and mathematical skills required for entering the design field. To effectively improve the accuracy of overall computational performance and numerical calculations and to shorten the gap between simulation results and actual production, this study integrated a perfectly matched layer (PML), perfectly reflecting boundary (PRB), object meshing method (OMM), and boundary meshing method (BMM) into the finite element method (FEM) and eigenmode expansion method (EEM). The integrated method enables designers to easily and flexibly design optical fiber communication systems that conform to the specific spectral characteristic by using the simulation data in this paper, which includes bandwidth, number of channels, and band gap size. PMID:26861322
A ghost cell expansion method for reducing communications in solving PDE problems
Ding, Chris H.Q.; He, Yun
2001-05-01
In solving Partial Differential Equations, such as the Barotropic equations in ocean models, on Distributed Memory Computers, finite difference methods are commonly used. Most often, processor subdomain boundaries must be updated at each time step. This boundary update process involves many messages of small sizes, therefore large communication overhead. Here we propose a new approach which expands the ghost cell layers and thus updates boundaries much less frequently ---reducing total message volume and grouping small messages into bigger ones. Together with a technique for eliminating diagonal communications, the method speedup communication substantially, up to 170%. We explain the method and implementation in details, provide systematic timing results and performance analysis on Cray T3E and IBM SP.
Analysis of double-hybrid density functionals along the adiabatic connection
NASA Astrophysics Data System (ADS)
Cornaton, Yann; Franck, Odile; Teale, Andrew M.; Fromager, Emmanuel
2013-07-01
We present a graphical analysis of the adiabatic connections underlying double-hybrid density-functional methods that employ second-order perturbation theory. Approximate adiabatic connection formulae relevant to the construction of these functionals are derived and compared directly with those calculated using accurate ab initio methods. The discontinuous nature of the approximate adiabatic integrands is emphasised, the discontinuities occurring at interaction strengths which mark the transitions between regions that are: (i) described predominantly by second-order perturbation theory; (ii) described by a mixture of density-functional and second-order perturbation theory contributions; and (iii) described purely by density-functional theory. Numerical examples are presented for a selection of small molecular systems and van der Waals dimers. The impacts of commonly used approximations in each of the three sections of the adiabatic connection are discussed along with possible routes for the development of improved double-hybrid methodologies.
Action First--Understanding Follows: An Expansion of Skills-Based Training Using Action Method.
ERIC Educational Resources Information Center
Martin, Colin
1988-01-01
This paper discusses the concept of training trainers in the skills they need to perform competently as trainers and how they follow their skills mastery with discussion on their new theoretical insight. Moreno's action method (psychodrama, sociodrama, sociometry, and role training) is the model used. (JOW)
AB INITIO SIMULATIONS FOR MATERIAL PROPERTIES ALONG THE JUPITER ADIABAT
French, Martin; Becker, Andreas; Lorenzen, Winfried; Nettelmann, Nadine; Bethkenhagen, Mandy; Redmer, Ronald; Wicht, Johannes
2012-09-15
We determine basic thermodynamic and transport properties of hydrogen-helium-water mixtures for the extreme conditions along Jupiter's adiabat via ab initio simulations, which are compiled in an accurate and consistent data set. In particular, we calculate the electrical and thermal conductivity, the shear and longitudinal viscosity, and diffusion coefficients of the nuclei. We present results for associated quantities like the magnetic and thermal diffusivity and the kinematic shear viscosity along an adiabat that is taken from a state-of-the-art interior structure model. Furthermore, the heat capacities, the thermal expansion coefficient, the isothermal compressibility, the Grueneisen parameter, and the speed of sound are calculated. We find that the onset of dissociation and ionization of hydrogen at about 0.9 Jupiter radii marks a region where the material properties change drastically. In the deep interior, where the electrons are degenerate, many of the material properties remain relatively constant. Our ab initio data will serve as a robust foundation for applications that require accurate knowledge of the material properties in Jupiter's interior, e.g., models for the dynamo generation.
Breakdown of adiabatic electron behavior in expanding magnetic fields
NASA Astrophysics Data System (ADS)
Lichko, Emily; Egedal, Jan; Daughton, William
2015-11-01
During magnetic reconnection the incoming magnetic flux tubes expand in the inflow region. If this expansion is sufficiently slow the results are well described by a previously developed adiabatic model. Using kinetic simulations in a simple geometry and applying rapid magnetic perturbations, this study investigates the point at which the adiabatic assumption fails. To this end a 2D VPIC simulation was constructed, where the magnetic field in a uniform plasma is perturbed by externally driven currents. By varying the onset speed of the magnetic perturbation and the electron thermal speed, we found a sharp threshold at which this model breaks down. We believe that this point is determined by the time of the magnetic pumping compared to the electron transit time through the region, i.e. ω ~ Ḃ / B ~vthe / L . This threshold was also characterized by the launching of Whistler waves and with time domain structures, such as electron holes and double layers, which agree with those seen during magnetic reconnection and may relate to similar structures in the Van Allen Belts. NSF GEM award 1405166 and NASA grant NNX14AC68G.
Fluctuations of work in nearly adiabatically driven open quantum systems.
Suomela, S; Salmilehto, J; Savenko, I G; Ala-Nissila, T; Möttönen, M
2015-02-01
We extend the quantum jump method to nearly adiabatically driven open quantum systems in a way that allows for an accurate account of the external driving in the system-environment interaction. Using this framework, we construct the corresponding trajectory-dependent work performed on the system and derive the integral fluctuation theorem and the Jarzynski equality for nearly adiabatic driving. We show that such identities hold as long as the stochastic dynamics and work variable are consistently defined. We numerically study the emerging work statistics for a two-level quantum system and find that the conventional diabatic approximation is unable to capture some prominent features arising from driving, such as the continuity of the probability density of work. Our results reveal the necessity of using accurate expressions for the drive-dressed heat exchange in future experiments probing jump time distributions. PMID:25768477
Assessment of total efficiency in adiabatic engines
NASA Astrophysics Data System (ADS)
Mitianiec, W.
2016-09-01
The paper presents influence of ceramic coating in all surfaces of the combustion chamber of SI four-stroke engine on working parameters mainly on heat balance and total efficiency. Three cases of engine were considered: standard without ceramic coating, fully adiabatic combustion chamber and engine with different thickness of ceramic coating. Consideration of adiabatic or semi-adiabatic engine was connected with mathematical modelling of heat transfer from the cylinder gas to the cooling medium. This model takes into account changeable convection coefficient based on the experimental formulas of Woschni, heat conductivity of multi-layer walls and also small effect of radiation in SI engines. The simulation model was elaborated with full heat transfer to the cooling medium and unsteady gas flow in the engine intake and exhaust systems. The computer program taking into account 0D model of engine processes in the cylinder and 1D model of gas flow was elaborated for determination of many basic engine thermodynamic parameters for Suzuki DR-Z400S 400 cc SI engine. The paper presents calculation results of influence of the ceramic coating thickness on indicated pressure, specific fuel consumption, cooling and exhaust heat losses. Next it were presented comparisons of effective power, heat losses in the cooling and exhaust systems, total efficiency in function of engine rotational speed and also comparison of temperature inside the cylinder for standard, semi-adiabatic and full adiabatic engine. On the basis of the achieved results it was found higher total efficiency of adiabatic engines at 2500 rpm from 27% for standard engine to 37% for full adiabatic engine.
Graph isomorphism and adiabatic quantum computing
NASA Astrophysics Data System (ADS)
Gaitan, Frank; Clark, Lane
2014-02-01
In the graph isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G →G'. If yes, then G and G' are said to be isomorphic; otherwise they are nonisomorphic. The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. In this paper we present a quantum algorithm that solves arbitrary instances of GI and which also provides an approach to determining all automorphisms of a given graph. We show how the GI problem can be converted to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. We numerically simulate the algorithm's quantum dynamics and show that it correctly (i) distinguishes nonisomorphic graphs; (ii) recognizes isomorphic graphs and determines the permutation(s) that connect them; and (iii) finds the automorphism group of a given graph G. We then discuss the GI quantum algorithm's experimental implementation, and close by showing how it can be leveraged to give a quantum algorithm that solves arbitrary instances of the NP-complete subgraph isomorphism problem. The computational complexity of an adiabatic quantum algorithm is largely determined by the minimum energy gap Δ (N) separating the ground and first-excited states in the limit of large problem size N ≫1. Calculating Δ (N) in this limit is a fundamental open problem in adiabatic quantum computing, and so it is not possible to determine the computational complexity of adiabatic quantum algorithms in general, nor consequently, of the specific adiabatic quantum algorithms presented here. Adiabatic quantum computing has been shown to be equivalent to the circuit model of quantum computing, and so development of adiabatic quantum algorithms continues to be of great interest.
Method of Producing Controlled Thermal Expansion Coat for Thermal Barrier Coatings
NASA Technical Reports Server (NTRS)
Brindley, William J. (Inventor); Miller, Robert A. (Inventor); Aikin, Beverly J. M. (Inventor)
2000-01-01
An improved thermal barrier coating and method for producing and applying such is disclosed herein. The thermal barrier coatings includes a high temperature substrate, a first bond coat layer applied to the substrate of MCrAlX and a second bond coat layer of MCrAlX with particles of a particulate dispersed throughout the MCrAlX and the preferred particulate is Al2O3. The particles of the particulate dispersed throughout the second bond coat layer preferably have a diameter of less then the height of the peaks of the second bond coat layer or a diameter of less than 5 micron. The method of producing the second bond coat layer may either include the steps of mechanical alloying of particles throughout the second bond coat layer, attrition milling the particles of the particulate throughout the second bond coat layer, or using electrophoresis to disperse the particles throughout the second bond coat layer. In the preferred embodiment of the invention the first bond coat layer is applied to the substrate. and then the second bond coat layer is thermally sprayed onto the first bond coat layer. Further, in a preferred embodiment of the invention a ceramic insulating layer covers the second bond coat layer.
Shortcut to Adiabaticity for an Anisotropic Gas Containing Quantum Defects.
Papoular, D J; Stringari, S
2015-07-10
We present a shortcut to adiabaticity (STA) protocol applicable to 3D unitary Fermi gases and 2D weakly interacting Bose gases containing defects such as vortices or solitons. Our protocol relies on a new class of exact scaling solutions in the presence of anisotropic time-dependent harmonic traps. It connects stationary states in initial and final traps having the same frequency ratios. The resulting scaling laws exhibit a universal form and also apply to the classical Boltzmann gas. The duration of the STA can be made very short so as to realize a quantum quench from one stationary state to another. When applied to an anisotropically trapped superfluid gas, the STA conserves the shape of the quantum defects hosted by the cloud, thereby acting like a perfect microscope, which sharply contrasts with their strong distortion occurring during the free expansion of the cloud.
Shortcut to Adiabaticity for an Anisotropic Gas Containing Quantum Defects
NASA Astrophysics Data System (ADS)
Papoular, D. J.; Stringari, S.
2015-07-01
We present a shortcut to adiabaticity (STA) protocol applicable to 3D unitary Fermi gases and 2D weakly interacting Bose gases containing defects such as vortices or solitons. Our protocol relies on a new class of exact scaling solutions in the presence of anisotropic time-dependent harmonic traps. It connects stationary states in initial and final traps having the same frequency ratios. The resulting scaling laws exhibit a universal form and also apply to the classical Boltzmann gas. The duration of the STA can be made very short so as to realize a quantum quench from one stationary state to another. When applied to an anisotropically trapped superfluid gas, the STA conserves the shape of the quantum defects hosted by the cloud, thereby acting like a perfect microscope, which sharply contrasts with their strong distortion occurring during the free expansion of the cloud.
Model of TPTC Stirling engine with adiabatic working spaces
NASA Astrophysics Data System (ADS)
Renfroe, D. A.; Counts, M.
1988-10-01
A Stirling engine incorporating a phase-changing component of the working fluid has been modeled with the assumption that the compression and expansion space are adiabatic, and that the heat exchanger consists of a cooler, regenerator, and heater of finite size where the fluid follows an idealized temperature profile. Differential equations for the rate of change of mass in any cell and pressure over the entire engine were derived from the energy, continuity, state equations, and Dalton's law. From the simultaneous solution of these equations, all of the information necessary for calculation of power output and efficiency were obtained. Comparison of the results from this model with previous studies shows that the advantage of adding a phase-changing component to the working fluid may have been overstated.
Model of TPTC stirling engine with adiabatic working spaces
Renfroe, D.A.; Counts, M.
1988-10-01
A Stirling engine incorporating a phase-changing component of the working fluid has been modeled with the assumption that the compression and expansion space are adiabatic, and that the heat exchanger consists of a cooler, regenerator, and heater of finite size where the fluid follows an idealized temperature profile. Differential equations for the rate of change of mass in any cell and pressure over the entire engine were derived from the energy, continuity, state equations, and Dalton's law. From the simultaneous solution of these equations, all of the information necessary for calculation of power output and efficiency were obtained. Comparison of the results from this model with previous studies shows that the advantage of adding a phase-changing component to the working fluid may have been overstated.
Shortcut to Adiabaticity for an Anisotropic Gas Containing Quantum Defects.
Papoular, D J; Stringari, S
2015-07-10
We present a shortcut to adiabaticity (STA) protocol applicable to 3D unitary Fermi gases and 2D weakly interacting Bose gases containing defects such as vortices or solitons. Our protocol relies on a new class of exact scaling solutions in the presence of anisotropic time-dependent harmonic traps. It connects stationary states in initial and final traps having the same frequency ratios. The resulting scaling laws exhibit a universal form and also apply to the classical Boltzmann gas. The duration of the STA can be made very short so as to realize a quantum quench from one stationary state to another. When applied to an anisotropically trapped superfluid gas, the STA conserves the shape of the quantum defects hosted by the cloud, thereby acting like a perfect microscope, which sharply contrasts with their strong distortion occurring during the free expansion of the cloud. PMID:26207476
Vagov, A; Schomerus, H; Zalipaev, V V
2009-11-01
We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field. PMID:20365055
A maximal chromatic expansion method of mapping multichannel imagery into color space. [North Dakota
NASA Technical Reports Server (NTRS)
Juday, R. D.; Abotteen, R. A. (Principal Investigator)
1978-01-01
The author has identified the following significant results. A color film generation method that maximally expands the chromaticity and aligns Kauth brightness with the gray axis was presented. In comparison with the current LACIE film product, the new color film product has more contrast and more colors and appears to be brighter. The field boundaries in the new product were more pronounced than in the current LACIE product. The speckle effect was one problem in the new product. The yellowness speckle can be treated using an equation. This equation can be used to eliminate any speckle introduced by the greenness. This product leads logically toward another that will employ quantitative colorimetry which will account for some of the eye's perception of color stimuli.
VUV generation by adiabatically expanded and excited by a DC electrical discharge Argon gas
Pipergias, K.; Yasemidis, D.; Reppa, E.; Pentaris, D.; Efthimiopoulos, T.; Merlemis, N.; Giannetas, V.
2010-11-10
We investigate the emission of Argon (Ar) gas which is adiabatically expanded through a nozzle and excited using a DC electrical discharge. Because of the expansion and the electronic excitation, Ar dimers and clusters are formed, which give radiation in the second (2nd) and in the third (3rd) continua of Ar, centered at about 126 and 254 nm respectively. We particularly focus our study on the 2nd continuum, in order to develop a laser at this wavelength.
Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator
Chen Xi; Muga, J. G.
2010-11-15
We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes ('shortcuts to adiabaticity') designed to reproduce the initial populations at some predetermined final frequency and time. We provide lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.
Accurate adiabatic correction in the hydrogen molecule
NASA Astrophysics Data System (ADS)
Pachucki, Krzysztof; Komasa, Jacek
2014-12-01
A new formalism for the accurate treatment of adiabatic effects in the hydrogen molecule is presented, in which the electronic wave function is expanded in the James-Coolidge basis functions. Systematic increase in the size of the basis set permits estimation of the accuracy. Numerical results for the adiabatic correction to the Born-Oppenheimer interaction energy reveal a relative precision of 10-12 at an arbitrary internuclear distance. Such calculations have been performed for 88 internuclear distances in the range of 0 < R ⩽ 12 bohrs to construct the adiabatic correction potential and to solve the nuclear Schrödinger equation. Finally, the adiabatic correction to the dissociation energies of all rovibrational levels in H2, HD, HT, D2, DT, and T2 has been determined. For the ground state of H2 the estimated precision is 3 × 10-7 cm-1, which is almost three orders of magnitude higher than that of the best previous result. The achieved accuracy removes the adiabatic contribution from the overall error budget of the present day theoretical predictions for the rovibrational levels.
Accurate adiabatic correction in the hydrogen molecule
Pachucki, Krzysztof; Komasa, Jacek
2014-12-14
A new formalism for the accurate treatment of adiabatic effects in the hydrogen molecule is presented, in which the electronic wave function is expanded in the James-Coolidge basis functions. Systematic increase in the size of the basis set permits estimation of the accuracy. Numerical results for the adiabatic correction to the Born-Oppenheimer interaction energy reveal a relative precision of 10{sup −12} at an arbitrary internuclear distance. Such calculations have been performed for 88 internuclear distances in the range of 0 < R ⩽ 12 bohrs to construct the adiabatic correction potential and to solve the nuclear Schrödinger equation. Finally, the adiabatic correction to the dissociation energies of all rovibrational levels in H{sub 2}, HD, HT, D{sub 2}, DT, and T{sub 2} has been determined. For the ground state of H{sub 2} the estimated precision is 3 × 10{sup −7} cm{sup −1}, which is almost three orders of magnitude higher than that of the best previous result. The achieved accuracy removes the adiabatic contribution from the overall error budget of the present day theoretical predictions for the rovibrational levels.
Accurate adiabatic correction in the hydrogen molecule.
Pachucki, Krzysztof; Komasa, Jacek
2014-12-14
A new formalism for the accurate treatment of adiabatic effects in the hydrogen molecule is presented, in which the electronic wave function is expanded in the James-Coolidge basis functions. Systematic increase in the size of the basis set permits estimation of the accuracy. Numerical results for the adiabatic correction to the Born-Oppenheimer interaction energy reveal a relative precision of 10(-12) at an arbitrary internuclear distance. Such calculations have been performed for 88 internuclear distances in the range of 0 < R ⩽ 12 bohrs to construct the adiabatic correction potential and to solve the nuclear Schrödinger equation. Finally, the adiabatic correction to the dissociation energies of all rovibrational levels in H2, HD, HT, D2, DT, and T2 has been determined. For the ground state of H2 the estimated precision is 3 × 10(-7) cm(-1), which is almost three orders of magnitude higher than that of the best previous result. The achieved accuracy removes the adiabatic contribution from the overall error budget of the present day theoretical predictions for the rovibrational levels. PMID:25494728
Numerical modeling of the expansion phase of steam explosions. Part 1, Method and validation
Hyder, M.L.; Farawila, Y.M.; Abdel-Khalik, S.I.; Halvorson, P.J.
1992-05-01
In the development of the Severe Accident Analysis Program for the Savannah River production reactors, it was recognized that certain accidents have -the potential for causing damaging steam explosions. Steam explosions can occur when metals, such as the aluminum-based fuel used at Savannah River, are melted and come into contact with water. This condition is unstable, and local turbulence can lead to the generation of great quantities of steam within a few milliseconds. This phenomenon has been observed in several reactor incidents and experiments (BORAX, SPERT-1, SL-1, probably Chernobyl) where it caused damage to the reactor and associated structures. The massive SRS reactor buildings are likely to withstand any imaginable steam explosion. However, reactor components and building structures including hatches, ventilation ducts, etc., could be at risk if such an explosion occurred. The goal for this study was to develop a computer code that could be used parametrically to predict the effects of various steam explosions on their surroundings. This would be able to predict whether a steam explosion of a given magnitude would be likely to fail a particular structure. This would require, of course, that the magnitude of the explosion be specified through some combination of judgment and calculation. The requested code, identified as the K-FIX(GT) code, was developed and delivered by the contractor, along with extensive documentation. The several individual reports that constitute the documentation are each being issued as a separate WSRC report. Documentation includes several model calculations, and. representation of these in graphic form. This report incorporates Report GTRSR-006, which gives an overview of the methods used in the development of K-FIX(GT), and the results of a comparison with experiments in the literature. The authors conclude that the results of the comparison calculation are in reasonable agreement with observations.
ERIC Educational Resources Information Center
McArdle, Heather K.
1997-01-01
Describes a week-long activity for general to honors-level students that addresses Hubble's law and the universal expansion theory. Uses a discrepant event-type activity to lead up to the abstract principles of the universal expansion theory. (JRH)
Hayami, Masao; Seino, Junji; Nakai, Hiromi
2015-05-28
An efficient algorithm for the rapid evaluation of electron repulsion integrals is proposed. The present method, denoted by accompanying coordinate expansion and transferred recurrence relation (ACE-TRR), is constructed using a transfer relation scheme based on the accompanying coordinate expansion and recurrence relation method. Furthermore, the ACE-TRR algorithm is extended for the general-contraction basis sets. Numerical assessments clarify the efficiency of the ACE-TRR method for the systems including heavy elements, whose orbitals have long contractions and high angular momenta, such as f- and g-orbitals.
Numerical study of polaron problem in the adiabatic limit
NASA Astrophysics Data System (ADS)
Marsiglio, Frank; Li, Zhou; Blois, Cindy; Baillie, Devin
2010-03-01
We study the polaron problem in a one dimensional chain and on a two dimensional square lattice. The models we have used are the Holstein model and the Su-Schrieffer-Heeger (SSH) model. By a variational procedure based on the Lanczos method, we are able to examine the polaron problem in the limit when the mass of the ion is very large, i.e. close to the adiabatic limit. It is known that for the Holstein model there is no phase transition [1] for any nonzero phonon energy. It is also known that for the one dimensional Holstein or SSH model there will be long range order [2] (e.g. dimerization) in the adiabatic limit at half-filling. It is then interesting to study the long range order on a two dimensional square lattice in and away from the adiabatic limit. Moreover, recent progress for the single polaron near an impurity (disorder) [3] make it an interesting problem for studying bond length disorder which can change the hopping energy in a specific direction in the Holstein model. Reference: [1] H. Lowen, Phys.Rev.B 37, 8661 (1988) [2] J.E.Hirsch and E. Frandkin, Phys. Rev. Lett. 49, 402 (1982) [3]A.S.Mishchenko et.al Phys.Rev.B 79(2009) 180301(R)
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
NASA Technical Reports Server (NTRS)
Smelyanskiy, Vadius; vonToussaint, Udo V.; Timucin, Dogan A.; Clancy, Daniel (Technical Monitor)
2002-01-01
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
NASA Technical Reports Server (NTRS)
Smelyanskiy, V. N.; Toussaint, U. V.; Timucin, D. A.
2002-01-01
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
Energy efficiency of adiabatic superconductor logic
NASA Astrophysics Data System (ADS)
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-01-01
Adiabatic superconductor logic (ASL), including adiabatic quantum-flux-parametron (AQFP) logic, exhibits high energy efficiency because its bit energy can be decreased below the thermal energy through adiabatic switching operations. In the present paper, we present the general scaling laws of ASL and compare the energy efficiency of ASL with those of other energy-efficient logics. Also, we discuss the minimum energy-delay product (EDP) of ASL at finite temperature. Our study shows that there is a maximum temperature at which the EDP can reach the quantum limit given by ħ/2, which is dependent on the superconductor material and the Josephson junction quality, and that it is reasonable to operate ASL at cryogenic temperatures in order to achieve an EDP that approaches ħ/2.
Adiabatic approximation for the density matrix
NASA Astrophysics Data System (ADS)
Band, Yehuda B.
1992-05-01
An adiabatic approximation for the Liouville density-matrix equation which includes decay terms is developed. The adiabatic approximation employs the eigenvectors of the non-normal Liouville operator. The approximation is valid when there exists a complete set of eigenvectors of the non-normal Liouville operator (i.e., the eigenvectors span the density-matrix space), the time rate of change of the Liouville operator is small, and an auxiliary matrix is nonsingular. Numerical examples are presented involving efficient population transfer in a molecule by stimulated Raman scattering, with the intermediate level of the molecule decaying on a time scale that is fast compared with the pulse durations of the pump and Stokes fields. The adiabatic density-matrix approximation can be simply used to determine the density matrix for atomic or molecular systems interacting with cw electromagnetic fields when spontaneous emission or other decay mechanisms prevail.
Adiabaticity and viscosity in deep mantle convection
NASA Technical Reports Server (NTRS)
Quareni, F.; Yuen, D. A.; Saari, M. R.
1986-01-01
A study has been conducted of steady convection with adiabatic and viscous heating for variable viscosity in the Boussinesq limit using the mean-field theory. A strong nonlinear coupling is found between the thermodynamic constants governing adiabatic heating and the rheological parameters. The range of rheological values for which adiabaticity would occur throughout the mantle has been established. Too large an activation volume, greater than 6 cu cm/mol for the cases examined, would produce unreasonably high temperature at the bottom of the mantle (greater than 6000 K) and superadiabatic gradients, especially in the lower mantle. Radiogenic heating plays a profound role in controlling dynamically mantle temperatures. Present values for the averaged mantle heat production would yield objectionably high temperatures in the lower mantle.
Nonadiabatic exchange dynamics during adiabatic frequency sweeps
NASA Astrophysics Data System (ADS)
Barbara, Thomas M.
2016-04-01
A Bloch equation analysis that includes relaxation and exchange effects during an adiabatic frequency swept pulse is presented. For a large class of sweeps, relaxation can be incorporated using simple first order perturbation theory. For anisochronous exchange, new expressions are derived for exchange augmented rotating frame relaxation. For isochronous exchange between sites with distinct relaxation rate constants outside the extreme narrowing limit, simple criteria for adiabatic exchange are derived and demonstrate that frequency sweeps commonly in use may not be adiabatic with regard to exchange unless the exchange rates are much larger than the relaxation rates. Otherwise, accurate assessment of the sensitivity to exchange dynamics will require numerical integration of the rate equations. Examples of this situation are given for experimentally relevant parameters believed to hold for in-vivo tissue. These results are of significance in the study of exchange induced contrast in magnetic resonance imaging.
Novel developments and applications of the classical adiabatic dynamics technique
NASA Astrophysics Data System (ADS)
Rosso, Lula
The present work aims to apply and develop modern molecular dynamics techniques based on a novel analysis of the classical adiabatic dynamics approach. In the first part of this thesis, Car-Parrinello ab-initio molecular dynamics, a successful technique based on adiabatic dynamics, is used to study the charge transport mechanism in solid ammonium perchlorate (AP) crystal exposed to an ammonia-rich environment. AP is a solid-state proton conductor composed of NH+4 and ClO-4 units that can undergo a decomposition process at high temperature, leading to its use such as rocket fuel. After computing IR spectra and carefully analysing the dynamics at different temperatures, we found that the charge transport mechanism in the pure crystal is dominated by diffusion of the ammonium ions and that the translational diffusion is strongly coupled to rotational diffusion of the two types of ions present. When the pure ammonium-perchlorate crystal is doped with neutral ammonia, another mechanism comes into play, namely, the Grotthuss proton hopping mechanism via short-lived N2H+7 complexes. In the second part of this thesis, adiabatic dynamics will be used to develop an alternative approach to the calculation of free energy profiles along reaction paths. The new method (AFED) is based on the creation of an adiabatic separation between the reaction coordinate subspace and the remaining degrees of freedom within a molecular dynamics run. This is achieved by associating with the reaction coordinate(s) a high temperature and large mass. These conditions allow the activated process to occur while permitting the remaining degrees of freedom to respond adiabatically. In this limit, by applying a formal multiple time scale Liouville operator factorization, it can be rigorously shown that the free energy profile is obtained directly from the probability distribution of the reaction coordinate subspace and, therefore, no postprocessing of the output data is required. The new method is
Spontaneous emission in stimulated Raman adiabatic passage
Ivanov, P. A.; Vitanov, N. V.; Bergmann, K.
2005-11-15
This work explores the effect of spontaneous emission on the population transfer efficiency in stimulated Raman adiabatic passage (STIRAP). The approach uses adiabatic elimination of weakly coupled density matrix elements in the Liouville equation, from which a very accurate analytic approximation is derived. The loss of population transfer efficiency is found to decrease exponentially with the factor {omega}{sub 0}{sup 2}/{gamma}, where {gamma} is the spontaneous emission rate and {omega}{sub 0} is the peak Rabi frequency. The transfer efficiency increases with the pulse delay and reaches a steady value. For large pulse delay and large spontaneous emission rate STIRAP degenerates into optical pumping.
NASA Astrophysics Data System (ADS)
Chen, Zaigao; Wang, Jianguo; Wang, Yue
2016-09-01
The cathode plasma expansion has been widely investigated and is recognized as impedance collapse in a relativistic backward wave oscillator (RBWO). However, the process of formation and expansion of cathode plasma is very complicated, and the thickness of plasma is only several millimeters, so the simulation of cathode plasma requires high temporal and spatial resolutions. Only the scaled-down diode model and the thin gas layer model are considered in the previous hybrid simulation, and there are few numerical studies on the effect of cathode plasma expansion on the RBWO. In this paper, the moving-boundary conformal particle-in-cell method is proposed; the cathode plasma front is treated in this novel method as the actual cathode surface, and the explosive electron emission boundary moves as the expansion of cathode plasma. Moreover, in order to accurately simulate the electromagnetic field near the cathode surface, the conformal finite-difference time-domain method based on the enlarged cell technique is adopted. The numerical simulation indicates that the diode voltage decreases and the beam current increases as cathode plasma expands; when the cathode plasma velocity is 10 cm/μs, the pulse duration of the generated microwave decreases from 30 ns to 10 ns, the working frequency decreases from 9.83 GHz to 9.64 GHz, and the output power decreases 30% in the course of cathode plasma expansion.
NASA Astrophysics Data System (ADS)
Feller, David
2016-01-01
Benchmark quality adiabatic electron affinities for a collection of atoms and small molecules were obtained with the Feller-Peterson-Dixon composite coupled cluster theory method. Prior applications of this method demonstrated its ability to accurately predict atomization energies/heats of formation for more than 170 molecules. In the current work, the 1-particle expansion involved very large correlation consistent basis sets, ranging up to aug-cc-pV9Z (aug-cc-pV10Z for H and H2), with the goal of minimizing the residual basis set truncation error that must otherwise be approximated with extrapolation formulas. The n-particle expansion begins with coupled cluster calculations through iterative single and double excitations plus a quasiperturbative treatment of "connected" triple excitations (CCSD(T)) pushed to the complete basis set limit followed by CCSDT, CCSDTQ, or CCSDTQ5 corrections. Due to the small size of the systems examined here, it was possible in many cases to extend the n-particle expansion to the full configuration interaction wave function limit. Additional, smaller corrections associated with core/valence correlation, scalar relativity, anharmonic zero point vibrational energies, and non-adiabatic effects were also included. The overall root mean square (RMS) deviation was 0.005 eV (0.12 kcal/mol). This level of agreement was comparable to what was found with molecular heats of formation. A 95% confidence level corresponds to roughly twice the RMS value or 0.01 eV. While the atomic electron affinities are known experimentally to high accuracy, the molecular values are less certain. This contributes to the difficulty of gauging the accuracy of the theoretical results. A limited number of electron affinities were determined with the explicitly correlated CCSD(T)-F12b method. After extending the VnZ-F12 orbital basis sets with additional diffuse functions, the F12b method was found to accurately reproduce the best F/F- value obtained with standard
Feller, David
2016-01-01
Benchmark quality adiabatic electron affinities for a collection of atoms and small molecules were obtained with the Feller-Peterson-Dixon composite coupled cluster theory method. Prior applications of this method demonstrated its ability to accurately predict atomization energies/heats of formation for more than 170 molecules. In the current work, the 1-particle expansion involved very large correlation consistent basis sets, ranging up to aug-cc-pV9Z (aug-cc-pV10Z for H and H2), with the goal of minimizing the residual basis set truncation error that must otherwise be approximated with extrapolation formulas. The n-particle expansion begins with coupled cluster calculations through iterative single and double excitations plus a quasiperturbative treatment of "connected" triple excitations (CCSD(T)) pushed to the complete basis set limit followed by CCSDT, CCSDTQ, or CCSDTQ5 corrections. Due to the small size of the systems examined here, it was possible in many cases to extend the n-particle expansion to the full configuration interaction wave function limit. Additional, smaller corrections associated with core/valence correlation, scalar relativity, anharmonic zero point vibrational energies, and non-adiabatic effects were also included. The overall root mean square (RMS) deviation was 0.005 eV (0.12 kcal/mol). This level of agreement was comparable to what was found with molecular heats of formation. A 95% confidence level corresponds to roughly twice the RMS value or 0.01 eV. While the atomic electron affinities are known experimentally to high accuracy, the molecular values are less certain. This contributes to the difficulty of gauging the accuracy of the theoretical results. A limited number of electron affinities were determined with the explicitly correlated CCSD(T)-F12b method. After extending the VnZ-F12 orbital basis sets with additional diffuse functions, the F12b method was found to accurately reproduce the best F/F(-) value obtained with standard
Feller, David
2016-01-01
Benchmark quality adiabatic electron affinities for a collection of atoms and small molecules were obtained with the Feller-Peterson-Dixon composite coupled cluster theory method. Prior applications of this method demonstrated its ability to accurately predict atomization energies/heats of formation for more than 170 molecules. In the current work, the 1-particle expansion involved very large correlation consistent basis sets, ranging up to aug-cc-pV9Z (aug-cc-pV10Z for H and H2), with the goal of minimizing the residual basis set truncation error that must otherwise be approximated with extrapolation formulas. The n-particle expansion begins with coupled cluster calculations through iterative single and double excitations plus a quasiperturbative treatment of "connected" triple excitations (CCSD(T)) pushed to the complete basis set limit followed by CCSDT, CCSDTQ, or CCSDTQ5 corrections. Due to the small size of the systems examined here, it was possible in many cases to extend the n-particle expansion to the full configuration interaction wave function limit. Additional, smaller corrections associated with core/valence correlation, scalar relativity, anharmonic zero point vibrational energies, and non-adiabatic effects were also included. The overall root mean square (RMS) deviation was 0.005 eV (0.12 kcal/mol). This level of agreement was comparable to what was found with molecular heats of formation. A 95% confidence level corresponds to roughly twice the RMS value or 0.01 eV. While the atomic electron affinities are known experimentally to high accuracy, the molecular values are less certain. This contributes to the difficulty of gauging the accuracy of the theoretical results. A limited number of electron affinities were determined with the explicitly correlated CCSD(T)-F12b method. After extending the VnZ-F12 orbital basis sets with additional diffuse functions, the F12b method was found to accurately reproduce the best F/F(-) value obtained with standard
From free expansion to abrupt compression of an ideal gas
NASA Astrophysics Data System (ADS)
Anacleto, Joaquim; Pereira, Mário G.
2009-01-01
Using macroscopic thermodynamics, the general law for adiabatic processes carried out by an ideal gas was studied. It was shown that the process reversibility is characterized by the adiabatic reversibility coefficient r, in the range 0 <= r <= 1 for expansions and r >= 1 for compressions. The particular cases of free expansion and reversible adiabatic processes correspond to r = 0 and r = 1, respectively. To conclude the interpretation of r, the relation between r and the variation of the system entropy was also obtained. Comparison between this study and one restricted to expansions following a microscopic point of view showed not only equivalent interpretations but also that our approach is more general, since it also comprises compressions, provides an objective relation between r and entropy change and considers instantaneous varying values of the adiabatic reversibility coefficient. Finally, simulations of selected adiabatic processes are performed and numerical calculations of r are presented. This paper is intended primarily for the undergraduate student, although a comparison with the aforementioned work also requires a background in thermodynamics and kinetic theory.
Towards fault tolerant adiabatic quantum computation.
Lidar, Daniel A
2008-04-25
I show how to protect adiabatic quantum computation (AQC) against decoherence and certain control errors, using a hybrid methodology involving dynamical decoupling, subsystem and stabilizer codes, and energy gaps. Corresponding error bounds are derived. As an example, I show how to perform decoherence-protected AQC against local noise using at most two-body interactions.
Adiabatic Compression in a Fire Syringe.
ERIC Educational Resources Information Center
Hayn, Carl H.; Baird, Scott C.
1985-01-01
Suggests using better materials in fire syringes to obtain more effective results during demonstrations which show the elevation in temperature upon a very rapid (adiabatic) compression of air. Also describes an experiment (using ignition temperatures) which introduces students to the use of thermocouples for high temperature measurements. (DH)
Apparatus to Measure Adiabatic and Isothermal Processes.
ERIC Educational Resources Information Center
Lamb, D. W.; White, G. M.
1996-01-01
Describes a simple manual apparatus designed to serve as an effective demonstration of the differences between isothermal and adiabatic processes for the general or elementary physics student. Enables students to verify Boyle's law for slow processes and identify the departure from this law for rapid processes and can also be used to give a clear…
ATAT@WIEN2k: An interface for cluster expansion based on the linearized augmented planewave method
NASA Astrophysics Data System (ADS)
Chakraborty, Monodeep; Spitaler, Jürgen; Puschnig, Peter; Ambrosch-Draxl, Claudia
2010-05-01
We have developed an interface between the all-electron density functional theory code WIEN2k, and the MIT Ab-initio Phase Stability (MAPS) code of the Alloy-Theoretic Automated Toolkit (ATAT). WIEN2k is an implementation of the full-potential linearized augmented planewave method which yields highly accurate total energies and optimized geometries for any given structure. The ATAT package consists of two parts. The first one is the MAPS code, which constructs a cluster expansion (CE) in conjunction with a first-principles code. These results form the basis for the second part, which computes the thermodynamic properties of the alloy. The main task of the CE is to calculate the many-body potentials or effective cluster interactions (ECIs) from the first-principles total energies of different structures or supercells using the structure-inversion technique. By linking MAPS seamlessly with WIEN2k we have created a tool to obtain the ECIs for any lattice type of an alloy. We have chosen fcc Al-Ti and bcc W-Re to evaluate our implementation. Our calculated ECIs exhibit all features of a converged CE and compare well with literature results.
Giese, Timothy J.; York, Darrin M.
2010-01-01
We extend the Kohn–Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a “Jacob’s ladder” comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn–Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements. PMID:21197976
Giese, Timothy J; York, Darrin M
2010-12-28
We extend the Kohn-Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a "Jacob's ladder" comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn-Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.
Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics
NASA Astrophysics Data System (ADS)
Albert, Julian; Kaiser, Dustin; Engel, Volker
2016-05-01
Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion is treated on the same footing.
Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics.
Albert, Julian; Kaiser, Dustin; Engel, Volker
2016-05-01
Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion is treated on the same footing.
Shortcuts to adiabaticity in classical and quantum processes for scale-invariant driving
NASA Astrophysics Data System (ADS)
Deffner, Sebastian; Jarzynski, Christopher; Del Campo, Adolfo
2014-03-01
All real physical processes in classical as well as in quantum devices operate in finite-time. For most applications, however, adiabatic, i.e. infinitely-slow processes, are more favorable, as these do not cause unwanted, parasitic excitations. A shortcut to adiabaticity is a driving protocol which reproduces in a short time the same final state that would result from an adiabatic process. A particular powerful technique to engineer such shortcuts is transitionless quantum driving by means of counterdiabatic fields. However, determining closed form expressions for the counterdiabatic field has generally proven to be a daunting task. In this paper, we introduce a novel approach, with which we find the explicit form of the counterdiabatic driving field in arbitrary scale-invariant dynamical processes, encompassing expansions and transport. Our approach originates in the formalism of generating functions, and unifies previous approaches independently developed for classical and quantum systems. We show how this new approach allows to design shortcuts to adiabaticity for a large class of classical and quantum, single-particle, non-linear, and many-body systems. SD and CJ acknowledge support from the National Science Foundation (USA) under grant DMR-1206971. This research is further supported by the U.S Department of Energy through the LANL/LDRD Program and a LANL J. Robert Oppenheimer fellowship (AdC).
The dynamic instability of adiabatic blast waves
NASA Technical Reports Server (NTRS)
Ryu, Dongsu; Vishniac, Ethan T.
1991-01-01
Adiabatic blastwaves, which have a total energy injected from the center E varies as t(sup q) and propagate through a preshock medium with a density rho(sub E) varies as r(sup -omega) are described by a family of similarity solutions. Previous work has shown that adiabatic blastwaves with increasing or constant postshock entropy behind the shock front are susceptible to an oscillatory instability, caused by the difference between the nature of the forces on the two sides of the dense shell behind the shock front. This instability sets in if the dense postshock layer is sufficiently thin. The stability of adiabatic blastwaves with a decreasing postshock entropy is considered. Such blastwaves, if they are decelerating, always have a region behind the shock front which is subject to convection. Some accelerating blastwaves also have such region, depending on the values of q, omega, and gamma where gamma is the adiabatic index. However, since the shock interface stabilizes dynamically induced perturbations, blastwaves become convectively unstable only if the convective zone is localized around the origin or a contact discontinuity far from the shock front. On the other hand, the contact discontinuity of accelerating blastwaves is subject to a strong Rayleigh-Taylor instability. The frequency spectra of the nonradial, normal modes of adiabatic blastwaves have been calculated. The results have been applied to the shocks propagating through supernovae envelopes. It is shown that the metal/He and He/H interfaces are strongly unstable against the Rayleigh-Taylor instability. This instability will induce mixing in supernovae envelopes. In addition the implications of this work for the evolution of planetary nebulae is discussed.
Adiabatic burst evaporation from bicontinuous nanoporous membranes
Ichilmann, Sachar; Rücker, Kerstin; Haase, Markus; Enke, Dirk
2015-01-01
Evaporation of volatile liquids from nanoporous media with bicontinuous morphology and pore diameters of a few 10 nm is an ubiquitous process. For example, such drying processes occur during syntheses of nanoporous materials by sol–gel chemistry or by spinodal decomposition in the presence of solvents as well as during solution impregnation of nanoporous hosts with functional guests. It is commonly assumed that drying is endothermic and driven by non-equilibrium partial pressures of the evaporating species in the gas phase. We show that nearly half of the liquid evaporates in an adiabatic mode involving burst-like liquid-to-gas conversions. During single adiabatic burst evaporation events liquid volumes of up to 107 μm3 are converted to gas. The adiabatic liquid-to-gas conversions occur if air invasion fronts get unstable because of the built-up of high capillary pressures. Adiabatic evaporation bursts propagate avalanche-like through the nanopore systems until the air invasion fronts have reached new stable configurations. Adiabatic cavitation bursts thus compete with Haines jumps involving air invasion front relaxation by local liquid flow without enhanced mass transport out of the nanoporous medium and prevail if the mean pore diameter is in the range of a few 10 nm. The results reported here may help optimize membrane preparation via solvent-based approaches, solution-loading of nanopore systems with guest materials as well as routine use of nanoporous membranes with bicontinuous morphology and may contribute to better understanding of adsorption/desorption processes in nanoporous media. PMID:25926406
Expansion-cooled Lyman-alpha clouds
NASA Astrophysics Data System (ADS)
Duncan, Robert C.; Vishniac, Ethan T.; Ostriker, Jeremiah P.
1991-02-01
It is shown that recent observations by Pettini et al. (1990) which indicate that low-N H I Ly-alpha forest lines have small velocity widths and that the velocity widths are positively correlated with N (H I) can be understood as the result of adiabatic cooling of expanding clouds. It is argued that expansion cooling can efficiently lower temperatures and velocity widths of diffuse ionized clouds, and that this trend of diminishing temperature and velocity width in a wide range of plausible cloud models is consistent with double-quasar data. Expansion can provide a natural explanation for the steep z-evolution of the cloud numbers.
NASA Astrophysics Data System (ADS)
Tasbozan, Orkun; Çenesiz, Yücel; Kurt, Ali
2016-07-01
In this paper, the Jacobi elliptic function expansion method is proposed for the first time to construct the exact solutions of the time conformable fractional two-dimensional Boussinesq equation and the combined KdV-mKdV equation. New exact solutions are found. This method is based on Jacobi elliptic functions. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.
Expansion: A Plan for Success.
ERIC Educational Resources Information Center
Callahan, A.P.
This report provides selling brokers' guidelines for the successful expansion of their operations outlining a basic method of preparing an expansion plan. Topic headings are: The Pitfalls of Expansion (The Language of Business, Timely Financial Reporting, Regulatory Agencies of Government, Preoccupation with the Facade of Business, A Business Is a…
NASA Astrophysics Data System (ADS)
Hollenberg, Sebastian; Päs, Heinrich
2012-01-01
The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat such phenomena in a novel way, we propose a unified approach to both adiabatic and nonadiabatic two-flavor oscillations in neutrino ensembles with finite temperature and generic (e.g., matter) potentials. Neglecting effects of ensemble decoherence for now, we study the evolution of a neutrino ensemble governed by the associated quantum kinetic equations, which apply to systems with finite temperature. The quantum kinetic equations are solved formally using the Magnus expansion and it is shown that a convenient choice of the quantum mechanical picture (e.g., the interaction picture) reveals suitable parameters to characterize the physics of the underlying system (e.g., an effective oscillation length). It is understood that this method also provides a promising starting point for the treatment of the more general case in which decoherence is taken into account.
A simple method for one-loop renormalization in curved space-time
Markkanen, Tommi; Tranberg, Anders E-mail: anders.tranberg@uis.no
2013-08-01
We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.
Salt materials testing for a spacecraft adiabatic demagnetization refrigerator
NASA Astrophysics Data System (ADS)
Savage, M. L.; Kittel, P.; Roellig, T.
As part of a technology development effort to qualify adiabatic demagnetization refrigerators for use in a NASA spacecraft, such as the Space Infrared Telescope Facility, a study of low temperature characteristics, heat capacity and resistance to dehydration was conducted for different salt materials. This report includes results of testing with cerrous metaphosphate, several synthetic rubies, and chromic potassium alum (CPA). Preliminary results show that CPA may be suitable for long-term spacecraft use, provided that the salt is property encapsulated. Methods of salt pill construction and testing for all materials are discussed, as well as reliability tests. Also, the temperature regulation scheme and the test cryostat design are briefly discussed.
Magnetic shielding for a spaceborne adiabatic demagnetization refrigerator (ADR)
NASA Technical Reports Server (NTRS)
Warner, Brent A.; Shirron, Peter J.; Castles, Stephen H.; Serlemitsos, Aristides T.
1991-01-01
The Goddard Space Flight Center has studied magnetic shielding for an adiabatic demagnetization refrigerator. Four types of shielding were studied: active coils, passive ferromagnetic shells, passive superconducting coils, and passive superconducting shells. The passive superconducting shells failed by allowing flux penetration. The other three methods were successful, singly or together. Experimental studies of passive ferromagnetic shielding are compared with calculations made using the Poisson Group of programs, distributed by the Los Alamos Accelerator Code Group of the Los Alamos National Laboratory. Agreement between calculation and experiment is good. The ferromagnetic material is a silicon iron alloy.
Salt materials testing for a spacecraft adiabatic demagnetization refrigerator
NASA Technical Reports Server (NTRS)
Savage, M. L.; Kittel, P.; Roellig, T.
1990-01-01
As part of a technology development effort to qualify adiabatic demagnetization refrigerators for use in a NASA spacecraft, such as the Space Infrared Telescope Facility, a study of low temperature characteristics, heat capacity and resistance to dehydration was conducted for different salt materials. This report includes results of testing with cerrous metaphosphate, several synthetic rubies, and chromic potassium alum (CPA). Preliminary results show that CPA may be suitable for long-term spacecraft use, provided that the salt is property encapsulated. Methods of salt pill construction and testing for all materials are discussed, as well as reliability tests. Also, the temperature regulation scheme and the test cryostat design are briefly discussed.
Many-body effects on adiabatic passage through Feshbach resonances
NASA Astrophysics Data System (ADS)
Tikhonenkov, I.; Pazy, E.; Band, Y. B.; Fleischhauer, M.; Vardi, A.
2006-04-01
We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Γ on sweep rate α , into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law Γ∝α is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law Γ∝α1/3 is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.
Many-body effects on adiabatic passage through Feshbach resonances
Tikhonenkov, I.; Pazy, E.; Band, Y. B.; Vardi, A.; Fleischhauer, M.
2006-04-15
We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms {gamma} on sweep rate {alpha}, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law {gamma}{proportional_to}{alpha} is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law {gamma}{proportional_to}{alpha}{sup 1/3} is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.
Non-adiabatic perturbations in multi-component perfect fluids
Koshelev, N.A.
2011-04-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models.
Sullivan, P.; Eurek, K.; Margolis, R.
2014-07-01
Because solar power is a rapidly growing component of the electricity system, robust representations of solar technologies should be included in capacity-expansion models. This is a challenge because modeling the electricity system--and, in particular, modeling solar integration within that system--is a complex endeavor. This report highlights the major challenges of incorporating solar technologies into capacity-expansion models and shows examples of how specific models address those challenges. These challenges include modeling non-dispatchable technologies, determining which solar technologies to model, choosing a spatial resolution, incorporating a solar resource assessment, and accounting for solar generation variability and uncertainty.
Adiabatic quantum simulation of quantum chemistry.
Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán
2014-10-13
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
Trapped Ion Quantum Computation by Adiabatic Passage
Feng Xuni; Wu Chunfeng; Lai, C. H.; Oh, C. H.
2008-11-07
We propose a new universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-01
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Adiabatic Heating of Contracting Turbulent Fluids
NASA Astrophysics Data System (ADS)
Robertson, Brant; Goldreich, Peter
2012-05-01
Turbulence influences the behavior of many astrophysical systems, frequently by providing non-thermal pressure support through random bulk motions. Although turbulence is commonly studied in systems with constant volume and mean density, turbulent astrophysical gases often expand or contract under the influence of pressure or gravity. Here, we examine the behavior of turbulence in contracting volumes using idealized models of compressed gases. Employing numerical simulations and an analytical model, we identify a simple mechanism by which the turbulent motions of contracting gases "adiabatically heat," experiencing an increase in their random bulk velocities until the largest eddies in the gas circulate over a Hubble time of the contraction. Adiabatic heating provides a mechanism for sustaining turbulence in gases where no large-scale driving exists. We describe this mechanism in detail and discuss some potential applications to turbulence in astrophysical settings.
ADIABATIC HEATING OF CONTRACTING TURBULENT FLUIDS
Robertson, Brant; Goldreich, Peter
2012-05-10
Turbulence influences the behavior of many astrophysical systems, frequently by providing non-thermal pressure support through random bulk motions. Although turbulence is commonly studied in systems with constant volume and mean density, turbulent astrophysical gases often expand or contract under the influence of pressure or gravity. Here, we examine the behavior of turbulence in contracting volumes using idealized models of compressed gases. Employing numerical simulations and an analytical model, we identify a simple mechanism by which the turbulent motions of contracting gases 'adiabatically heat', experiencing an increase in their random bulk velocities until the largest eddies in the gas circulate over a Hubble time of the contraction. Adiabatic heating provides a mechanism for sustaining turbulence in gases where no large-scale driving exists. We describe this mechanism in detail and discuss some potential applications to turbulence in astrophysical settings.
Adiabatic Quantum Simulation of Quantum Chemistry
NASA Astrophysics Data System (ADS)
Babbush, Ryan; Love, Peter J.; Aspuru-Guzik, Alán
2014-10-01
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
Shortcuts to adiabaticity from linear response theory
Acconcia, Thiago V.; Bonança, Marcus V. S.; Deffner, Sebastian
2015-10-23
A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. Moreover, with the help of phenomenological response functions, a simple expression for the excess work is found—quantifying the nonequilibrium excitations. For two specific examples, i.e., the quantum parametric oscillator and the spin 1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. We finally propose a degenerate family of protocols, which facilitates shortcuts to adiabaticity for specific and very short driving times.
Shortcuts to adiabaticity from linear response theory
Acconcia, Thiago V.; Bonança, Marcus V. S.; Deffner, Sebastian
2015-10-23
A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. Moreover, with the help of phenomenological response functions, a simple expression for the excess work is found—quantifying the nonequilibrium excitations. For two specific examples, i.e., the quantum parametric oscillator and the spin 1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. We finally propose a degenerate family of protocols, which facilitates shortcuts tomore » adiabaticity for specific and very short driving times.« less
Siphon flows in isolated magnetic flux tubes. II - Adiabatic flows
NASA Technical Reports Server (NTRS)
Montesinos, Benjamin; Thomas, John H.
1989-01-01
This paper extends the study of steady siphon flows in isolated magnetic flux tubes surrounded by field-free gas to the case of adiabatic flows. The basic equations governing steady adiabatic siphon flows in a thin, isolated magnetic flux tube are summarized, and qualitative features of adiabatic flows in elevated, arched flux tubes are discussed. The equations are then cast in nondimensional form and the results of numerical computations of adiabatic siphon flows in arched flux tubes are presented along with comparisons between isothermal and adiabatic flows. The effects of making the interior of the flux tube hotter or colder than the surrounding atmosphere at the upstream footpoint of the arch is considered. In this case, is it found that the adiabatic flows are qualitatively similar to the isothermal flows, with adiabatic cooling producing quantitative differences. Critical flows can produce a bulge point in the rising part of the arch and a concentration of magnetic flux above the bulge point.
Siphon flows in isolated magnetic flux tubes. II. Adiabatic flows
Montesinos, B.; Thomas, J.H.
1989-02-01
This paper extends the study of steady siphon flows in isolated magnetic flux tubes surrounded by field-free gas to the case of adiabatic flows. The basic equations governing steady adiabatic siphon flows in a thin, isolated magnetic flux tube are summarized, and qualitative features of adiabatic flows in elevated, arched flux tubes are discussed. The equations are then cast in nondimensional form and the results of numerical computations of adiabatic siphon flows in arched flux tubes are presented along with comparisons between isothermal and adiabatic flows. The effects of making the interior of the flux tube hotter or colder than the surrounding atmosphere at the upstream footpoint of the arch is considered. In this case, is it found that the adiabatic flows are qualitatively similar to the isothermal flows, with adiabatic cooling producing quantitative differences. Critical flows can produce a bulge point in the rising part of the arch and a concentration of magnetic flux above the bulge point. 15 references.
Adiabatic Calorimetry as Support to the Certification of High-Purity Liquid Reference Materials
NASA Astrophysics Data System (ADS)
Baldan, A.; Bosma, R.; Peruzzi, A.; van der Veen, A. M. H.; Shimizu, Y.
2009-02-01
The certification of high-purity liquid reference materials is supported by several analytical techniques (e.g., gas chromatography, liquid chromatography, Karl Fischer coulometry, inductively coupled plasma mass spectrometry, differential scanning calorimetry, adiabatic calorimetry). Most of them provide information on a limited set of specific impurities present in the sample (indirect methods). Adiabatic calorimetry [1] complementarily provides the overall molar fraction of impurities with sensitivity down to few μmol · mol-1 without giving any information about the nature of the impurities present in the sample (direct method). As the combination of adiabatic calorimetry with one (or more than one) indirect chemical techniques was regarded as an optimal methodology, NMi VSL developed an adiabatic calorimetry facility for the purity determination of high-purity liquid reference materials [2]. Within the framework of collaboration with NMIJ, a benzene-certified reference material (NMIJ CRM 4002) from NMIJ was analyzed by adiabatic calorimetry at NMi VSL. The results of this measurement are reported in this paper. Good agreement with the NMIJ-certified purity value (99.992 ± 0.003) cmol · mol-1 was found. The influence of different data analysis approaches (e.g., extrapolation functions, melting ranges) on the measurement results is reported. The uncertainty of the measured purity was estimated.
Computer Code For Turbocompounded Adiabatic Diesel Engine
NASA Technical Reports Server (NTRS)
Assanis, D. N.; Heywood, J. B.
1988-01-01
Computer simulation developed to study advantages of increased exhaust enthalpy in adiabatic turbocompounded diesel engine. Subsytems of conceptual engine include compressor, reciprocator, turbocharger turbine, compounded turbine, ducting, and heat exchangers. Focus of simulation of total system is to define transfers of mass and energy, including release and transfer of heat and transfer of work in each subsystem, and relationship among subsystems. Written in FORTRAN IV.
Adiabatic charging of nickel-hydrogen batteries
NASA Astrophysics Data System (ADS)
Lurie, Chuck; Foroozan, S.; Brewer, Jeff; Jackson, Lorna
1995-02-01
Battery management during prelaunch activities has always required special attention and careful planning. The transition from nickel-cadium to nickel-hydrogen batteries, with their high self discharge rate and lower charge efficiency, as well as longer prelaunch scenarios, has made this aspect of spacecraft battery management even more challenging. The AXAF-I Program requires high battery state of charge at launch. The use of active cooling, to ensure efficient charging, was considered and proved to be difficult and expensive. Alternative approaches were evaluated. Optimized charging, in the absence of cooling, appeared promising and was investigated. Initial testing was conducted to demonstrate the feasibility of the 'Adiabatic Charging' approach. Feasibility was demonstrated and additional testing performed to provide a quantitative, parametric data base. The assumption that the battery is in an adiabatic environment during prelaunch charging is a conservative approximation because the battery will transfer some heat to its surroundings by convective air cooling. The amount is small compared to the heat dissipated during battery overcharge. Because the battery has a large thermal mass, substantial overcharge can occur before the cells get too hot to charge efficiently. The testing presented here simulates a true adiabatic environment. Accordingly the data base may be slightly conservative. The adiabatic charge methodology used in this investigation begins with stabilizing the cell at a given starting temperature. The cell is then fully insulated on all sides. Battery temperature is carefully monitored and the charge terminated when the cell temperature reaches 85 F. Charging has been evaluated with starting temperatures from 55 to 75 F.
Advanced Adiabatic Demagnetization Refrigerators for Continuous Cooling
NASA Technical Reports Server (NTRS)
Chu, Paul C. W.
2004-01-01
The research at Houston was focused on optimizing the design of superconducting magnets for advanced adiabatic demagnetization refrigerators (ADRs), assessing the feasibility of using high temperature superconducting (HTS) magnets in ADRs in the future, and developing techniques to deposit HTS thin and thick films on high strength, low thermal conductivity substrates for HTS magnet leads. Several approaches have been tested for the suggested superconducting magnets.
Random matrix model of adiabatic quantum computing
Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.
2005-05-15
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of random matrix theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances - i.e., those having a critical ratio of clauses to variables - the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to nonadiabatic Landau-Zener-type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size.
Anderson, Robert C.; Jones, Jack M.; Kollie, Thomas G.
1982-01-01
The present invention is directed to the fabrication of an article of uranium-2.4 wt. % niobium alloy in which the linear thermal expansion in the direction transverse to the extrusion direction is less than about 0.98% between 22.degree. C. and 600.degree. C. which corresponds to a value greater than the 1.04% provided by previous extrusion operations over the same temperature range. The article with the improved thermal expansion possesses a yield strength at 0.2% offset of at least 400 MPa, an ultimate tensile strength of 1050 MPa, a compressive yield strength of at least 0.2% offset of at least 675 MPa, and an elongation of at least 25% over 25.4 mm/sec. To provide this article with the improved thermal expansion, the uranium alloy billet is heated to 630.degree. C. and extruded in the alpha phase through a die with a reduction ratio of at least 8.4:1 at a ram speed no greater than 6.8 mm/sec. These critical extrusion parameters provide the article with the desired decrease in the linear thermal expansion while maintaining the selected mechanical properties without encountering crystal disruption in the article.
Influence of viscosity and the adiabatic index on planetary migration
NASA Astrophysics Data System (ADS)
Bitsch, B.; Boley, A.; Kley, W.
2013-02-01
Context. The strength and direction of migration of low mass embedded planets depends on the disk's thermodynamic state. It has been shown that in active disks, where the internal dissipation is balanced by radiative transport, migration can be directed outwards, a process which extends the lifetime of growing embryos. Very important parameters determining the structure of disks, and hence the direction of migration, are the viscosity and the adiabatic index. Aims: In this paper we investigate the influence of different viscosity prescriptions (α-type and constant) and adiabatic indices on disk structures. We then determine how this affects the migration rate of planets embedded in such disks. Methods: We perform three-dimensional numerical simulations of accretion disks with embedded planets. We use the explicit/implicit hydrodynamical code NIRVANA that includes full tensor viscosity and radiation transport in the flux-limited diffusion approximation, as well as a proper equation of state for molecular hydrogen. The migration of embedded 20 MEarth planets is studied. Results: Low-viscosity disks have cooler temperatures and the migration rates of embedded planets tend toward the isothermal limit. Hence, in these disks, planets migrate inwards even in the fully radiative case. The effect of outward migration can only be sustained if the viscosity in the disk is large. Overall, the differences between the treatments for the equation of state seem to play a more important role in disks with higher viscosity. A change in the adiabatic index and in the viscosity changes the zero-torque radius that separates inward from outward migration. Conclusions: For larger viscosities, temperatures in the disk become higher and the zero-torque radius moves to larger radii, allowing outward migration of a 20-MEarth planet to persist over an extended radial range. In combination with large disk masses, this may allow for an extended period of the outward migration of growing
Vibrational dynamics of the bifluoride ion. II. Adiabatic separation and proton dynamics
NASA Astrophysics Data System (ADS)
Epa, V. C.; Thorson, W. R.
1990-01-01
Vibrational dynamics of the bifluoride ion FHF-, which exhibits strongly anharmonic and nonseparable vibrations, is studied using the extended ab initio model potential surface described in the first paper of this series. Adiabatic separation of the proton motion from the F-F (ν1) motion forms a zero-order basis for description, although strong coupling of adiabatic states by the ν1 motion is important in higher vibrational levels and must be considered to understand the spectrum. The adiabatic protonic eigenstates at F-F separations R from 3.75 to 6.40 a.u. have been determined using the self-consistent field approximation in prolate spheroidal coordinates to provide a basis set for configuration interaction expansion of the exact eigenstates. 78 SCF eigenstates (21 σg, 21 σu, 21 πu, and 15 πg) were computed by ``exact'' numerical solution of the SCF equations. The adiabatic CI eigenstates are shown to be converged in energy to better than 1.0 cm-1 for the ground state of each symmetry type and usually better than 10 cm-1 for the lowest three to five states, and pass critical tests of accuracy such as the Hellmann-Feynman theorem. The resulting CI potential energy curves closely resemble corresponding SCF energy curves and justify the concept of mode separation even in this very anharmonic system. The adiabatic CI potential energy curves explain most aspects of the dynamics relevant to the IR and Raman spectra of FHF- (e.g., in KHF2), and calculations of ν1 dynamics within the adiabatic approximation suffice to assign most of the observed IR spectrum of KHF2(s) (to about 6000 cm-1). States corresponding qualitatively to modal overtone and combination levels such as 3ν2 and (ν2+2ν3) however exhibit avoided crossings in the neighborhood of the equilibrium configuration and ``Fermi resonance'' involving interactions of two or more such adiabatic states via the ν1 motion must be treated by close-coupling to predict both frequencies and intensities in the
Selective excitation in a three-state system using a hybrid adiabatic-nonadiabatic interaction
NASA Astrophysics Data System (ADS)
Song, Yunheung; Lee, Han-gyeol; Jo, Hanlae; Ahn, Jaewook
2016-08-01
The chirped-pulse interaction in the adiabatic coupling regime induces cyclic permutations of the energy states of a three-level system in the V -type configuration, which process is known as the three-level chirped rapid adiabatic passage (RAP). Here we show that a spectral hole in a chirped pulse can turn on or off the level mixing at adiabatic crossing points of this process, reducing the system to an effective two-level system. The given hybrid adiabatic-nonadiabatic transition enables selective excitation of the three-level system, controlled by the laser intensity and spectral position of the hole, as well as the sign of the chirp parameter. Experiments performed with shaped femtosecond laser pulses and the three lowest energy levels (5 S1 /2 , 5 P1 /2 , and 5 P3 /2 ) of atomic rubidium (Rb) show good agreement with the theoretically analyzed dynamics. The result indicates that our method, when being combined with the ordinary chirped RAP, implements an adiabatic transition between the Raman-coupled excited states. Furthermore, our laser intensity-dependent control may have applications including selective excitations of atoms or ions arranged in space when being used in conjunction with laser beam profile programming.
NASA Astrophysics Data System (ADS)
Hofmann, C.; Zimmermann, T.; Zielinski, A.; Landsman, A. S.
2016-04-01
The validity of the adiabatic approximation in strong field ionization under typical experimental conditions has recently become a topic of great interest. Experimental results have been inconclusive, in part, due to the uncertainty in experimental calibration of intensity. Here we turn to the time-dependent Schrödinger equation, where all the laser parameters are known exactly. We find that the centre of the electron momentum distribution (typically used for calibration of elliptically and circularly polarized light) is sensitive to non-adiabatic effects, leading to intensity shifts in experimental data that can significantly affect the interpretation of results. On the other hand, the transverse momentum spread in the plane of polarization is relatively insensitive to such effects, even in the Keldysh parameter regime approaching γ ≈ 3. This suggests the transverse momentum spread in the plane of polarization as a good alternative to the usual calibration method, particularly for experimental investigation of non-adiabatic effects using circularly polarized light.
NASA Technical Reports Server (NTRS)
Xu, Y. J.; Khandelwal, G. S.; Wilson, John W.
1989-01-01
A simple formula for the transition probability for electron exchange between unlike ions and atoms is established within the adiabatic approximation by employing the Linear Combination of Atomic Orbitals (LCAO) method. The formula also involves an adiabatic parameter, introduced by Massey, and thus the difficulties arising from the internal energy defect and the adiabatic approximation are avoided. Specific reactions Li(+++) + H to Li(++) + H(+) and Be(4+) + H to Be(3+) + H(+) are considered as examples. The calculated capture cross section results of the present work are compared with the experimental data and with the calculation of other authors over the velocity range of 10(7) cm/sec to 10(8) cm/sec.
Determination of the spin torque non-adiabaticity in perpendicularly magnetized nanowires.
Heinen, J; Hinzke, D; Boulle, O; Malinowski, G; Swagten, H J M; Koopmans, B; Ulysse, C; Faini, G; Ocker, B; Wrona, J; Kläui, M
2012-01-18
Novel nanofabrication methods and the discovery of an efficient manipulation of local magnetization based on spin polarized currents has generated a tremendous interest in the field of spintronics. The search for materials allowing for fast domain wall dynamics requires fundamental research into the effects involved (Oersted fields, adiabatic and non-adiabatic spin torque, Joule heating) and possibilities for a quantitative comparison. Theoretical descriptions reveal a material and geometry dependence of the non-adiabaticity factor β, which governs the domain wall velocity. Here, we present two independent approaches for determining β: (i) measuring the dependence of the dwell times for which a domain wall stays in a metastable pinning state on the injected current and (ii) the current-field equivalence approach. The comparison of the deduced β values highlights the problems of using one-dimensional models to describe two-dimensional dynamics and allows us to ascertain the reliability, robustness and limits of the approaches used. PMID:22172802
NASA Astrophysics Data System (ADS)
González, Leticia; Kröner, Dominik; Solá, Ignacio R.
2001-08-01
Different strategies to separate enantiomers from a racemate using analytical laser pulses in the ultraviolet frequency domain are proposed for the prototype model system H2POSH. Wave-packet propagations on ab initio ground- and electronic-excited state potentials show that it is possible to produce 100% of enantiomeric excess in a sub-picosecond time scale using a sequence of π and half-π pulses. Alternatively, the previous transitions can be substituted by adiabatic counterparts, using chirped laser pulses and a half-STIRAP (stimulated Raman adiabatic passage) method which only transfers half of the population between appropriate levels. Such an overall adiabatic mechanism gains stability concerning the pulse areas and frequencies at the expense of introducing new control variables, like the chirp and time delay.
High Energy Signatures of POST Adiabatic Supernova Remnants
NASA Astrophysics Data System (ADS)
Telezhinsky, Igor; Hnatyk, Bohdan
Between the well-known adiabatic and radiative stages of the Supernova remnant (SNR) evolution there is, in fact, a transition stage with a duration comparable to the duration of adiabatic one. Physical existence of the transition stage is motivated by cooling of some part of the downstream hot gas with formation of a thin cold shell that is joined to a shell of swept up interstellar medium (ISM). We give an approximate analytical method for full hydrodynamical description of the transition stage. On its base we investigate the evolution of X-ray and γ-ray radiation during this stage. It is shown that formation of a dense shell during the transition stage is accompanied by the decrease of X-ray luminosity because of hot gas cooling and increase of gamma-ray flux according to the increase of target proton density and CR energy in the newly born shell. The role of nonuniformity of ISM and its influence on the high energy fluxes from the SNRs is also discussed.
Shortcut to adiabaticity in full-wave optics for ultra-compact waveguide junctions
NASA Astrophysics Data System (ADS)
Della Valle, Giuseppe; Perozziello, Gerardo; Longhi, Stefano
2016-09-01
We extend the concept of shortcuts to adiabaticity to full-wave optics and provide an application to the design of an ultra-compact waveguide junction. In particular, we introduce a procedure allowing one to synthesize a purely dielectric optical potential that precisely compensates for non-adiabatic losses of the transverse electric fundamental mode in any (sufficiently regular) two-dimensional waveguide junction. Our results are corroborated by finite-element method numerical simulations in a Pöschl–Teller waveguide mode expander.
Towards disentangling coupled electronic-vibrational dynamics in ultrafast non-adiabatic processes
Blanchet; Lochbrunner; Schmitt; Shaffer; Larsen; Zgierski; Seideman; Stolow
2000-01-01
Femtosecond time-resolved photoelectron spectroscopy is emerging as a new technique for investigating polyatomic excited state dynamics. Due to the sensitivity of photoelectron spectroscopy to both electronic configurations and vibrational dynamics, it is well suited to the study of non-adiabatic processes such as internal conversion, which often occur on sub-picosecond time scales. We discuss the technical requirements for such experiments, including lasers systems, energy- and angle-resolved photoelectron spectrometers and new detectors for coincidence experiments. We present a few examples of these methods applied to problems in diatomic wavepacket dynamics and ultrafast non-adiabatic processes in polyatomic molecules.
NASA Astrophysics Data System (ADS)
Fishman, S.; Soffer, A.
2016-07-01
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.
Pfaffian statistics through adiabatic transport in the 1D coherent state representation.
Seidel, Alexander
2008-11-01
Recent work has shown that the low energy sector of certain quantum Hall states is adiabatically connected to simple charge-density-wave patterns that appear, e.g., when the system is deformed into a thin torus. Here it is shown that the patterns emerging in this limit already determine the non-Abelian statistics of the nu=1 Moore-Read state. Aside from the knowledge of these patterns, the method only relies on the principle of adiabatic continuity, the effectively noncommutative geometry in a strong magnetic field, and topological as well as locality arguments.
Bond selective chemistry beyond the adiabatic approximation
Butler, L.J.
1993-12-01
One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.
Cosmological consequences of an adiabatic matter creation process
NASA Astrophysics Data System (ADS)
Nunes, Rafael C.; Pan, Supriya
2016-06-01
In this paper, we investigate the cosmological consequences of a continuous matter creation associated with the production of particles by the gravitational field acting on the quantum vacuum. To illustrate this, three phenomenological models are considered. An equivalent scalar field description is presented for each models. The effects on the cosmic microwave background power spectrum are analysed for the first time in the context of adiabatic matter creation cosmology. Further, we introduce a model independent treatment, Om, which depends only on the Hubble expansion rate and the cosmological redshift to distinguish any cosmological model from Λ cold dark matter by providing a null test for the cosmological constant, meaning that, for any two redshifts z1, z2, Om(z) is same, i.e. Om(z1) - Om(z2) = 0. Also, this diagnostic can differentiate between several cosmological models by indicating their quintessential/phantom behaviour without knowing the accurate value of the matter density, and the present value of the Hubble parameter. For our models, we find that particle production rate is inversely proportional to Om. Finally, the validity of the generalized second law of thermodynamics bounded by the apparent horizon has been examined.
NASA Astrophysics Data System (ADS)
Sakaguchi, Toshimasa; Fujigaki, Motoharu; Murata, Yorinobu
2015-03-01
Accurate and wide-range shape measurement method is required in industrial field. The same technique is possible to be used for a shape measurement of a human body for the garment industry. Compact 3D shape measurement equipment is also required for embedding in the inspection system. A shape measurement by a phase shifting method can measure the shape with high spatial resolution because the coordinates can be obtained pixel by pixel. A key-device to develop compact equipment is a grating projector. Authors developed a linear LED projector and proposed a light source stepping method (LSSM) using the linear LED projector. The shape measurement euipment can be produced with low-cost and compact without any phase-shifting mechanical systems by using this method. Also it enables us to measure 3D shape in very short time by switching the light sources quickly. A phase unwrapping method is necessary to widen the measurement range with constant accuracy for phase shifting method. A general phase unwrapping method with difference grating pitches is often used. It is one of a simple phase unwrapping method. It is, however, difficult to apply the conventional phase unwrapping algorithm to the LSSM. Authors, therefore, developed an expansion unwrapping algorithm for the LSSM. In this paper, an expansion algorithm of measurement range suited for 3D shape measurement using two pitches of projected grating with the LSSM was evaluated.
Generalized Ramsey numbers through adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
Phase avalanches in near-adiabatic evolutions
Vertesi, T.; Englman, R.
2006-02-15
In the course of slow, nearly adiabatic motion of a system, relative changes in the slowness can cause abrupt and high magnitude phase changes, ''phase avalanches,'' superimposed on the ordinary geometric phases. The generality of this effect is examined for arbitrary Hamiltonians and multicomponent (>2) wave packets and is found to be connected (through the Blaschke term in the theory of analytic signals) to amplitude zeros in the lower half of the complex time plane. Motion on a nonmaximal circle on the Poincare-sphere suppresses the effect. A spectroscopic transition experiment can independently verify the phase-avalanche magnitudes.
Local entanglement generation in the adiabatic regime
Cliche, M.; Veitia, Andrzej
2010-09-15
We study entanglement generation in a pair of qubits interacting with an initially correlated system. Using time-independent perturbation theory and the adiabatic theorem, we show conditions under which the qubits become entangled as the joint system evolves into the ground state of the interacting theory. We then apply these results to the case of qubits interacting with a scalar quantum field. We study three different variations of this setup; a quantum field subject to Dirichlet boundary conditions, a quantum field interacting with a classical potential, and a quantum field that starts in a thermal state.
Gravothermal Expansion in N-Body Systems
NASA Astrophysics Data System (ADS)
Endoh, Hitoshi; Fukushige, Toshiyuki; Makino, Junichiro
1997-06-01
We investigated whether gravothermal expansion occurs in N-body systems. As the most idealized case, we studied the evolution of an N-body system in a spherical adiabatic wall which is initially in thermal equilibrium. Such a system is thermodynamically unstable if the central density is more than 709 times higher than the density just inside the wall. We performed simulation of a 2048-body system with and without artificial perturbations. We found that gravothermal expansion took place as well as gravothermal contraction. Whether gravothermal expansion occurs or not is determined by the perturbation or statistical fluctuation on the temperature structure in the initial model. The results were compared with that of a self-gravitating gas system.
Work distribution for the adiabatic compression of a dilute and interacting classical gas.
Crooks, Gavin E; Jarzynski, Christopher
2007-02-01
We consider a simple, physically motivated model of a dilute classical gas of interacting particles, initially equilibrated with a heat bath, undergoing adiabatic and quasistatic compression or expansion. This provides an example of a thermodynamic process for which non-Gaussian work fluctuations can be computed exactly from microscopic principles. We find that the work performed during this process is described statistically by a gamma distribution, and we use this result to show that the model satisfies the nonequilibrium work and fluctuation theorems, but not a prediction based on linear response theory.
Mode-expanded semiconductor laser with tapered-rib adiabatic-following fiber coupler
Vawter, G.A.; Smith, R.E.; Hou, H.; Wendt, J.R.
1996-12-01
Expanded-mode semiconductor lasers are of great interest due to the benefits of reduced far-field divergence and improved coupling efficiency to optical fiber. The authors present a new diode laser using a Tapered-Rib Adiabatic-Following Fiber Coupler (TRAFFiC) to achieve 2D mode expansion without epitaxial regrowth or sharply-defined tips on tapered waveguides. The expanded mode size would allow 0.25 to 1 dB coupling loss to standard telecommunications fiber making smaller-core specialty fibers unnecessary, increasing misalignment tolerance, and eliminating the need for coupling optics.
NASA Astrophysics Data System (ADS)
Ivanov, V. A.
2010-12-01
The possibility of ensuring equivalence in operation and efficiency of real cycles with intermediate cooling (heating) and isothermal-adiabatic compressions (expansion) in ideal simple cycles formed on the T- S diagrams in the second stage of real cycles. The possibility of using the equivalence of cycles for determining the maximum efficiency of operation of real cycles is demonstrated.
Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics
Hoover, W.G.
1980-05-28
Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility.
Adiabatic cooling of solar wind electrons
NASA Technical Reports Server (NTRS)
Sandbaek, Ornulf; Leer, Egil
1992-01-01
In thermally driven winds emanating from regions in the solar corona with base electron densities of n0 not less than 10 exp 8/cu cm, a substantial fraction of the heat conductive flux from the base is transfered into flow energy by the pressure gradient force. The adiabatic cooling of the electrons causes the electron temperature profile to fall off more rapidly than in heat conduction dominated flows. Alfven waves of solar origin, accelerating the basically thermally driven solar wind, lead to an increased mass flux and enhanced adiabatic cooling. The reduction in electron temperature may be significant also in the subsonic region of the flow and lead to a moderate increase of solar wind mass flux with increasing Alfven wave amplitude. In the solar wind model presented here the Alfven wave energy flux per unit mass is larger than that in models where the temperature in the subsonic flow is not reduced by the wave, and consequently the asymptotic flow speed is higher.
Kovalchuk, V. I.; Kozlovsky, I. V.; Tartakovsky, V. K.
2011-05-15
A method for solving Faddeev equations in configuration space for a bound state and a continuous spectrum of the system of three nucleons was developed on the basis of expansions in K harmonics. Coulomb interaction and particle spins were not taken into account in this study. The method in question was used to describe the triton bound state and differential cross sections for neutron-deuteron scattering at subthreshold incident-neutron energies. The Volkov, Malfliet-Tjon, and Eikemeier-Hackenbroich local nucleon-nucleon potentials were employed in the present calculations.
NASA Technical Reports Server (NTRS)
Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.
1998-01-01
We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.
NASA Astrophysics Data System (ADS)
Hamazaki, Takashi
2011-07-01
In the full nonlinear cosmological perturbation theory in the leading order of the gradient expansion, all the types of the gauge invariant perturbation variables are defined. The metric junction conditions across the spacelike transition hypersurface are formulated in a manifestly gauge invariant manner. It is manifestly shown that all the physical laws such as the evolution equations, the constraint equations, and the junction conditions can be written using the gauge invariant variables which we defined only. Based on the existence of the universal adiabatic growing mode in the nonlinear perturbation theory and the ρ philosophy where the physical evolution are described using the energy density ρ as the evolution parameter, we give the definitions of the adiabatic perturbation variable and the entropic perturbation variables in the full nonlinear perturbation theory. In order to give the analytic order estimate of the nonlinear parameter fNL, we present the exponent evaluation method. As the models where fNL changes continuously and becomes large, using the ρ philosophy, we investigate the non-Gaussianity induced by the entropic perturbation of the component which does not govern the cosmic energy density, and we show that in order to obtain the significant non-Gaussianity it is necessary that the scalar field which supports the entropic perturbation is extremely small compared with the scalar field which supports the adiabatic perturbation.
NASA Astrophysics Data System (ADS)
Mandrà, Salvatore; Guerreschi, Gian Giacomo; Aspuru-Guzik, Alán
2015-12-01
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the minimum energy gap encountered during the dynamics. Unfortunately, the direct calculation of the gap is strongly limited by the exponential growth in the dimensionality of the Hilbert space associated to the quantum system. Although many special-purpose methods have been devised to reduce the effective dimensionality, they are strongly limited to particular classes of problems with evident symmetries. Moreover, little is known about the computational power of adiabatic quantum optimizers in real-world conditions. Here we propose and implement a general purposes reduction method that does not rely on any explicit symmetry and which requires, under certain general conditions, only a polynomial amount of classical resources. Thanks to this method, we are able to analyze the performance of "nonideal" quantum adiabatic optimizers to solve the well-known Grover problem, namely the search of target entries in an unsorted database, in the presence of discrete local defects. In this case, we show that adiabatic quantum optimization, even if affected by random noise, is still potentially faster than any classical algorithm.
Gao, Jiali; Wang, Yingjie
2012-02-21
A fragment-based variational many-body (VMB) expansion method is described to directly account for exchange repulsion, charge delocalization (charge transfer) and dispersion interactions in the explicit polarization (X-Pol) method. The present VMB/X-Pol approach differs from other fragment molecular orbital (FMO) techniques in two major aspects. First, the wave function for the monomeric system is variationally optimized using standard X-Pol method, as opposed to the iterative update procedure adopted in FMO. Second, the mutual polarizations in the dimeric terms are also variationally determined, whereas single-point energy calculations of the individual dimers embedded in a static monomer field are used in FMO. The second-order (two-body) VMB (VMB2) expansion method is illustrated on a series of water hexamer complexes and one decamer cluster, making use of Hartree-Fock theory, MP2, and the PBE1 and M06 density functionals to represent the monomer and dimer fragments. The computed binding energies are within 2 kcal/mol of the corresponding results from fully delocalized calculations. Energy decomposition analyses reveal specific dimeric contributions to exchange repulsion, charge delocalization, and dispersion. Since the wave functions for one-body and all two-body terms are variationally optimized in VMB2 and X-Pol, it is straightforward to obtain analytic gradient without the additional coupled-perturbed Hartree-Fock step. Thus, the method can be useful for molecular dynamics simulations.
Wigner phase space distribution via classical adiabatic switching
Bose, Amartya; Makri, Nancy
2015-09-21
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.
Accelerating the loop expansion
Ingermanson, R.
1986-07-29
This thesis introduces a new non-perturbative technique into quantum field theory. To illustrate the method, I analyze the much-studied phi/sup 4/ theory in two dimensions. As a prelude, I first show that the Hartree approximation is easy to obtain from the calculation of the one-loop effective potential by a simple modification of the propagator that does not affect the perturbative renormalization procedure. A further modification then susggests itself, which has the same nice property, and which automatically yields a convex effective potential. I then show that both of these modifications extend naturally to higher orders in the derivative expansion of the effective action and to higher orders in the loop-expansion. The net effect is to re-sum the perturbation series for the effective action as a systematic ''accelerated'' non-perturbative expansion. Each term in the accelerated expansion corresponds to an infinite number of terms in the original series. Each term can be computed explicitly, albeit numerically. Many numerical graphs of the various approximations to the first two terms in the derivative expansion are given. I discuss the reliability of the results and the problem of spontaneous symmetry-breaking, as well as some potential applications to more interesting field theories. 40 refs.
Novel Foraminal Expansion Technique
Senturk, Salim; Ciplak, Mert; Oktenoglu, Tunc; Sasani, Mehdi; Egemen, Emrah; Yaman, Onur; Suzer, Tuncer
2016-01-01
The technique we describe was developed for cervical foraminal stenosis for cases in which a keyhole foraminotomy would not be effective. Many cervical stenosis cases are so severe that keyhole foraminotomy is not successful. However, the technique outlined in this study provides adequate enlargement of an entire cervical foraminal diameter. This study reports on a novel foraminal expansion technique. Linear drilling was performed in the middle of the facet joint. A small bone graft was placed between the divided lateral masses after distraction. A lateral mass stabilization was performed with screws and rods following the expansion procedure. A cervical foramen was linearly drilled medially to laterally, then expanded with small bone grafts, and a lateral mass instrumentation was added with surgery. The patient was well after the surgery. The novel foraminal expansion is an effective surgical method for severe foraminal stenosis. PMID:27559460
Novel Foraminal Expansion Technique.
Ozer, Ali Fahir; Senturk, Salim; Ciplak, Mert; Oktenoglu, Tunc; Sasani, Mehdi; Egemen, Emrah; Yaman, Onur; Suzer, Tuncer
2016-08-01
The technique we describe was developed for cervical foraminal stenosis for cases in which a keyhole foraminotomy would not be effective. Many cervical stenosis cases are so severe that keyhole foraminotomy is not successful. However, the technique outlined in this study provides adequate enlargement of an entire cervical foraminal diameter. This study reports on a novel foraminal expansion technique. Linear drilling was performed in the middle of the facet joint. A small bone graft was placed between the divided lateral masses after distraction. A lateral mass stabilization was performed with screws and rods following the expansion procedure. A cervical foramen was linearly drilled medially to laterally, then expanded with small bone grafts, and a lateral mass instrumentation was added with surgery. The patient was well after the surgery. The novel foraminal expansion is an effective surgical method for severe foraminal stenosis. PMID:27559460
Novel Foraminal Expansion Technique.
Ozer, Ali Fahir; Senturk, Salim; Ciplak, Mert; Oktenoglu, Tunc; Sasani, Mehdi; Egemen, Emrah; Yaman, Onur; Suzer, Tuncer
2016-08-01
The technique we describe was developed for cervical foraminal stenosis for cases in which a keyhole foraminotomy would not be effective. Many cervical stenosis cases are so severe that keyhole foraminotomy is not successful. However, the technique outlined in this study provides adequate enlargement of an entire cervical foraminal diameter. This study reports on a novel foraminal expansion technique. Linear drilling was performed in the middle of the facet joint. A small bone graft was placed between the divided lateral masses after distraction. A lateral mass stabilization was performed with screws and rods following the expansion procedure. A cervical foramen was linearly drilled medially to laterally, then expanded with small bone grafts, and a lateral mass instrumentation was added with surgery. The patient was well after the surgery. The novel foraminal expansion is an effective surgical method for severe foraminal stenosis.
NASA Astrophysics Data System (ADS)
Wang, Jintao; Liu, Ziyong; Xu, Changhong; Li, Zhanhong
2014-07-01
The accurate measurement on the compressibility and thermal expansion coefficients of density standard liquid at 2329kg/m3 (DSL-2329) plays an important role in the quality control for silicon single crystal manufacturing. A new method is developed based on hydrostatic suspension principle in order to determine the two coefficients with high measurement accuracy. Two silicon single crystal samples with known density are immersed into a sealed vessel full of DSL-2329. The density of liquid is adjusted with varying liquid temperature and static pressure, so that the hydrostatic suspension of two silicon single crystal samples is achieved. The compression and thermal expansion coefficients are then calculated by using the data of temperature and static pressure at the suspension state. One silicon single crystal sample can be suspended at different state, as long as the liquid temperature and static pressure function linearly according to a certain mathematical relationship. A hydrostatic suspension experimental system is devised with the maximal temperature control error ±50 μK; Silicon single crystal samples can be suspended by adapting the pressure following the PID method. By using the method based on hydrostatic suspension principle, the two key coefficients can be measured at the same time, and measurement precision can be improved due to avoiding the influence of liquid surface tension. This method was further validated experimentally, where the mixture of 1, 2, 3-tribromopropane and 1,2-dibromoethane is used as DSL-2329. The compressibility and thermal expansion coefficients were measured, as 8.5×10-4 K-1 and 5.4×1010 Pa-1, respectively.
Adiabatic invariants in stellar dynamics. 1: Basic concepts
NASA Technical Reports Server (NTRS)
Weinberg, Martin D.
1994-01-01
The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results that precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. The mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.
Vertical and adiabatic electronic excitations in biphenylene: A theoretical study
NASA Astrophysics Data System (ADS)
Beck, M. E.; Rebentisch, R.; Hohlneicher, G.; Fülscher, M. P.; Serrano-Andrés, L.; Roos, B. O.
1997-12-01
The low-lying singlet states of biphenylene have been studied using ab initio methods. Vertical excitation energies were calculated by multiconfigurational perturbation theory (CASPT2), starting from a complete active space self-consistent field (CASSCF) reference. The geometries of the most important low-lying excited states were individually optimized at the CASSCF level to study the difference between vertical and adiabatic excitations. Extended atomic natural orbital (ANO)-type basis sets were used to calculate state energies. Geometry optimizations were done with smaller ANO-type basis sets. Excitations from the ground state to the 1 1B3g and 1 1B2u excited singlet states lead to pronounced geometry changes which alter the bond alternation pattern. The theoretical results provide a solid basis for the assignment and interpretation of experimental spectra.
Perspective: Stimulated Raman adiabatic passage: The status after 25 years
NASA Astrophysics Data System (ADS)
Bergmann, Klaas; Vitanov, Nikolay V.; Shore, Bruce W.
2015-05-01
The first presentation of the STIRAP (stimulated Raman adiabatic passage) technique with proper theoretical foundation and convincing experimental data appeared 25 years ago, in the May 1st, 1990 issue of The Journal of Chemical Physics. By now, the STIRAP concept has been successfully applied in many different fields of physics, chemistry, and beyond. In this article, we comment briefly on the initial motivation of the work, namely, the study of reaction dynamics of vibrationally excited small molecules, and how this initial idea led to the documented success. We proceed by providing a brief discussion of the physics of STIRAP and how the method was developed over the years, before discussing a few examples from the amazingly wide range of applications which STIRAP now enjoys, with the aim to stimulate further use of the concept. Finally, we mention some promising future directions.
Laser-nucleus interactions: The quasi-adiabatic regime
NASA Astrophysics Data System (ADS)
Pálffy, Adriana; Buss, Oliver; Hoefer, Axel; Weidenmüller, Hans A.
2015-10-01
The interaction between nuclei and a strong zeptosecond laser pulse with coherent MeV photons is investigated theoretically. We provide a first semiquantitative study of the quasi-adiabatic regime where the photon absorption rate is comparable to the nuclear equilibration rate. In that regime, multiple photon absorption leads to the formation of a compound nucleus in the so-far unexplored regime of excitation energies several hundred MeV above the yrast line. The temporal dynamics of the process is investigated by means of a set of master equations that account for dipole absorption, stimulated dipole emission, neutron decay, and induced fission in a chain of nuclei. That set is solved numerically by means of state-of-the-art matrix exponential methods also used in nuclear fuel burn-up and radioactivity transport calculations. Our quantitative estimates predict the excitation path and range of nuclei reached by neutron decay and provide relevant information for the layout of future experiments.
The Adiabatic Invariance of the Action Variable in Classical Dynamics
ERIC Educational Resources Information Center
Wells, Clive G.; Siklos, Stephen T. C.
2007-01-01
We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We present a new proof of the adiabatic invariance of this quantity and illustrate our arguments by means of…
Generation of atomic NOON states via shortcuts to adiabatic passage
NASA Astrophysics Data System (ADS)
Song, Chong; Su, Shi-Lei; Bai, Cheng-Hua; Ji, Xin; Zhang, Shou
2016-10-01
Based on Lewis-Riesenfeld invariants and quantum Zeno dynamics, we propose an effective scheme for generating atomic NOON states via shortcuts to adiabatic passage. The photon losses are efficiently suppressed by engineering shortcuts to adiabatic passage in the scheme. The numerical simulation shows that the atomic NOON states can be generated with high fidelity.
Kinetic Theory Derivation of the Adiabatic Law for Ideal Gases.
ERIC Educational Resources Information Center
Sobel, Michael I.
1980-01-01
Discusses how the adiabatic law for ideal gases can be derived from the assumption of a Maxwell-Boltzmann (or any other) distribution of velocities--in contrast to the usual derivations from thermodynamics alone, and the higher-order effect that leads to one-body viscosity. An elementary derivation of the adiabatic law is given. (Author/DS)
Adiabat-shaping in indirect drive inertial confinement fusion
Baker, K. L.; Robey, H. F.; Milovich, J. L.; Jones, O. S.; Smalyuk, V. A.; Casey, D. T.; MacPhee, A. G.; Pak, A.; Celliers, P. M.; Clark, D. S.; Landen, O. L.; Peterson, J. L.; Berzak-Hopkins, L. F.; Weber, C. R.; Haan, S. W.; Döppner, T. D.; Dixit, S.; Hamza, A. V.; Jancaitis, K. S.; Kroll, J. J.; and others
2015-05-15
Adiabat-shaping techniques were investigated in indirect drive inertial confinement fusion experiments on the National Ignition Facility as a means to improve implosion stability, while still maintaining a low adiabat in the fuel. Adiabat-shaping was accomplished in these indirect drive experiments by altering the ratio of the picket and trough energies in the laser pulse shape, thus driving a decaying first shock in the ablator. This decaying first shock is designed to place the ablation front on a high adiabat while keeping the fuel on a low adiabat. These experiments were conducted using the keyhole experimental platform for both three and four shock laser pulses. This platform enabled direct measurement of the shock velocities driven in the glow-discharge polymer capsule and in the liquid deuterium, the surrogate fuel for a DT ignition target. The measured shock velocities and radiation drive histories are compared to previous three and four shock laser pulses. This comparison indicates that in the case of adiabat shaping the ablation front initially drives a high shock velocity, and therefore, a high shock pressure and adiabat. The shock then decays as it travels through the ablator to pressures similar to the original low-adiabat pulses when it reaches the fuel. This approach takes advantage of initial high ablation velocity, which favors stability, and high-compression, which favors high stagnation pressures.
Shelley, Brandon C.; Gowing, Geneviève; Svendsen, Clive N.
2014-01-01
A cell expansion technique to amass large numbers of cells from a single specimen for research experiments and clinical trials would greatly benefit the stem cell community. Many current expansion methods are laborious and costly, and those involving complete dissociation may cause several stem and progenitor cell types to undergo differentiation or early senescence. To overcome these problems, we have developed an automated mechanical passaging method referred to as “chopping” that is simple and inexpensive. This technique avoids chemical or enzymatic dissociation into single cells and instead allows for the large-scale expansion of suspended, spheroid cultures that maintain constant cell/cell contact. The chopping method has primarily been used for fetal brain-derived neural progenitor cells or neurospheres, and has recently been published for use with neural stem cells derived from embryonic and induced pluripotent stem cells. The procedure involves seeding neurospheres onto a tissue culture Petri dish and subsequently passing a sharp, sterile blade through the cells effectively automating the tedious process of manually mechanically dissociating each sphere. Suspending cells in culture provides a favorable surface area-to-volume ratio; as over 500,000 cells can be grown within a single neurosphere of less than 0.5 mm in diameter. In one T175 flask, over 50 million cells can grow in suspension cultures compared to only 15 million in adherent cultures. Importantly, the chopping procedure has been used under current good manufacturing practice (cGMP), permitting mass quantity production of clinical-grade cell products. PMID:24962813
An adiabatic demagnetization refrigerator for SIRTF
NASA Technical Reports Server (NTRS)
Timbie, P. T.; Bernstein, G. M.; Richards, P. L.
1989-01-01
An adiabatic demagnetization refrigerator (ADR) has been proposed to cool bolometric infrared detectors on the multiband imaging photometer of the Space Infrared Telescope Facility (SIRTF). One such refrigerator has been built which uses a ferric ammonium alum salt pill suspended by nylon threads in a 3-T solenoid. The resonant modes of this suspension are above 100 Hz. The heat leak to the salt pill is less than 0.5 microW. The system has a hold time at 0.1K of more than 12 h. The cold stage temperature is regulated with a feedback loop that controls the magnetic field. A second, similar refrigerator is being built at a SIRTF prototype to fly on a ballon-borne telescope. It will use a ferromagnetic shield. The possibility of using a high-Tc solenoid-actuated heat switch is also discussed.
An adiabatic demagnetization refrigerator for SIRTF
Timbie, P.T.; Bernstein, G.M.; Richards, P.L.
1989-02-01
An adiabatic demagnetization refrigerator (ADR) has been proposed to cool bolometric infrared detectors on the Multiband Imaging Photometer of the Space Infrared Telescope Facility (SIRTF). The authors have built one such refrigerator which employs a ferric ammonium alum salt pill suspended by nylon threads in a 3 Tesla solenoid. The resonant modes of this suspension are above 100 Hz. The heat leak to the salt pill is <0.5 ..mu..W. The system has a hold time at 0.1 /sup 0/K of >12 hours. The cold stage temperature is regulated with a feedback loop that controls the magnetic field. A second, similar refrigerator is being built as a SIRTF prototype to fly on a balloon-borne telescope. It will employ a ferromagnetic shield. The possibility of using high T/sub c/ leads to the superconducting magnet and a solenoid-actuated heat switch are also discussed.
The HAWC and SAFIRE Adiabatic Demagnetization Refrigerators
NASA Technical Reports Server (NTRS)
Tuttle, Jim; Shirron, Peter; DiPirro, Michael; Jackson, Michael; Behr, Jason; Kunes, Evan; Hait, Tom; Krebs, Carolyn (Technical Monitor)
2001-01-01
The High-Resolution Airborne Wide-band Camera (HAWC) and Submillimeter and Far Infrared Experiment (SAFIRE) are far-infrared experiments which will fly on the Stratospheric Observatory for Infrared Astronomy (SOFIA) aircraft. HAWC's detectors will operate at 0.2 Kelvin, while those of SAFIRE will be at 0.1 Kelvin. Each instrument will include an adiabatic demagnetization refrigerator (ADR) to cool its detector stage from the liquid helium bath temperature (HAWC's at 4.2 Kelvin and SAFIRE's pumped to about 1.3 Kelvin) to its operating temperature. Except for the magnets used to achieve the cooling and a slight difference in the heat switch design, the two ADRs are nearly identical. We describe the ADR design and present the results of performance testing.
Number Partitioning via Quantum Adiabatic Computation
NASA Technical Reports Server (NTRS)
Smelyanskiy, Vadim N.; Toussaint, Udo; Clancy, Daniel (Technical Monitor)
2002-01-01
We study both analytically and numerically the complexity of the adiabatic quantum evolution algorithm applied to random instances of combinatorial optimization problems. We use as an example the NP-complete set partition problem and obtain an asymptotic expression for the minimal gap separating the ground and exited states of a system during the execution of the algorithm. We show that for computationally hard problem instances the size of the minimal gap scales exponentially with the problem size. This result is in qualitative agreement with the direct numerical simulation of the algorithm for small instances of the set partition problem. We describe the statistical properties of the optimization problem that are responsible for the exponential behavior of the algorithm.
Differential topology of adiabatically controlled quantum processes
NASA Astrophysics Data System (ADS)
Jonckheere, Edmond A.; Rezakhani, Ali T.; Ahmad, Farooq
2013-03-01
It is shown that in a controlled adiabatic homotopy between two Hamiltonians, H 0 and H 1, the gap or "anti-crossing" phenomenon can be viewed as the development of cusps and swallow tails in the region of the complex plane where two critical value curves of the quadratic map associated with the numerical range of H 0 + i H 1 come close. The "near crossing" in the energy level plots happens to be a generic situation, in the sense that a crossing is a manifestation of the quadratic numerical range map being unstable in the sense of differential topology. The stable singularities that can develop are identified and it is shown that they could occur near the gap, making those singularities of paramount importance. Various applications, including the quantum random walk, are provided to illustrate this theory.
Quantum Adiabatic Optimization and Combinatorial Landscapes
NASA Technical Reports Server (NTRS)
Smelyanskiy, V. N.; Knysh, S.; Morris, R. D.
2003-01-01
In this paper we analyze the performance of the Quantum Adiabatic Evolution (QAE) algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma = M / N. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (verses only energy) is used, and are able to show the existence of a dynamic threshold gamma = gammad, beyond which QAE should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz.
Adiabatic connection at negative coupling strengths
Seidl, Michael; Gori-Giorgi, Paola
2010-01-15
The adiabatic connection of density functional theory (DFT) for electronic systems is generalized here to negative values of the coupling strength alpha (with attractive electrons). In the extreme limit alpha->-infinity a simple physical solution is presented and its implications for DFT (as well as its limitations) are discussed. For two-electron systems (a case in which the present solution can be calculated exactly), we find that an interpolation between the limit alpha->-infinity and the opposite limit of infinitely strong repulsion (alpha->+infinity) yields a rather accurate estimate of the second-order correlation energy E{sub c}{sup GL2}[rho] for several different densities rho, without using virtual orbitals. The same procedure is also applied to the Be isoelectronic series, analyzing the effects of near degeneracy.
Sliding seal materials for adiabatic engines
NASA Technical Reports Server (NTRS)
Lankford, J.
1985-01-01
The sliding friction coefficients and wear rates of promising carbide, oxide, and nitride materials were measured under temperature, environmental, velocity, loading conditions that are representative of the adiabatic engine environment. In order to provide guidance needed to improve materials for this application, the program stressed fundamental understanding of the mechanisms involved in friction and wear. Microhardness tests were performed on the candidate materials at elevated temperatures, and in atmospheres relevant to the piston seal application, and optical and electron microscopy were used to elucidate the micromechanisms of wear following wear testing. X-ray spectroscopy was used to evaluate interface/environment interactions which seemed to be important in the friction and wear process. Electrical effects in the friction and wear processes were explored in order to evaluate the potential usefulness of such effects in modifying the friction and wear rates in service. However, this factor was found to be of negligible significance in controlling friction and wear.
Adiabatic theory for anisotropic cold molecule collisions
Pawlak, Mariusz; Shagam, Yuval; Narevicius, Edvardas; Moiseyev, Nimrod
2015-08-21
We developed an adiabatic theory for cold anisotropic collisions between slow atoms and cold molecules. It enables us to investigate the importance of the couplings between the projection states of the rotational motion of the atom about the molecular axis of the diatom. We tested our theory using the recent results from the Penning ionization reaction experiment {sup 4}He(1s2s {sup 3}S) + HD(1s{sup 2}) → {sup 4}He(1s{sup 2}) + HD{sup +}(1s) + e{sup −} [Lavert-Ofir et al., Nat. Chem. 6, 332 (2014)] and demonstrated that the couplings have strong effect on positions of shape resonances. The theory we derived provides cross sections which are in a very good agreement with the experimental findings.
An integrated programming and development environment for adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Humble, T. S.; McCaskey, A. J.; Bennink, R. S.; Billings, J. J.; DʼAzevedo, E. F.; Sullivan, B. D.; Klymko, C. F.; Seddiqi, H.
2014-01-01
Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware has raised challenging questions about how to evaluate adiabatic quantum optimization (AQO) programs. Processor behavior depends on multiple steps to synthesize an adiabatic quantum program, which are each highly tunable. We present an integrated programming and development environment for AQO called Jade Adiabatic Development Environment (JADE) that provides control over all the steps taken during program synthesis. JADE captures the workflow needed to rigorously specify the AQO algorithm while allowing a variety of problem types, programming techniques, and processor configurations. We have also integrated JADE with a quantum simulation engine that enables program profiling using numerical calculation. The computational engine supports plug-ins for simulation methodologies tailored to various metrics and computing resources. We present the design, integration, and deployment of JADE and discuss its potential use for benchmarking AQO programs by the quantum computer science community.
An Integrated Development Environment for Adiabatic Quantum Programming
Humble, Travis S; McCaskey, Alex; Bennink, Ryan S; Billings, Jay Jay; D'Azevedo, Eduardo; Sullivan, Blair D; Klymko, Christine F; Seddiqi, Hadayat
2014-01-01
Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware raises the question of how well quantum programs perform. Benchmarking behavior is challenging since the multiple steps to synthesize an adiabatic quantum program are highly tunable. We present an adiabatic quantum programming environment called JADE that provides control over all the steps taken during program development. JADE captures the workflow needed to rigorously benchmark performance while also allowing a variety of problem types, programming techniques, and processor configurations. We have also integrated JADE with a quantum simulation engine that enables program profiling using numerical calculation. The computational engine supports plug-ins for simulation methodologies tailored to various metrics and computing resources. We present the design, integration, and deployment of JADE and discuss its use for benchmarking adiabatic quantum programs.
Gubler, Philipp; Yamamoto, Naoki; Hatsuda, Tetsuo; Nishida, Yusuke
2015-05-15
Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.
Mareschi, Katia; Rustichelli, Deborah; Calabrese, Roberto; Gunetti, Monica; Sanavio, Fiorella; Castiglia, Sara; Risso, Alessandra; Ferrero, Ivana; Tarella, Corrado; Fagioli, Franca
2012-01-01
Mesenchymal stem cells (MSCs) are a promising source for cell therapy due to their pluripotency and immunomodulant proprieties. As the identification of “optimal” conditions is important to identify a standard procedure for clinical use. Percoll, Ficoll and whole bone marrow directly plated were tested from the same sample as separation methods. The cells were seeded at the following densities: 100 000, 10 000, 1000, 100, 10 cells/cm2. After reaching confluence, the cells were detached, pooled and re-plated at 1000, 500, 100, and 10 cells/cm2. Statistical analyses were performed. Cumulative Population Doublings (PD) did not show significant differences for the separation methods and seeding densities but only for the plating density. Some small quantity samples plated in T25 flasks at plating densities of 10 and 100 cells/cm2 did not produce any expansion. However, directly plated whole bone marrow resulted in a more advantageous method in terms of CFU-F number, cellular growth and minimal manipulation. No differences were observed in terms of gross morphology, differentiation potential or immunophenotype. These data suggest that plating whole bone marrow at a low cellular density may represent a good procedure for MSC expansion for clinical use. PMID:23715383
Mareschi, Katia; Rustichelli, Deborah; Calabrese, Roberto; Gunetti, Monica; Sanavio, Fiorella; Castiglia, Sara; Risso, Alessandra; Ferrero, Ivana; Tarella, Corrado; Fagioli, Franca
2012-01-01
Mesenchymal stem cells (MSCs) are a promising source for cell therapy due to their pluripotency and immunomodulant proprieties. As the identification of "optimal" conditions is important to identify a standard procedure for clinical use. Percoll, Ficoll and whole bone marrow directly plated were tested from the same sample as separation methods. The cells were seeded at the following densities: 100 000, 10 000, 1000, 100, 10 cells/cm(2). After reaching confluence, the cells were detached, pooled and re-plated at 1000, 500, 100, and 10 cells/cm(2). Statistical analyses were performed. Cumulative Population Doublings (PD) did not show significant differences for the separation methods and seeding densities but only for the plating density. Some small quantity samples plated in T25 flasks at plating densities of 10 and 100 cells/cm(2) did not produce any expansion. However, directly plated whole bone marrow resulted in a more advantageous method in terms of CFU-F number, cellular growth and minimal manipulation. No differences were observed in terms of gross morphology, differentiation potential or immunophenotype. These data suggest that plating whole bone marrow at a low cellular density may represent a good procedure for MSC expansion for clinical use.
The two-piston problem revisited: Generalization from reversible to irreversible expansion
NASA Astrophysics Data System (ADS)
Anacleto, Joaquim; Anacleto, Joaquim Alberto C.; Ferreira, J. M.
2011-10-01
We discuss the adiabatic two-piston problem for an ideal gas confined between two pistons of equal mass and extend recent work based on the reversible approximation. More realistic equations that account for the roles of the gas temperature and particle mass are applied to extend the analysis of the expansion of the gas from reversible to irreversible behavior to the limit of free expansion. The evolution of quantities, such as temperature, piston speed, adiabatic reversibility coefficients, and entropy, is obtained, and differences between the irreversible and the reversible solutions are investigated.
Adiabatic pulse propagation in coherent atomic media with the tripod level configuration
Mazets, I.E.
2005-02-01
We investigate the problem of propagation of three-component resonant light pulses with adiabatically varying amplitudes through a medium consisting of atoms with the tripod level configuration. By means of both analytic and numerical methods we find the two modes of shape-preserving pulse propagation. The pulse propagation velocity of the fast mode is equal to the speed of light in vacuum, whereas the group velocity of the other (slow) mode is significantly slowed down. These two modes represent a general asymptotic solution of the problem of adiabatic pulse propagation, i.e., a pulse of any shape, which is consistent with the adiabaticity conditions, and a finite duration evolves at large propagation distances (and, correspondingly, at large times of interaction with the medium) to a well-separated pair of fast and slow pulses. The experimental requirements for adiabatic pulse propagation in a tripod medium are similar to that needed for observation of slow light propagation in a medium with the {lambda} configuration of levels. However, the tripod scheme offers a different possibility, which is absent in the {lambda}-medium case: collisions of fast and slow pulses. It is found numerically that after such a collision the shapes of the pulses change, so these pulses do not match the classical definition of a soliton.
Stark-shift-chirped rapid-adiabatic-passage technique among three states
Rangelov, A. A.; Vitanov, N. V.; Yatsenko, L. P.; Shore, B. W.; Halfmann, T.; Bergmann, K.
2005-11-15
We show that the technique of Stark-chirped rapid adiabatic passage (SCRAP), hitherto used for complete population transfer between two quantum states, offers a simple and robust method for complete population transfer amongst three states in atoms and molecules. In this case SCRAP uses three laser pulses: a strong far-off-resonant pulse modifies the transition frequencies by inducing dynamic Stark shifts and thereby creating time-dependent level crossings amongst the three diabatic states, while near-resonant and moderately strong pump and Stokes pulses, appropriately offset in time, drive the population between the initial and final states via adiabatic passage. The population transfer efficiency is robust to variations in the intensities of the lasers, as long as these intensities are sufficiently large to enforce adiabatic evolution. With suitable pulse timings the population in the (possibly decaying) intermediate state can be minimized, as with stimulated Raman adiabatic passage (STIRAP). This technique applies to one-photon as well as multiphoton transitions and it is also applicable to media exhibiting inhomogeneous broadening; these features represent clear advantages over STIRAP by overcoming the inevitable dynamical Stark shifts that accompany multiphoton transitions as well as unwanted detunings, e.g., induced by Doppler shifts.
Phase relations and adiabats in boiling seafloor geothermal systems
Bischoff, J.L.; Pitzer, Kenneth S.
1985-01-01
Observations of large salinity variations and vent temperatures in the range of 380-400??C suggest that boiling or two-phase separation may be occurring in some seafloor geothermal systems. Consideration of flow rates and the relatively small differences in density between vapors and liquids at the supercritical pressures at depth in these systems suggests that boiling is occurring under closed-system conditions. Salinity and temperature of boiling vents can be used to estimate the pressure-temperature point in the subsurface at which liquid seawater first reached the two-phase boundary. Data are reviewed to construct phase diagrams of coexisting brines and vapors in the two-phase region at pressures corresponding to those of the seafloor geothermal systems. A method is developed for calculating the enthalpy and entropy of the coexisting mixtures, and results are used to construct adiabats from the seafloor to the P-T two-phase boundary. Results for seafloor vents discharging at 2300 m below sea level indicate that a 385??C vent is composed of a brine (7% NaCl equivalent) in equilibrium with a vapor (0.1% NaCl). Brine constitutes 45% by weight of the mixture, and the fluid first boiled at approximately 1 km below the seafloor at 415??C, 330 bar. A 400??C vent is primarily vapor (88 wt.%, 0.044% NaCl) with a small amount of brine (26% NaCl) and first boiled at 2.9 km below the seafloor at 500??C, 520 bar. These results show that adiabatic decompression in the two-phase region results in dramatic cooling of the fluid mixture when there is a large fraction of vapor. ?? 1985.
Kropf, Pascal; Shmuel, Amir
2016-07-01
Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested
Kropf, Pascal; Shmuel, Amir
2016-07-01
Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested
Regimes of expansion of a collisional plasma into a vacuum
NASA Astrophysics Data System (ADS)
Thaury, C.; Mora, P.; Adam, J. C.; Héron, A.
2009-09-01
The effect of elastic Coulomb collisions on the one-dimensional expansion of a plasma slab is studied in the classical limit, using an electrostatic particle-in-cell code. Two regimes of interest are identified. For a collision rate of few hundreds of the inverse of the expansion characteristic time τe, the electron distribution function remains isotropic and Maxwellian with a homogeneous temperature, during all the expansion. In this case, the expansion can be approached by a three-dimensional version of the hybrid model developed by Mora [P. Mora, Phys. Rev. E 72, 056401 (2005)]. When the collision rate becomes somewhat greater than 104τe-1, the plasma is divided in two parts: an inner part which expands adiabatically as an ideal gas and an outer part which undergoes an isothermal expansion.
NASA Astrophysics Data System (ADS)
Kumar, Rajinder; Nivarthi, Sriram S.; Davis, H. Ted; Kroll, D. M.; Maier, Robert S.
1999-11-01
The lattice-Boltzmann (LB) method, derived from lattice gas automata, is a relatively new technique for studying transport problems. The LB method is investigated for its accuracy to study fluid dynamics and dispersion problems. Two problems of relevance to flow and dispersion in porous media are addressed: (i) Poiseuille flow between parallel plates (which is analogous to flow in pore throats in two-dimensional porous networks), and (ii) flow through an expansion-contraction geometry (which is analogous to flow in pore bodies in two-dimensional porous networks). The results obtained from the LB simulations are compared with analytical solutions when available, and with solutions obtained from a finite element code (FIDAP) when analytical results are not available. Excellent agreement is found between the LB results and the analytical/FIDAP solutions in most cases, indicating the utility of the lattice-Boltzmann method for solving fluid dynamics and dispersion problems. Copyright
NASA Astrophysics Data System (ADS)
Tala-Tebue, E.; Tsobgni-Fozap, D. C.; Kenfack-Jiotsa, A.; Kofane, T. C.
2014-06-01
Using the Jacobi elliptic functions and the alternative ( G'/ G-expansion method including the generalized Riccati equation, we derive exact soliton solutions for a discrete nonlinear electrical transmission line in (2+1) dimension. More precisely, these methods are general as they lead us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines. This study seeks to show that it is not often necessary to transform the equation of the network into a well-known differential equation before finding its solutions. The solutions obtained by the current methods are generalized periodic solutions of nonlinear equations. The shape of solutions can be well controlled by adjusting the parameters of the network. These exact solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data.
Adiabatic and diabatic invariants in ion-molecule reactions.
Lorquet, J C
2009-12-28
A point charge interacting with a dipole (either induced or permanent) constitutes a completely integrable dynamical subsystem characterized by three first integrals of the motion (E, p(phi), and either l(2) or a Hamilton-Jacobi separation constant beta). An ion-molecule reaction (capture or fragmentation) can be seen as an interaction between such a subsystem and a bath of oscillators. This interaction is a perturbation that destroys some of the first integrals. However, the perturbation depends on the separation between the fragments and the destruction is gradual. The mathematical simplicity of the long-range electrostatic interaction potential leads to useful simplifications. A first-order perturbation treatment based on the structured and regular nature of the multipole expansion is presented. The separating integrals valid in the asymptotic limit are found to subsist at intermediate distances, although in a weaker form. As the reaction coordinate decreases, i.e., as the fragments approach, the asymptotic range is followed by an outer region where (i) the azimuthal momentum p(phi) remains a constant of the motion; (ii) the square angular momentum l(2) or the separation constant beta transform into a diabatic invariant in regions of phase space characterized by a high value of the translational momentum p(r); (iii) for low values of p(r), it is advantageous to use the action integral contour integral(p(theta)d theta), which is an adiabatic invariant. The conditions under which an effective potential obtained by adding centrifugal repulsion to an electrostatic attractive term can be validly constructed are specified. In short, the dynamics of ion-molecule interactions is still regular in parts of phase space corresponding to a range of the reaction coordinate where the interaction potential deviates from its asymptotic shape. PMID:20059072
Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation.
Zamstein, Noa; Tannor, David J
2012-12-14
We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)] to treat non-adiabatic transitions. Each trajectory evolves on a single surface according to Newton's laws with complex positions and momenta. The transfer of amplitude between surfaces stems naturally from the equations of motion, without the need for surface hopping. In this paper we derive the equations of motion and show results in the diabatic representation, which is rarely used in trajectory methods for calculating non-adiabatic dynamics. We apply our method to the first two benchmark models introduced by Tully [J. Chem. Phys. 93, 1061 (1990)]. Besides giving the probability branching ratios between the surfaces, the method also allows the reconstruction of the time-dependent wavepacket. Our results are in quantitative agreement with converged quantum mechanical calculations.
Effects of EOS adiabat on hot spot dynamics
NASA Astrophysics Data System (ADS)
Cheng, Baolian; Kwan, Thomas; Wang, Yi-Ming; Batha, Steven
2013-10-01
Equation of state (EOS) and adiabat of the pusher play significant roles in the dynamics and formation of the hot spot of an ignition capsule. For given imploding energy, they uniquely determine the partition of internal energy, mass, and volume between the pusher and the hot spot. In this work, we apply the new scaling laws recently derived by Cheng et al. to the National Ignition Campaign (NIC) ignition capsules and study the impacts of EOS and adiabat of the pusher on the hot spot dynamics by using the EOS adiabat index as an adjustable model parameter. We compare our analysis with the NIC data, specifically, for shots N120321 and N120205, and with the numerical simulations of these shots. The predictions from our theoretical model are in good agreements with the NIC data when a hot adiabat was used for the pusher, and with code simulations when a cold adiabat was used for the pusher. Our analysis indicates that the actual adiabat of the pusher in NIC experiments may well be higher than the adiabat assumed in the simulations. This analysis provides a physical and systematic explanation to the ongoing disagreements between the NIC experimental results and the multi-dimensional numerical simulations. This work was performed under the auspices of the U.S. Department of Energy by the Los Alamos National Laboratory under contract number W-7405-ENG-36.
Optimality of partial adiabatic search and its circuit model
NASA Astrophysics Data System (ADS)
Mei, Ying; Sun, Jie; Lu, Songfeng; Gao, Chao
2014-08-01
In this paper, we first uncover a fact that a partial adiabatic quantum search with time complexity is in fact optimal, in which is the total number of elements in an unstructured database, and () of them are the marked ones(one) . We then discuss how to implement a partial adiabatic search algorithm on the quantum circuit model. From the implementing procedure on the circuit model, we can find out that the approximating steps needed are always in the same order of the time complexity of the adiabatic algorithm.
Adiabatic control of atomic dressed states for transport and sensing
NASA Astrophysics Data System (ADS)
Cooper, N. R.; Rey, A. M.
2015-08-01
We describe forms of adiabatic transport that arise for dressed-state atoms in optical lattices. Focusing on the limit of weak tunnel-coupling between nearest-neighbor lattice sites, we explain how adiabatic variation of optical dressing allows control of atomic motion between lattice sites: allowing adiabatic particle transport in a direction that depends on the internal state, and force measurements via spectroscopic preparation and readout. For uniformly filled bands these systems display topologically quantized particle transport. An implementation of the dressing scheme using optical transitions in alkaline-earth atoms is discussed as well as its favorable features for precise force sensing.
NASA Technical Reports Server (NTRS)
Yos, William T. (Inventor); Cantrell, John H., Jr. (Inventor)
2004-01-01
A method and apparatus for measuring changes in intracranial pressure (ICP) utilizing the variation of the surface wave propagation parameters of the patient's skull to determine the change in ICP. In one embodiment, the method comprises the steps of transmitting an ultrasonic bulk compressional wave onto the surface of the skull at a predetermined angle with respect to the skull so as to produce a surface wave, receiving the surface wave at an angle with respect tn the skull which is substantially the same as the predetermined angle and at a location that is a predetermined distance from where the ultrasonic bulk compressional wave was transmitted upon the skull, determining the retardation or advancement in phase of the received surface wave with respect to a reference phase, and processing the determined retardation or advancement in phase to determine circumferential expansion or contraction of the skull and utilizing the determined circumferential change to determine the change in intracranial pressure.
Hsue, Young-Chung; Yang, Tzong-Jer
2004-01-01
We propose a modified plane-wave expansion method to calculate transmittivity and reflectivity of a semi-infinite photonic crystal (PC) with interface. This method is based on an expanded completeness basis, including both the propagation and evanescence modes. We use this approach to deal with two kinds of problems: one is to determine the normal direction of the largest attenuation strength for a semi-infinite PC in the gap frequencies; the other is to calculate the transmittivity and reflectivity of a PC slab. To demonstrate the extensive utilization of our approach, we revisit the same system as studied by Phys. Rev. B 52, 8992 (1995)] and find that our results are in good agreement with ones obtained by Sakoda's paper.
Samin, Adib; Lahti, Erik; Zhang, Jinsuo
2015-08-15
Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.
Tissue expansion in perspective.
Sharpe, D. T.; Burd, R. M.
1989-01-01
Tissue expansion is a recent advance in skin cover technique. Its empirical use has enabled many previously difficult reconstructions to be completed without recourse to distant flaps. Its high complication rate and lack of basic scientific understanding at present restrict its use to selected cases, but the quality of repairs possible by this method encourage further serious scientific study. Images fig. 1 fig. 2 fig. 3 fig. 4 fig. 5 PMID:2589784
Kittell, Aaron W; Hyde, James S
2015-06-01
Non-adiabatic rapid passage (NARS) electron paramagnetic resonance (EPR) spectroscopy was introduced by Kittell et al. (2011) as a general purpose technique to collect the pure absorption response. The technique has been used to improve sensitivity relative to sinusoidal magnetic field modulation, increase the range of inter-spin distances that can be measured under near physiological conditions (Kittell et al., 2012), and enhance spectral resolution in copper (II) spectra (Hyde et al., 2013). In the present work, the method is extended to CW microwave power saturation of spin-labeled T4 Lysozyme (T4L). As in the cited papers, rapid triangular sweep of the polarizing magnetic field was superimposed on slow sweep across the spectrum. Adiabatic rapid passage (ARP) effects were encountered in samples undergoing very slow rotational diffusion as the triangular magnetic field sweep rate was increased. The paper reports results of variation of experimental parameters at the interface of adiabatic and non-adiabatic rapid sweep conditions. Comparison of the forward (up) and reverse (down) triangular sweeps is shown to be a good indicator of the presence of rapid passage effects. Spectral turning points can be distinguished from spectral regions between turning points in two ways: differential microwave power saturation and differential passage effects. Oxygen accessibility data are shown under NARS conditions that appear similar to conventional field modulation data. However, the sensitivity is much higher, permitting, in principle, experiments at substantially lower protein concentrations. Spectral displays were obtained that appear sensitive to rotational diffusion in the range of rotational correlation times of 10(-3) to 10(-7) s in a manner that is analogous to saturation transfer spectroscopy.
NASA Astrophysics Data System (ADS)
Kittell, Aaron W.; Hyde, James S.
2015-06-01
Non-adiabatic rapid passage (NARS) electron paramagnetic resonance (EPR) spectroscopy was introduced by Kittell et al. (2011) as a general purpose technique to collect the pure absorption response. The technique has been used to improve sensitivity relative to sinusoidal magnetic field modulation, increase the range of inter-spin distances that can be measured under near physiological conditions (Kittell et al., 2012), and enhance spectral resolution in copper (II) spectra (Hyde et al., 2013). In the present work, the method is extended to CW microwave power saturation of spin-labeled T4 Lysozyme (T4L). As in the cited papers, rapid triangular sweep of the polarizing magnetic field was superimposed on slow sweep across the spectrum. Adiabatic rapid passage (ARP) effects were encountered in samples undergoing very slow rotational diffusion as the triangular magnetic field sweep rate was increased. The paper reports results of variation of experimental parameters at the interface of adiabatic and non-adiabatic rapid sweep conditions. Comparison of the forward (up) and reverse (down) triangular sweeps is shown to be a good indicator of the presence of rapid passage effects. Spectral turning points can be distinguished from spectral regions between turning points in two ways: differential microwave power saturation and differential passage effects. Oxygen accessibility data are shown under NARS conditions that appear similar to conventional field modulation data. However, the sensitivity is much higher, permitting, in principle, experiments at substantially lower protein concentrations. Spectral displays were obtained that appear sensitive to rotational diffusion in the range of rotational correlation times of 10-3 to 10-7 s in a manner that is analogous to saturation transfer spectroscopy.
Kittell, Aaron W; Hyde, James S
2015-06-01
Non-adiabatic rapid passage (NARS) electron paramagnetic resonance (EPR) spectroscopy was introduced by Kittell et al. (2011) as a general purpose technique to collect the pure absorption response. The technique has been used to improve sensitivity relative to sinusoidal magnetic field modulation, increase the range of inter-spin distances that can be measured under near physiological conditions (Kittell et al., 2012), and enhance spectral resolution in copper (II) spectra (Hyde et al., 2013). In the present work, the method is extended to CW microwave power saturation of spin-labeled T4 Lysozyme (T4L). As in the cited papers, rapid triangular sweep of the polarizing magnetic field was superimposed on slow sweep across the spectrum. Adiabatic rapid passage (ARP) effects were encountered in samples undergoing very slow rotational diffusion as the triangular magnetic field sweep rate was increased. The paper reports results of variation of experimental parameters at the interface of adiabatic and non-adiabatic rapid sweep conditions. Comparison of the forward (up) and reverse (down) triangular sweeps is shown to be a good indicator of the presence of rapid passage effects. Spectral turning points can be distinguished from spectral regions between turning points in two ways: differential microwave power saturation and differential passage effects. Oxygen accessibility data are shown under NARS conditions that appear similar to conventional field modulation data. However, the sensitivity is much higher, permitting, in principle, experiments at substantially lower protein concentrations. Spectral displays were obtained that appear sensitive to rotational diffusion in the range of rotational correlation times of 10(-3) to 10(-7) s in a manner that is analogous to saturation transfer spectroscopy. PMID:25917132
Topological States and Adiabatic Pumping in Quasicrystals
NASA Astrophysics Data System (ADS)
Kraus, Yaakov; Lahini, Yoav; Ringel, Zohar; Verbin, Mor; Zilberberg, Oded
2012-02-01
We find a connection between quasicrystals and topological matter, namely that quasicrystals exhibit non-trivial topological phases attributed to dimensions higher than their own [1]. Quasicrystals are materials which are neither ordered nor disordered, i.e. they exhibit only long-range order [2]. This long-range order is usually expressed as a projection from a higher dimensional ordered system. Recently, the unrelated discovery of Topological Insulators [3] defined a new type of materials classified by their topology. We show theoretically and experimentally using photonic lattices, that one-dimensional quasicrystals exhibit topologically-protected boundary states equivalent to the edge states of the two-dimensional Integer Quantum Hall Effect. We harness this property to adiabatically pump light across the quasicrystal, and generalize our results to higher dimensional systems. Hence, quasicrystals offer a new platform for the study of topological phases while their topology may better explain their surface properties.[4pt] [1] Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, arXiv:1109.5983 (2011).[0pt] [2] C. Janot, Quasicrystals (Clarendon, Oxford, 1994), 2nd ed.[0pt] [3] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
On the persistence of adiabatic shear bands
NASA Astrophysics Data System (ADS)
Boakye-Yiadom, S.; Bassim, M. N.; Al-Ameeri, S.
2012-08-01
It is generally agreed that the initiation and development of adiabatic shear bands (ASBs) are manifestations of damage in metallic materials subjected to high strain rates and large strains as those due to impact in a Hopkinson Bar system. Models for evolution of these bands have been described in the literature. One question that has not received attention is how persistent these bands are and whether their presence and effect can be reversed or eliminated by using a process of thermal (heat treatment) or thermo-mechanical treatment that would relieve the material from the high strain associated with ASBs and their role as precursors to crack initiation and subsequent failure. Since ASBs are more prevalent and more defined in BCC metals including steels, a study was conducted to investigate the best conditions of generating ASBs in a heat treatable steel, followed by determining the best conditions for heat treatment of specimens already damaged by the presence of ASBs in order to relieve the strains due to ASBs and restore the material to an apparent microstructure without the "scars" due to the previous presence of ASBs. It was found that heat treatment achieves the curing from ASBs. This presentation documents the process undertaken to achieve this objective.
Adiabatic quantum algorithm for search engine ranking.
Garnerone, Silvano; Zanardi, Paolo; Lidar, Daniel A
2012-06-01
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in "q-sampling" protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank. PMID:23003933
Graph isomorphism and adiabatic quantum computing
NASA Astrophysics Data System (ADS)
Gaitan, Frank; Clark, Lane
2014-03-01
In the Graph Isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and maps G --> G'. If yes (no), then G and G' are said to be isomorphic (non-isomorphic). The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. We present a quantum algorithm that solves arbitrary instances of GI, and which provides a novel approach to determining all automorphisms of a graph. The algorithm converts a GI instance to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. Numerical simulation of the algorithm's quantum dynamics shows that it correctly distinguishes non-isomorphic graphs; recognizes isomorphic graphs; and finds the automorphism group of a graph. We also discuss the algorithm's experimental implementation and show how it can be leveraged to solve arbitrary instances of the NP-Complete Sub-Graph Isomorphism problem.
Design of the PIXIE Adiabatic Demagnetization Refrigerators
NASA Technical Reports Server (NTRS)
Shirron, Peter J.; Kimball, Mark Oliver; Fixsen, Dale J.; Kogut, Alan J.; Li, Xiaoyi; DiPirro, Michael
2012-01-01
The Primordial Inflation Explorer (PIXIE) is a proposed mission to densely map the polarization of the cosmic microwave background. It will operate in a scanning mode from a sun-synchronous orbit, using low temperature detectors (at 0.1 K) and located inside a teslescope that is cooled to approximately 2.73 K - to match the background temperature. A mechanical cryocooler operating at 4.5 K establishes a low base temperature from which two adiabatic demagnetization refrigerator (ADR) assemblies will cool the telescope and detectors. To achieve continuous scanning capability, the ADRs must operate continuously. Complicating the design are two factors: 1) the need to systematically vary the temperature of various telescope components in order to separate the small polarization signal variations from those that may arise from temperature drifts and changing gradients within the telescope, and 2) the orbital and monthly variations in lunar irradiance into the telescope barrels. These factors require the telescope ADR to reject quasi-continuous heat loads of 2-3 millwatts, while maintaining a peak heat reject rate of less than 12 milliwatts. The detector heat load at 0.1 K is comparatively small at 1-2 microwatts. This paper will describe the 3-stage and 2-stage continuous ADRs that will be used to meet the cooling power and temperature stability requirements of the PIXIE detectors and telescope.
Isotropic Negative Thermal Expansion Metamaterials.
Wu, Lingling; Li, Bo; Zhou, Ji
2016-07-13
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale.
Isotropic Negative Thermal Expansion Metamaterials.
Wu, Lingling; Li, Bo; Zhou, Ji
2016-07-13
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale. PMID:27333052
Adiabaticity and spectral splits in collective neutrino transformations
Raffelt, Georg G.; Smirnov, Alexei Yu.
2007-12-15
Neutrinos streaming off a supernova core transform collectively by neutrino-neutrino interactions, leading to 'spectral splits' where an energy E{sub split} divides the transformed spectrum sharply into parts of almost pure but different flavors. We present a detailed description of the spectral-split phenomenon which is conceptually and quantitatively understood in an adiabatic treatment of neutrino-neutrino effects. Central to this theory is a self-consistency condition in the form of two sum rules (integrals over the neutrino spectra that must equal certain conserved quantities). We provide explicit analytic and numerical solutions for various neutrino spectra. We introduce the concept of the adiabatic reference frame and elaborate on the relative adiabatic evolution. Violating adiabaticity leads to the spectral split being 'washed out'. The sharpness of the split appears to be represented by a surprisingly universal function.
Coherent transfer by adiabatic passage in two-dimensional lattices
Longhi, Stefano
2014-09-15
Coherent tunneling by adiabatic passage (CTAP) is a well-established technique for robust spatial transport of quantum particles in linear chains. Here we introduce two exactly-solvable models where the CTAP protocol can be extended to two-dimensional lattice geometries. Such bi-dimensional lattice models are synthesized from time-dependent second-quantization Hamiltonians, in which the bosonic field operators evolve adiabatically like in an ordinary three-level CTAP scheme thus ensuring adiabatic passage in Fock space. - Highlights: • New ways of coherent transport by adiabatic passage (CTAP) in 2D lattices. • Synthesis of exactly-solvable 2D lattices from a simple three-well model. • CTAP in 2D lattices can be exploited for quantum state transfer.
Adiabatic and isocurvature perturbation projections in multi-field inflation
Gordon, Chris; Saffin, Paul M. E-mail: Paul.Saffin@nottingham.ac.uk
2013-08-01
Current data are in good agreement with the predictions of single field inflation. However, the hemispherical asymmetry, seen in the cosmic microwave background data, may hint at a potential problem. Generalizing to multi-field models may provide one possible explanation. A useful way of modeling perturbations in multi-field inflation is to investigate the projection of the perturbation along and perpendicular to the background fields' trajectory. These correspond to the adiabatic and isocurvature perturbations. However, it is important to note that in general there are no corresponding adiabatic and isocurvature fields. The purpose of this article is to highlight the distinction between a field redefinition and a perturbation projection. We provide a detailed derivation of the evolution of the isocurvature perturbation to show that no assumption of an adiabatic or isocurvature field is needed. We also show how this evolution equation is consistent with the field covariant evolution equations for the adiabatic perturbation in the flat field space limit.
Ultrafast stimulated Raman parallel adiabatic passage by shaped pulses
Dridi, G.; Guerin, S.; Hakobyan, V.; Jauslin, H. R.; Eleuch, H.
2009-10-15
We present a general and versatile technique of population transfer based on parallel adiabatic passage by femtosecond shaped pulses. Their amplitude and phase are specifically designed to optimize the adiabatic passage corresponding to parallel eigenvalues at all times. We show that this technique allows the robust adiabatic population transfer in a Raman system with the total pulse area as low as 3{pi}, corresponding to a fluence of one order of magnitude below the conventional stimulated Raman adiabatic passage process. This process of short duration, typically picosecond and subpicosecond, is easily implementable with the modern pulse shaper technology and opens the possibility of ultrafast robust population transfer with interesting applications in quantum information processing.
Hydrogen and nitrogen turboexpanders with high gas expansion ratios
NASA Astrophysics Data System (ADS)
Davydenkov, I. A.; Davydov, A. B.; Perestoronin, G. A.
The paper examines the design features of a four-stage hydrogen turboexpander with an expansion ratio of 80 and two-stage nitrogen turboexpander with an expansion ratio of 120. The test results obtained under imitations in air are presented. The adiabatic efficiency of the hydrogen and nitrogen turboexpanders under operating conditions has reached 0,65 and 0, 78, respectively. The use of high-performance high-pressure hydrogen and nitrogen turboexpanders has considerably increased the capacity of a large hydrogen liquefier.
NASA Astrophysics Data System (ADS)
Lee, Keonhee; Oh, Jumi
2016-01-01
A notion of measure expansivity for flows was introduced by Carrasco-Olivera and Morales in [3] as a generalization of expansivity, and they proved that there were no measure expansive flows on closed surfaces. In this paper we introduce a concept of weak measure expansivity for flows which is really weaker than that of measure expansivity, and show that there is a weak measure expansive flow on a closed surface. Moreover we show that any C1 stably weak measure expansive flow on a C∞ closed manifold M is Ω-stable, and any C1 stably measure expansive flow on M satisfies both Axiom A and the quasi-transversality condition.
Adiabatic invariant value variation under shortwave band subcritical conditions
NASA Astrophysics Data System (ADS)
Svistunov, K. V.; Tinin, M. V.
1985-04-01
The possibility of significant variations of the adiabatic invariant is examined for the propagation of radio waves in an irregular Earth-ionosphere waveguide with a parabolic dependence of permittivity on height. Numerical and analytical results indicate that nonexponential deviations of the adiabatic invariant can occur not only when the characteristic size of horizontal irregularity decreases (e.g., during resonant beam excitation) but also in quasi-critical conditions and for smoothly irregular waveguides.
Shortcuts to adiabaticity for non-Hermitian systems
Ibanez, S.; Martinez-Garaot, S.; Torrontegui, E.; Muga, J. G.; Chen Xi
2011-08-15
Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on counter-diabatic (transitionless driving) algorithms or on dynamical invariants. We work out the basic theory and examples described by two-level Hamiltonians: the acceleration of rapid adiabatic passage with a decaying excited level and of the dynamics of a classical particle on an expanding harmonic oscillator.
Semiclassical Monte-Carlo approach for modelling non-adiabatic dynamics in extended molecules
Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2013-01-01
Modelling of non-adiabatic dynamics in extended molecular systems and solids is a next frontier of atomistic electronic structure theory. The underlying numerical algorithms should operate only with a few quantities (that can be efficiently obtained from quantum chemistry), provide a controlled approximation (which can be systematically improved) and capture important phenomena such as branching (multiple products), detailed balance and evolution of electronic coherences. Here we propose a new algorithm based on Monte-Carlo sampling of classical trajectories, which satisfies the above requirements and provides a general framework for existing surface hopping methods for non-adiabatic dynamics simulations. In particular, our algorithm can be viewed as a post-processing technique for analysing numerical results obtained from the conventional surface hopping approaches. Presented numerical tests for several model problems demonstrate efficiency and accuracy of the new method. PMID:23864100
Semiclassical Monte-Carlo approach for modelling non-adiabatic dynamics in extended molecules.
Gorshkov, Vyacheslav N; Tretiak, Sergei; Mozyrsky, Dmitry
2013-01-01
Modelling of non-adiabatic dynamics in extended molecular systems and solids is a next frontier of atomistic electronic structure theory. The underlying numerical algorithms should operate only with a few quantities (that can be efficiently obtained from quantum chemistry), provide a controlled approximation (which can be systematically improved) and capture important phenomena such as branching (multiple products), detailed balance and evolution of electronic coherences. Here we propose a new algorithm based on Monte-Carlo sampling of classical trajectories, which satisfies the above requirements and provides a general framework for existing surface hopping methods for non-adiabatic dynamics simulations. In particular, our algorithm can be viewed as a post-processing technique for analysing numerical results obtained from the conventional surface hopping approaches. Presented numerical tests for several model problems demonstrate efficiency and accuracy of the new method. PMID:23864100
NASA Astrophysics Data System (ADS)
Human, Hendrik G. C.
1997-01-01
Selective dissociation of UF6 using three wavelength IR irradiation did not yield the desired results initially. Various spectroscopic methods such as UV and IR absorption of UF6, fluorescence of UF6 and Time-of-Flight Mass Spectrometry of the products of irradiation, were implemented to investigate the nature of the interaction. These techniques identified the source of the problem as the presence of condensates in the flow-cooled gas, and were used to select conditions to minimise this effect.
NASA Technical Reports Server (NTRS)
Wagner, Richard D., Jr.
1959-01-01
In a recent article on hypersonic flow, Lees and Kubota suggested a modification of the local-expansion method to predict the surface pressures in the region of a nose-cylinder junction where Newtonian theory fails. The modification consists of matching the Newtonian pressure distribution and the Prandtl-Meyer relation at the point on the nose surface where both the pressure and the pressure gradient, predicted by these two solution, are equal. With this approximation, the pressure distribution can be predicted quite accurately up to the nose-cylinder junction for blunt-nosed bodies of continuous curvature, provided centrifugal-force effects are negligible. The purpose of this note is to facilitate the application of Lees' suggestion and to draw attention to some of its consequences.
Dalir, Nemat
2014-01-01
An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary combination of homogenous boundary condition of the first or second kind can be applied in the angular and azimuthal directions. Nevertheless, solution is valid for nonhomogeneous boundary conditions of the third kind (convection) in the radial direction. A case study problem for the three-layer quarter-spherical region is solved and the results are discussed. PMID:27433511
A computer analysis of regenerator losses in a Stirling cryocooler with multiple expansion stages
NASA Astrophysics Data System (ADS)
Urieli, Israel; Tang, Kuo-Chiang
An Ideal Adiabatic analysis of a Stirling cryocooler with multiple expansion stages has been presented previously. In this analysis the compression space and the various expansion spaces are adiabatic, the heat exchangers are isothermal and the regenerators are ideal. This paper is an extension of that analysis to evaluate the enthalpy losses associated with the interstage regenerators. The regenerator effectiveness is defined in terms of the total unidirectional heat flow from the regenerator matrix to the working gas. A new definition of regenerator figure-of-merit is proposed for the intermediate expansion stages based on a stage energy balance, and its evaluation and uses in design are discussed. The analysis of a typical three expansion stage cryocooler is presented.
Adiabatic population transfer in a three-level system driven by delayed laser pulses
NASA Astrophysics Data System (ADS)
Kuklinski, J. R.; Gaubatz, U.; Hioe, F. T.; Bergmann, K.
1989-12-01
We give a simple analytic solution that describes a novel method for population transfer in a three-level system driven by delayed pulses and which accounts for recent experimental results. This solution describes a procedure that is counterintuitive, and yet it is shown to be, in fact, one of the simplest solutions for multilevel systems arising from the adiabatic theorem. Its possible application to many-level systems is suggested.
Expansion techniques for collisionless stellar dynamical simulations
NASA Astrophysics Data System (ADS)
Meiron, Yohai
2016-02-01
We present ETICS, a collisionless N-body code based on two kinds of series expansions of the Poisson equation, implemented for graphics processing units (GPUs). The code is publicly available and can be used as a standalone program or as a library (an AMUSE plugin is included). One of the two expansion methods available is the self-consistent field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other is the multipole expansion (MEX) method, which is a Taylor-like expansion of the Green's function. MEX, which has been advocated in the past, has not gained as much popularity as SCF. Both are particle-field methods and optimized for collisionless galactic dynamics, but while SCF is a ``pure'' expansion, MEX is an expansion in just the angular part; thus, MEX is capable of capturing radial structure easily, while SCF needs a large number of radial terms.
GREEN'S FUNCTIONS FOR FAR-SIDE SEISMIC IMAGES: A POLAR-EXPANSION APPROACH
Perez Hernandez, F.; Gonzalez Hernandez, I. E-mail: irenegh@noao.ed
2010-03-10
We have computed seismic images of magnetic activity on the far surface of the Sun by using a seismic-holography technique. As in previous works, the method is based on the comparison of waves going in and out of a particular point in the Sun, but we have computed here Green's functions from a spherical polar expansion of the adiabatic wave equations in the Cowling approximation instead of using the ray-path approximation previously used in the far-side holography. A comparison between the results obtained using the ray theory and the spherical polar expansion is shown. We use the gravito-acoustic wave equation in the local plane-parallel limit in both cases and for the latter we take the asymptotic approximation for the radial dependences of Green's function. As a result, improved images of the far side can be obtained from the polar-expansion approximation, especially when combining Green's functions corresponding to two and three skips. We also show that the phase corrections in Green's functions due to the incorrect modeling of the uppermost layers of the Sun can be estimated from the eigenfrequencies of the normal modes of oscillation.
Semiclassical Monte Carlo: a first principles approach to non-adiabatic molecular dynamics.
White, Alexander J; Gorshkov, Vyacheslav N; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-14
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.
Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics
White, Alexander J.; Gorshkov, Vyacheslav N.; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-14
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.
Semiclassical Monte Carlo: a first principles approach to non-adiabatic molecular dynamics.
White, Alexander J; Gorshkov, Vyacheslav N; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-14
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement. PMID:25399126
Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics
NASA Astrophysics Data System (ADS)
White, Alexander J.; Gorshkov, Vyacheslav N.; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-01
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.
Flammability zone prediction using calculated adiabatic flame temperatures
Mashuga, C.V.; Crowl, D.A.
1999-11-01
This paper describes work to predict the flammability zone for any mixture of fuel, oxygen and nitrogen. The method utilizes a commercially available equilibrium program to determine the calculated adiabatic flame temperature (CAFT). The model is compared with extensive experimental data obtained in a 20 L sphere at an initial pressure of 1 atm and 298 K. The data and model compare well over the entire flammability zone for two pure species, methane and ethylene, and not as well for a 50/50 mixture of methane/ethylene. Results show that a good prediction of the flammability zone is obtained using a CAFT criterion of 1200 K. Furthermore, the intermediate species and solid carbon must be included in the equilibrium calculation to fit the fuel rich part of the zone. The intermediate species were selected by the equilibrium program using a built-in species selection criteria. For a gas mixture of methane and ethylene, the authors were unable to identify mixing rules for estimating K{sub G} and P{sub max} from pure component data. This method provides a direct approach to full flammability zone prediction.
Shortt, Alex J; Secker, Genevieve A; Lomas, Richard J; Wilshaw, Stacy P; Kearney, John N; Tuft, Stephen J; Daniels, Julie T
2009-02-01
Human amniotic membrane (HAM) is employed as a substrate for the ex-vivo expansion of limbal epithelial cells (LECs) used to treat corneal epithelial stem cell deficiency in humans. The optimal method of HAM preparation for this purpose is unknown. This study evaluated the ability of different preparations of stored HAM to serve as substrates for LEC expansion ex-vivo. The effect of removing the amniotic epithelial cells (decellularisation) from HAM prior to seeding of LECs, the effect of glycerol cryopreservation and the effect of peracetic acid (PAA) sterilization and antibiotic disinfection were evaluated using different HAM test groups. Human LECs were cultured on each preparation and the following outcomes were assessed: confluence of growth, cell density, cell morphology and expression of the putative LESC markers deltaN-p63alpha and ABCG2. Removing amniotic epithelial cells prior to seeding of LECs resulted in a higher percentage of confluence but a lower cell density than intact HAM suggesting that decellularisation does not increase proliferation, but rather that it facilitates migration of LECs resulting in larger cells. Decellularisation did not affect the percentage of cells expressing the putative LESC markers deltaN-p63alpha (< or =4% in both intact and acellular groups) and ABCG2 (< or =3% in both intact and acellular groups). Glycerol cryopreservation of HAM resulted in poor morphology and a low proportion of cells expressing deltaN-p63alpha (< or =6%) and ABCG2 (< or =8%). HAM frozen at -80 degrees C in Hank's Balanced Salt Solution (HBSS) was superior, demonstrating excellent morphology of cultured LECs and high levels of deltaN-p63alpha (< or =68%) and ABCG2 (< or =62%) expression (p<0.001). The use of PAA or antibiotics to decontaminate HAM does not appear to affect this function. The variables affecting the ability of HAM to serve as a substrate for LEC expansion ex-vivo are poorly understood. The use of glycerol as a cryoprotectant impairs
Instability of a planar expansion wave.
Velikovich, A L; Zalesak, S T; Metzler, N; Wouchuk, J G
2005-10-01
An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent gamma. At gamma > 3, the mass modulation amplitude delta(m) in a rippled expansion wave exhibits a power-law growth with time alpha(t)beta, where beta = (gamma - 3)/(gamma - 1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme gamma - 1 < 1, delta(m) exhibits oscillatory growth, approximately linear with time, until it reaches its peak value approximately (gamma - 1)(-1/2), and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac's instability of a blast wave in a gas with low . Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results.
Instability of a planar expansion wave
NASA Astrophysics Data System (ADS)
Velikovich, A. L.; Zalesak, S. T.; Metzler, N.; Wouchuk, J. G.
2005-10-01
An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent γ . At γ>3 , the mass modulation amplitude δm in a rippled expansion wave exhibits a power-law growth with time ∝ tβ , where β= (γ-3) / (γ-1) . This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme γ-1≪1 , δm exhibits oscillatory growth, approximately linear with time, until it reaches its peak value ˜ (γ-1)-1/2 , and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac’s instability of a blast wave in a gas with low γ . Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results.
Instability of a planar expansion wave.
Velikovich, A L; Zalesak, S T; Metzler, N; Wouchuk, J G
2005-10-01
An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent gamma. At gamma > 3, the mass modulation amplitude delta(m) in a rippled expansion wave exhibits a power-law growth with time alpha(t)beta, where beta = (gamma - 3)/(gamma - 1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme gamma - 1 < 1, delta(m) exhibits oscillatory growth, approximately linear with time, until it reaches its peak value approximately (gamma - 1)(-1/2), and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac's instability of a blast wave in a gas with low . Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results. PMID:16383532
Imani, S Misagh; Goudarzi, A M; Ghasemi, S E; Kalani, A; Mahdinejad, J
2014-10-01
In this article, finite element method is used to investigate the mechanical behavior of a stent and to determine the biomechanical interaction between the stent and the artery in a stenting procedure. The main objective of this study is to reach to a model close to a real condition of coronary stent placement. Unlike most of the models proposed in the literature, all the steps of the deployment of a stent in the stenotic vessel (i.e. pressure increasing, constant load pressure and pressure decreasing) are simulated in this article to show the behavior of the stent in different stages of implantation. The results indicate that the first step of deployment, that is, pressure increasing, plays a main role in the success of stent implantation. So that, in order to compare the behavior of different types of stents, it is sufficient to compare their behavior at the end of pressure increasing step. In order to show the application of the findings in stent versus stent studies, three commercially available stents (the Palmaz-Schatz, Multi-Link and NIR stents) are modeled and their behavior is compared at the end of pressure increasing step. The effect of stent design on the restenosis rate is investigated. According to the findings, the possibility of restenosis is lower for Multi-Link and NIR stents in comparison with Palmaz-Schatz stent which is in good agreement with clinical results. Therefore, the testing methodology outlined here is proposed as a simple and economical alternative for "stent versus stent" complicated clinical trials.
Exploiting initial-state dependence to improve the performance of adiabatic TDDFT
NASA Astrophysics Data System (ADS)
Fuks, Johanna I.; Nielsen, Soeren E. B.; Ruggenthaler, Michael; Maitra, Neepa T.; Hunter college City University of New York Collaboration; Max-Planck-Institut für Struktur und Dynamik der Materie, Hamburg Collaboration
Although time-dependent density functional theory (TDDFT) descriptions of dynamics in non-equilibrium situations have seen exciting successes recently, there have also been studies that throw into doubt the reliability of the approximate exchange-correlation functionals to accurately describe the dynamics. Here we study exact exchange-correlation potentials for few electron systems, found using the global fixed-point iteration method [NRL]. We find that the size of dynamical correlation features that are missing in the currently-used adiabatic approximations depend strongly on the choice of the initial Kohn-Sham wavefunction. With a judicious choice, the dynamical effects can be small over a finite time duration, but sometimes they can get large at longer times. We also examine different starting points, in particular an orbital-dependent potential directly obtained from the Kohn-Sham hole [LFSEM14], for approximate xc functionals: instead of building on an adiabatic approximation.
Heavy-Ion-Acoustic Solitary and Shock Waves in an Adiabatic Multi-Ion Plasma
NASA Astrophysics Data System (ADS)
Hossen, M. A.; Rahman, M. M.; Hossen, M. R.; Mamun, A. A.
2015-08-01
The standard reductive perturbation method has been employed to derive the Korteweg-deVries (K-dV) and Burgers (BG) equations to investigate the basic properties of heavy-ion-acoustic (HIA) waves in a plasma system which is supposed to be composed of nonthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions. The HIA solitary and shock structures are found to exist with either positive or negative potential. It is found that the effects of adiabaticity of inertial heavy ions, nonthermality of electrons, and number densities of plasma components significantly modify the basic properties of the HIA solitary and shock waves. The implications of our results may be helpful in understanding the electrostatic perturbations in various laboratory and astrophysical plasma environments.
Shortcuts to adiabatic passage for generation of W states of distant atoms
NASA Astrophysics Data System (ADS)
Song, Kun-Huang; Chen, Ming-Feng
2016-08-01
With the help of quantum Zeno dynamics, we propose fast and noise-resistant schemes for preparing the W states in the indirectly coupled cavity systems via the inverse engineering-based Lewis-Riesenfeld invariant (IBLR). Comparing with the original adiabatic passage method, the results show that the time needed to prepare the desired state is reduced and the effects of the atomic spontaneous emission and the cavity decay on the fidelity are suppressed. Moreover, this scheme can also be generalized to generation of N-atom W states. Not only the total operation time, but also the robustness against decoherence is insensitive to the number of atoms. It proves that our scheme is useful in scalable distributed quantum information processing and contributes to the understanding of more complex systems via shortcuts to adiabatic passage based on Lewis-Riesenfeld invariants.
Nebogatov, V. A.; Pastukhov, V. P.
2013-06-15
A closed set of reduced equations describing low-frequency nonlinear flute magnetohydrodynamic (MHD) convection and the resulting nondiffusive processes of particle and energy transport in a weakly collisional cylindrical plasma with an anisotropic pressure is derived. The Chew-Goldberger-Low anisotropic magnetohydrodynamics is used as the basic dynamic model, because this model is applicable to describing flute convection in a cylindrical plasma column even in the low-frequency limit. The reduced set of equations was derived using the method of adiabatic separation of fast and slow motions. It is shown that the structure of the adiabatic transformation and the corresponding velocity field are identical to those obtained earlier in the isotropic MHD model. However, the derived heat transfer equations differ drastically from the isotropic pressure model. In particular, they indicate a tendency toward maintaining different radial profiles of the longitudinal and transverse pressures.
Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.
1994-06-01
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation.
Non-adiabatic effects in the pseudorotational motion of triatomic molecules
NASA Astrophysics Data System (ADS)
Hagelberg, Frank; Deumens, Erik
2002-03-01
Electron-Nuclear Dynamics (END) theory simulations have been performed with the aim to understand the dynamic aspects of triatomic molecules in pseudorotational motion. More specifically, the units H_3^+ and Li_3^+ are investigated close to the threshold of dissociation. For both species, the dynamic response of the electronic system to the nuclear motion is examined by the computation of electronic angular momentum expectation values. The respective results differ markedly for alpha and beta spin orientations, reflecting the emergence of rapid spin oscillations. This phenomenon is investigated by a detailed analysis of the electronic excitation content in both molecules. This is achieved by projection of the dynamic wavefunction on adiabatic electronic states which are evaluated along the nuclear trajectories. From an inspection of the phase relations between the expansion coefficients for electronic excitations with alpha and beta spin orientation, we conclude that the systems maximize the observed spin polarization effects.
Adiabatic quantum pump in a zigzag graphene nanoribbon junction
NASA Astrophysics Data System (ADS)
Zhang, Lin
2015-11-01
The adiabatic electron transport is theoretically studied in a zigzag graphene nanoribbon (ZGNR) junction with two time-dependent pumping electric fields. By modeling a ZGNR p-n junction and applying the Keldysh Green’s function method, we find that a pumped charge current is flowing in the device at a zero external bias, which mainly comes from the photon-assisted tunneling process and the valley selection rule in an even-chain ZGNR junction. The pumped charge current and its ON and OFF states can be efficiently modulated by changing the system parameters such as the pumping frequency, the pumping phase difference, and the Fermi level. A ferromagnetic ZGNR device is also studied to generate a pure spin current and a fully polarized spin current due to the combined spin pump effect and the valley valve effect. Our finding might pave the way to manipulate the degree of freedom of electrons in a graphene-based electronic device. Project supported by the National Natural Science Foundation of China (Grant No. 110704033), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010416), and the Natural Science Foundation for Colleges and Universities in Jiangsu Province, China (Grant No. 13KJB140005).
Evolution of f{sub NL} to the adiabatic limit
Elliston, Joseph; Mulryne, David J.; Tavakol, Reza; Seery, David E-mail: D.Mulryne@qmul.ac.uk E-mail: R.Tavakol@qmul.ac.uk
2011-11-01
We study inflationary perturbations in multiple-field models, for which ζ typically evolves until all isocurvature modes decay — the {sup a}diabatic limit{sup .} We use numerical methods to explore the sensitivity of the local-shape bispectrum to the process by which this limit is achieved, finding an appreciable dependence on model-specific data such as the time at which slow-roll breaks down or the timescale of reheating. In models with a sum-separable potential where the isocurvature modes decay before the end of the slow-roll phase we give an analytic criterion for the asymptotic value of f{sub NL} to be large. Other examples can be constructed using a waterfall field to terminate inflation while f{sub NL} is transiently large, caused by descent from a ridge or convergence into a valley. We show that these two types of evolution are distinguished by the sign of the bispectrum, and give approximate expressions for the peak f{sub NL}.
Adiabatic continuity, wave-function overlap, and topological phase transitions
NASA Astrophysics Data System (ADS)
Gu, Jiahua; Sun, Kai
2016-09-01
In this paper, we study the relation between wave-function overlap and adiabatic continuity in gapped quantum systems. We show that for two band insulators, a scalar function can be defined in the momentum space, which characterizes the wave-function overlap between Bloch states in the two insulators. If this overlap is nonzero for all momentum points in the Brillouin zone, these two insulators are adiabatically connected, i.e., we can deform one insulator into the other smoothly without closing the band gap. In addition, we further prove that this adiabatic path preserves all the symmetries of the insulators. The existence of such an adiabatic path implies that two insulators with nonzero wave-function overlap belong to the same topological phase. This relation, between adiabatic continuity and wave-function overlap, can be further generalized to correlated systems. The generalized relation cannot be applied to study generic many-body systems in the thermodynamic limit, because of the orthogonality catastrophe. However, for certain interacting systems (e.g., quantum Hall systems), the quantum wave-function overlap can be utilized to distinguish different quantum states. Experimental implications are also discussed.
Adiabatic condition and the quantum hitting time of Markov chains
Krovi, Hari; Ozols, Maris; Roland, Jeremie
2010-08-15
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P{sup '} where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP{sup '} and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.
NASA Astrophysics Data System (ADS)
Third, J. R.; Chen, Y.; Müller, C. R.
2016-07-01
Lattice-Boltzmann method (LBM) simulations of a gas-fluidised bed have been performed. In contrast to the current state-of-the-art coupled computational fluid dynamics-discrete element method (CFD-DEM) simulations, the LBM does not require a closure relationship for the particle-fluid interaction force. Instead, the particle-fluid interaction can be calculated directly from the detailed flow profile around the particles. Here a comparison is performed between CFD-DEM and LBM simulations of a small fluidised bed. Simulations are performed for two different values of the superficial gas velocity and it is found that the LBM predicts a larger bed expansion for both flowrates. Furthermore the particle-fluid interaction force obtained for LBM simulations is compared to the force which would be predicted by a CFD-DEM model under the same conditions. On average the force predicted by the CFD-DEM closure relationship is found to be significantly smaller than the force obtained from the LBM.
Hsu, Jin-Chen; Wu, Tsung-Tsong
2008-02-01
Based on Mindlin's piezoelectric plate theory and the plane wave expansion method, a formulation is proposed to study the frequency band gaps and dispersion relations of the lower-order Lamb waves in two-dimensional piezoelectric phononic plates. The method is applied to analyze the phononic plates composed of solid-solid and airsolid constituents with square and triangular lattices, respectively. Factors that influence the opening and width of the complete Lamb wave gaps are identified and discussed. For solid/solid phononic plates, it is suggested that the filling material be chosen with larger mass density, proper stiffness, and weak anisotropic factor embedded in a soft matrix in order to obtain wider complete band gaps of the lower-order Lamb waves. By comparing to the calculated results without considering the piezoelectricity, the influences of piezoelectric effect on Lamb waves are analyzed as well. On the other hand, for air/solid phononic plates, a background material itself with proper anisotropy and a high filling fraction of air may favor the opening of the complete Lamb wave gaps.
Nonequilibrium Statistical Mechanics for Adiabatic Piston Problem
NASA Astrophysics Data System (ADS)
Itami, Masato; Sasa, Shin-ichi
2015-01-01
We consider the dynamics of a freely movable wall of mass with one degree of freedom that separates a long tube into two regions, each of which is filled with rarefied gas particles of mass . The gases are initially prepared at equal pressure but different temperatures, and we assume that the pressure and temperature of gas particles before colliding with the wall are kept constant over time in each region. We elucidate the energetics of the setup on the basis of the local detailed balance condition, and then derive the expression for the heat transferred from each gas to the wall. Furthermore, by using the condition, we obtain the linear response formula for the steady velocity of the wall and steady energy flux through the wall. By using perturbation expansion in a small parameter , we calculate the steady velocity up to order.
Thermal Expansion of Polyurethane Foam
NASA Technical Reports Server (NTRS)
Lerch, Bradley A.; Sullivan, Roy M.
2006-01-01
expansion tests and the response of the microstructure. A novel optical method is described which is appropriate for measuring thermal expansion at high temperatures without influencing the thermal expansion measurement. Detailed microstructural investigations will also be described which show cell expansion as a function of temperature. Finally, a phenomenological model on thermal expansion will be described.
Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H2 reaction
NASA Astrophysics Data System (ADS)
Mielke, Steven L.; Garrett, Bruce C.; Fleming, Donald G.; Truhlar, Donald G.
2015-01-01
Isotopic substitution of muonium for hydrogen provides an unparalleled opportunity to deepen our understanding of quantum mass effects on chemical reactions. A recent topical review in this journal of the thermal and vibrationally state-selected reaction of Mu with H2 raises a number of issues that are addressed here. We show that some earlier quantum mechanical calculations of the Mu + H2 reaction, which are highlighted in this review, and which have been used to benchmark approximate methods, are in error by as much as 19% in the low-temperature limit. We demonstrate that an approximate treatment of the Born-Oppenheimer diagonal correction that was used in some recent studies is not valid for treating the vibrationally state-selected reaction. We also discuss why vibrationally adiabatic potentials that neglect bend zero-point energy are not a useful analytical tool for understanding reaction rates, and why vibrationally non-adiabatic transitions cannot be understood by considering tunnelling through vibrationally adiabatic potentials. Finally, we present calculations on a hierarchical family of potential energy surfaces to assess the sensitivity of rate constants to the quality of the potential surface.
Micromechanics of expansive mechanisms in expansive cement concretes
NASA Astrophysics Data System (ADS)
Cohen, M. D.
The kinetics of hydration were studied by monitoring the presence of various compounds by X-ray diffractometer, a chemical extraction method, and scanning electron microscope. These studies indicated that the rates of depletion of the expanding particles and sulfates are higher in the finer blends, which is why expansion stops earlier in these blends. It is shown that the double curvature phenomenon (strength-drop and sudden increase in the rate of expansion) is caused by mechanical failure (e.g., microcracking) of the matrix surrounding the expanding particles that are producing ettringite crystals. The theory of protective and partial protective coating is reviewed. A hypothesis is introduced which assumes that monosulfate is not formed immediately when ettringite stops forming but is preceded by an intermediate phase. Shrinkage studies show that expansive cements shrink more than portland cements. The results of these studies were used to develop a modified model of the expansive process. It was shown theoretically that the time of expansion is inversely proportional to the surface area of the expansive clinker and directly proportional to the amount of sulfate used.
Effect of dephasing on stimulated Raman adiabatic passage
Ivanov, P.A.; Vitanov, N.V.; Bergmann, K.
2004-12-01
This work explores the effect of phase relaxation on the population transfer efficiency in stimulated Raman adiabatic passage (STIRAP). The study is based on the Liouville equation, which is solved analytically in the adiabatic limit. The transfer efficiency of STIRAP is found to decrease exponentially with the dephasing rate; this effect is stronger for shorter pulse delays and weaker for larger delays, since the transition time is found to be inversely proportional to the pulse delay. Moreover, it is found that the transfer efficiency of STIRAP in the presence of dephasing does not depend on the peak Rabi frequencies at all, as long as they are sufficiently large to enforce adiabatic evolution; hence increasing the field intensity cannot reduce the dephasing losses. It is shown also that for any dephasing rate, the final populations of the initial state and the intermediate state are equal. For strong dephasing all three populations tend to (1/3)
Adiabatic Quantum Computation and the Theory of Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Kaminsky, William; Lloyd, Seth
2007-03-01
We present a general approach to determining the asymptotic scaling of adiabatic quantum computational resources (space, time, energy, and precision) on random instances of NP-complete graph theory problems. By utilizing the isomorphisms between certain NP-complete graph theory problems and certain frustrated spin models, we demonstrate that the asymptotic scaling of the minimum spectral gap that determines the asymptotic running time of adiabatic algorithms is itself determined by the presence and character of quantum phase transitions in these frustrated models. Most notably, we draw the conclusion that adiabatic quantum computers based on quantum Ising models are much less likely to be efficient than those based on quantum rotor or Heisenberg models. We then exhibit practical rotor and Heisenberg model based architectures using Josephson junction and quantum dot circuits.
Speeding up Adiabatic Quantum State Transfer by Using Dressed States
NASA Astrophysics Data System (ADS)
Baksic, Alexandre; Ribeiro, Hugo; Clerk, Aashish A.
2016-06-01
We develop new pulse schemes to significantly speed up adiabatic state transfer protocols. Our general strategy involves adding corrections to an initial control Hamiltonian that harness nonadiabatic transitions. These corrections define a set of dressed states that the system follows exactly during the state transfer. We apply this approach to stimulated Raman adiabatic passage protocols and show that a suitable choice of dressed states allows one to design fast protocols that do not require additional couplings, while simultaneously minimizing the occupancy of the "intermediate" level.
Quantum Adiabatic Pumping by Modulating Tunnel Phase in Quantum Dots
NASA Astrophysics Data System (ADS)
Taguchi, Masahiko; Nakajima, Satoshi; Kubo, Toshihiro; Tokura, Yasuhiro
2016-08-01
In a mesoscopic system, under zero bias voltage, a finite charge is transferred by quantum adiabatic pumping by adiabatically and periodically changing two or more control parameters. We obtained expressions for the pumped charge for a ring of three quantum dots (QDs) by choosing the magnetic flux penetrating the ring as one of the control parameters. We found that the pumped charge shows a steplike behavior with respect to the variance of the flux. The value of the step heights is not universal but depends on the trajectory of the control parameters. We discuss the physical origin of this behavior on the basis of the Fano resonant condition of the ring.
Adiabatic fluctuations from cosmic strings in a contracting universe
Brandenberger, Robert H.; Takahashi, Tomo; Yamaguchi, Masahide E-mail: tomot@cc.saga-u.ac.jp
2009-07-01
We show that adiabatic, super-Hubble, and almost scale invariant density fluctuations are produced by cosmic strings in a contracting universe. An essential point is that isocurvature perturbations produced by topological defects such as cosmic strings on super-Hubble scales lead to a source term which seeds the growth of curvature fluctuations on these scales. Once the symmetry has been restored at high temperatures, the isocurvature seeds disappear, and the fluctuations evolve as adiabatic ones in the expanding phase. Thus, cosmic strings may be resurrected as a mechanism for generating the primordial density fluctuations observed today.
Spatial adiabatic passage: a review of recent progress
NASA Astrophysics Data System (ADS)
Menchon-Enrich, R.; Benseny, A.; Ahufinger, V.; Greentree, A. D.; Busch, Th; Mompart, J.
2016-07-01
Adiabatic techniques are known to allow for engineering quantum states with high fidelity. This requirement is currently of large interest, as applications in quantum information require the preparation and manipulation of quantum states with minimal errors. Here we review recent progress on developing techniques for the preparation of spatial states through adiabatic passage, particularly focusing on three state systems. These techniques can be applied to matter waves in external potentials, such as cold atoms or electrons, and to classical waves in waveguides, such as light or sound.
Adiabatic effects in the dynamics of Langmuir solitons
Astrelin, V.T.; Breizman, B.N.; Sedlacek, Z.; Jungwirth, K.
1988-06-01
The adiabatic slowness with which the plasma density profile is reconstructed from localized in large-amplitude Langmuir solitons is characteristic of such solitons. Several examples making use of this feature in the description of the soliton dynamics are given. Specifically, long-lived states in the form of composite solitons ar found. Additional limitations are found on the interaction of solitons with each other and with sound waves. The effect of the adiabatic nature on the formation of solitons from free plasmons is discussed.
Adiabatic regularisation of power spectra in k-inflation
Alinea, Allan L.; Kubota, Takahiro; Nakanishi, Yukari; Naylor, Wade E-mail: kubota@celas.osaka-u.ac.jp E-mail: naylor@phys.sci.osaka-u.ac.jp
2015-06-01
We look at the question posed by Parker et al. about the effect of UV regularisation on the power spectrum for inflation. Focusing on the slow-roll k-inflation, we show that up to second order in the Hubble and sound flow parameters, the adiabatic regularisation of such model leads to no difference in the power spectrum apart from certain cases that violate near scale-invariant power spectra. Furthermore, extending to non-minimal k-inflation, we establish the equivalence of the subtraction terms in the adiabatic regularisation of the power spectrum in Jordan and Einstein frames.
Local control of non-adiabatic dissociation dynamics
NASA Astrophysics Data System (ADS)
Bomble, L.; Chenel, A.; Meier, C.; Desouter-Lecomte, M.
2011-05-01
We present a theoretical approach which consists of applying the strategy of local control to projectors based on asymptotic scattering states. This allows to optimize final state distributions upon laser excitation in cases where strong non-adiabatic effects are present. The approach, despite being based on a time-local formulation, can take non-adiabatic transitions that appear at later times fully into account and adopt a corresponding control strategy. As an example, we show various dissociation channels of HeH+, a system where the ultrafast dissociation dynamics is determined by strong non-Born-Oppenheimer effects.
Spatial adiabatic passage: a review of recent progress.
Menchon-Enrich, R; Benseny, A; Ahufinger, V; Greentree, A D; Busch, Th; Mompart, J
2016-07-01
Adiabatic techniques are known to allow for engineering quantum states with high fidelity. This requirement is currently of large interest, as applications in quantum information require the preparation and manipulation of quantum states with minimal errors. Here we review recent progress on developing techniques for the preparation of spatial states through adiabatic passage, particularly focusing on three state systems. These techniques can be applied to matter waves in external potentials, such as cold atoms or electrons, and to classical waves in waveguides, such as light or sound. PMID:27245462
Operator product expansion algebra
Holland, Jan; Hollands, Stefan
2013-07-15
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE,
Conflation: a new type of accelerated expansion
NASA Astrophysics Data System (ADS)
Fertig, Angelika; Lehners, Jean-Luc; Mallwitz, Enno
2016-08-01
In the framework of scalar-tensor theories of gravity, we construct a new kind of cosmological model that conflates inflation and ekpyrosis. During a phase of conflation, the universe undergoes accelerated expansion, but with crucial differences compared to ordinary inflation. In particular, the potential energy is negative, which is of interest for supergravity and string theory where both negative potentials and the required scalar-tensor couplings are rather natural. A distinguishing feature of the model is that, for a large parameter range, it does not significantly amplify adiabatic scalar and tensor fluctuations, and in particular does not lead to eternal inflation and the associated infinities. We also show how density fluctuations in accord with current observations may be generated by adding a second scalar field to the model. Conflation may be viewed as complementary to the recently proposed anamorphic universe of Ijjas and Steinhardt.
Expansion Dynamics of Ultracold Neutral Plasmas
NASA Astrophysics Data System (ADS)
Killian, Thomas
2006-05-01
Ultracold neutral plasmas [1], formed by photoionizing laser-cooled atoms near the ionization threshold, stretch the boundaries of traditional neutral plasma physics. The electron temperature in these plasmas is from 1-1000K and the ion temperature is around 1 K. The density can be as high as 10^10 cm-3. Fundamental interest stems from the possibility of creating strongly-coupled plasmas, but recent experimental and theoretical work has focused on the equilibration and expansion dynamics. Using optical absorption imaging [2], we study expansion dynamics during the first 30 microseconds after photoionization. Images record the spatial extent of the plasma, while the Doppler broadened absorption spectrum measures the ion velocity spectrally. The expansion is driven by the pressure of the electron gas, so the ion acceleration depends on the electron temperature. Evidence for terminal ion velocity supports predictions of adiabatic cooling of electrons during expansion [3]. Images confirm the self-similar nature of a Gaussian density distribution. Understanding expansion dynamics is important for plans to laser cool and trap the plasma. This work is supported by the National Science Foundation and David and Lucille Packard Foundation. [1] T. C. Killian, S. Kulin, S. D. Bergeson, L. A. Orozco, C. Orzel, and S. L. Rolston, Phys. Rev. Lett. 83, 4776 (1999). [2] C. E. Simien, Y.C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, Phys. Rev. Lett. 92, 143001 (2004). [3] F. Robicheaux and J. D. Hanson, Phys. Plasmas 10, 2217 (2003), T. Pohl, T. Pattard, and J. M. Rost, Phys. Rev. A 70, 033416 (2004).
NASA Astrophysics Data System (ADS)
Kimura, Jun-Ichi; Kawabata, Hiroshi
2014-06-01
numerical mass balance calculation model for the adiabatic melting of a dry to hydrous peridotite has been programmed in order to simulate the trace element compositions of basalts from mid-ocean ridges, back-arc basins, ocean islands, and large igneous provinces. The Excel spreadsheet-based calculator, Hydrous Adiabatic Mantle Melting Simulator version 1 (HAMMS1) uses (1) a thermodynamic model of fractional adiabatic melting of mantle peridotite, with (2) the parameterized experimental melting relationships of primitive to depleted mantle sources in terms of pressure, temperature, water content, and degree of partial melting. The trace element composition of the model basalt is calculated from the accumulated incremental melts within the adiabatic melting regime, with consideration for source depletion. The mineralogic mode in the primitive to depleted source mantle in adiabat is calculated using parameterized experimental results. Partition coefficients of the trace elements of mantle minerals are parameterized to melt temperature mostly from a lattice strain model and are tested using the latest compilations of experimental results. The parameters that control the composition of trace elements in the model are as follows: (1) mantle potential temperature, (2) water content in the source mantle, (3) depth of termination of adiabatic melting, and (4) source mantle depletion. HAMMS1 enables us to obtain the above controlling parameters using Monte Carlo fitting calculations and by comparing the calculated basalt compositions to primary basalt compositions. Additionally, HAMMS1 compares melting parameters with a major element model, which uses petrogenetic grids formulated from experimental results, thus providing better constraints on the source conditions.
NASA Astrophysics Data System (ADS)
Traaseth, Nathaniel J.; Chao, Fa-An; Masterson, Larry R.; Mangia, Silvia; Garwood, Michael; Michaeli, Shalom; Seelig, Burckhard; Veglia, Gianluigi
2012-06-01
NMR relaxation methods probe biomolecular motions over a wide range of timescales. In particular, the rotating frame spin-lock R1ρ and Carr-Purcell-Meiboom-Gill (CPMG) R2 experiments are commonly used to characterize μs to ms dynamics, which play a critical role in enzyme folding and catalysis. In an effort to complement these approaches, we introduced the Heteronuclear Adiabatic Relaxation Dispersion (HARD) method, where dispersion in rotating frame relaxation rate constants (longitudinal R1ρ and transverse R2ρ) is created by modulating the shape and duration of adiabatic full passage (AFP) pulses. Previously, we showed the ability of the HARD method to detect chemical exchange dynamics in the fast exchange regime (kex ˜ 104-105 s-1). In this article, we show the sensitivity of the HARD method to slower exchange processes by measuring R1ρ and R2ρ relaxation rates for two soluble proteins (ubiquitin and 10C RNA ligase). One advantage of the HARD method is its nominal dependence on the applied radio frequency field, which can be leveraged to modulate the dispersion in the relaxation rate constants. In addition, we also include product operator simulations to define the dynamic range of adiabatic R1ρ and R2ρ that is valid under all exchange regimes. We conclude from both experimental observations and simulations that this method is complementary to CPMG-based and rotating frame spin-lock R1ρ experiments to probe conformational exchange dynamics for biomolecules. Finally, this approach is germane to several NMR-active nuclei, where relaxation rates are frequency-offset independent.
Self-similar expansion of a warm dense plasma
Djebli, Mourad; Moslem, Waleed M.
2013-07-15
The properties of an expanding plasma composed of degenerate electron fluid and non-degenerate ions are studied. For our purposes, we use fluid equations for ions together with the electron momentum equation that include quantum forces (e.g., the quantum statistical pressure, forces due to the electron-exchange and electron correlations effects) and the quasi-neutrality condition. The governing equation is written in a tractable form by using a self-similar transformation. Numerical results for typical beryllium plasma parameters revealed that, during the expansion, the ion acoustic speed decreases for both isothermal and adiabatic ion pressure. When compared with classical hydrodynamic plasma expansion model, the electrons and ions are found to initially escape faster in vacuum creating thus an intense electric field that accelerates most of the particles into the vacuum ahead of the plasma expansion. The relevancy of the present model to beryllium plasma produced by a femto-second laser is highlighted.
Condensation in CO2 free jet expansions. I - Dimer formation.
NASA Technical Reports Server (NTRS)
Dorfeld, W. G.; Hudson, J. B.
1973-01-01
A theoretical and experimental investigation of the kinetics of CO2 dimer formation in the adiabatically expanding core of a free jet expansion has been carried out. The theoretical analysis is based on dimer formation by an efficient termolecular process and dimer destruction by bimolecular collisions. Account is taken of the expected variation of the specific heat ratio during the expansion and of the effective increase in the termolecular collision rate at low temperatures due to the presence of loosely bound orbiting pairs. Experimental dimer concentrations were measured mass spectrometrically by forming a molecular beam from the expanded gas mixture after the onset of molecular flow. Observed dimer concentrations, for a range of pre-expansion conditions of 400 to 900 torr pressure and room temperature, are in good agreement with the theoretical analysis, provided that account is taken of the effect of loosely bound orbiting pairs at low temperatures.
NASA Astrophysics Data System (ADS)
Strobel, George L.
1990-04-01
A hot dense vapor expanding adiabatically into a vacuum is studied. A condensed phase develops after saturation and supercooling conditions have been achieved. The final state of the system consists of liquid drops in a expanding, cooling vapor. The final condensed mole fraction depends on the drop growth rate compared to the fractional volume rate of expansion at the time saturation is achieved. Drops are produced by a nonequilibrium collision process during supercooling of the vapor. The dependence of the number of drops on various factors is established. The First Law of Thermodynamics is used to solve for the evolution of the system, assuming the volume expansion rate is known. The initial vapor can include an inert gas that does not condense in the temperature range of interest. The vapors are treated as ideal gases until saturation occurs. Slow expansions result in the highest condensed mole fractions. Slow expansions are the result of one-dimensional versus three-dimensional expansions and from saturation occurring at high temperatures and densities. The size per drop depends mostly on how many drops are formed in the nonequilibrium supercooling process.
Does temperature increase or decrease in adiabatic decompression of magma?
NASA Astrophysics Data System (ADS)
Kilinc, A. I.; Ghiorso, M. S.; Khan, T.
2011-12-01
We have modeled adiabatic decompression of an andesitic and a basaltic magma as an isentropic process using the Melts algorithm. Our modeling shows that during adiabatic decompression temperature of andesitic magma increases but temperature of basaltic magma decreases. In an isentropic process entropy is constant so change of temperature with pressure can be written as dT/dP=T (dV/dT)/Cp where T (dV/dT)/Cp is generally positive. If delta P is negative so is delta T. In general, in the absence of phase change, we expect the temperature to decrease with adiabatic decompression. The effect of crystallization is to turn a more entropic phase (liquid) into a less entropic phase (solid), which must be compensated by raising the temperature. If during adiabatic decompression there is small amount or no crystallization, T (dV/dT)/Cp effect which lowers the temperature overwhelms the small amount of crystallization, which raises the temperature, and overall system temperature decreases.
On adiabatic stabilization and geometry of Bunsen flames
Sun, C.J.; Sung, C.J.; Law, C.K.
1994-12-31
Two aspects of stretched flame dynamics are investigated via the model problem of the stabilization and geometry of Bunsen flames. Specifically, the possibility of stabilizing a Bunsen flame without heat loss to the burner rim is experimentally investigated by examining the temperature of the rim, the temperature gradient between the rim and the flame base, and the standoff distance of the flame base in relation to the flame thickness. Results show that, while heat loss is still the dominant stabilization mechanism for flames in uniform flows and for strong flames in parabolic flow, adiabatic stabilization and, subsequently, blowoff are indeed possible for weak flames in parabolic flows. The adiabatically stabilized flame is then modeled by using the scalar field formulation and by allowing for the effects of curvature and aerodynamic straining on the local flame speed. The calculated flame configuration agrees well with the experiment for the adiabatically stabilized flame but not for the nonadiabatic flame. Results further show that active modification of the flame curvature is the dominant cause for the flame to maintain adiabatic stabilization. Implications of the present results on turbulent flame modeling are discussed.
Digitized adiabatic quantum computing with a superconducting circuit
NASA Astrophysics Data System (ADS)
Barends, R.; Shabani, A.; Lamata, L.; Kelly, J.; Mezzacapo, A.; Heras, U. Las; Babbush, R.; Fowler, A. G.; Campbell, B.; Chen, Yu; Chen, Z.; Chiaro, B.; Dunsworth, A.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J. Y.; Neeley, M.; Neill, C.; O'Malley, P. J. J.; Quintana, C.; Roushan, P.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Solano, E.; Neven, H.; Martinis, John M.
2016-06-01
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Digitized adiabatic quantum computing with a superconducting circuit.
Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M
2016-06-01
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable. PMID:27279216
Digitized adiabatic quantum computing with a superconducting circuit.
Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M
2016-06-08
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques
NASA Astrophysics Data System (ADS)
Ho, Man-Ho
2016-09-01
In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation of the reduced eta-invariant.
A Kinetic Study of the Adiabatic Polymerization of Acrylamide.
ERIC Educational Resources Information Center
Thomson, R. A. M.
1986-01-01
Discusses theory, procedures, and results for an experiment which demonstrates the application of basic physics to chemical problems. The experiment involves the adiabatic process, in which polymerization carried out in a vacuum flask is compared to the theoretical prediction of the model with the temperature-time curve obtained in practice. (JN)
An easy to perform but often counterintuitive demonstration of gas expansion
NASA Astrophysics Data System (ADS)
Baker, Brad
1999-08-01
During their thermodynamics courses, students learn that the temperature of an ideal gas will drop during an adiabatic reversible expansion. They also usually learn that no change of temperature occurs as a result of a certain free expansion. These results often become intuitively connected with gas expansion. However when air expands freely into an evacuated chamber from a constant pressure atmosphere, its temperature increases. This can be easily demonstrated using only simple equipment and makes for a memorable lesson on the importance of identifying what exactly is the system and then simply applying the first law of thermodynamics.
NASA Astrophysics Data System (ADS)
Dattani, Nike; Tanburn, Richard; Lunt, Oliver
We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states. Our methods are even more general. They can be used to shift a Hamiltonian's density of states away from the ground state, so that fewer states occupy the low-lying energies near the minimum, hence allowing for faster adiabatic passages to find the ground state with less risk of getting caught in an undesired low-lying excited state during the passage. Even more generally, our methods can be used to transform a discrete optimization problem into a new one whose unique minimum still encodes the desired answer, but with the objective function's values forming a different landscape. Aspects of the landscape such as the objective function's range, or the values of certain coefficients, or how many different inputs lead to a given output value, can be decreased *or* increased. One of the many examples for which these methods are useful is in finding the ground state of a Hamiltonian using NMR. We apply our methods to an AQC algorithm for integer factorization, and the first method reduces the maximum runtime in our example by up to 754%, and the second method reduces the maximum runtime of another example by up to 250%.
Expansion techniques for collisionless stellar dynamical simulations
Meiron, Yohai; Li, Baile; Holley-Bockelmann, Kelly; Spurzem, Rainer
2014-09-10
We present graphics processing unit (GPU) implementations of two fast force calculation methods based on series expansions of the Poisson equation. One method is the self-consistent field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other method is the multipole expansion (MEX) method, which is a Taylor-like expansion of the Green's function. MEX, which has been advocated in the past, has not gained as much popularity as SCF. Both are particle-field methods and optimized for collisionless galactic dynamics, but while SCF is a 'pure' expansion, MEX is an expansion in just the angular part; thus, MEX is capable of capturing radial structure easily, while SCF needs a large number of radial terms. We show that despite the expansion bias, these methods are more accurate than direct techniques for the same number of particles. The performance of our GPU code, which we call ETICS, is profiled and compared to a CPU implementation. On the tested GPU hardware, a full force calculation for one million particles took ∼0.1 s (depending on expansion cutoff), making simulations with as many as 10{sup 8} particles fast for a comparatively small number of nodes.
Expansion of the planetary disturbing function.
NASA Technical Reports Server (NTRS)
Broucke, R.; Smith, G.
1971-01-01
Some methods are described for the expansion of the disturbing function in planetary theory. One method uses the classical binomial expansion theorem or a successive approximation process derived from it. Another method is a direct application of the Laplace series expansions. For both methods it is proposed to first prepare the series to be manipulated by a scaling operation. These methods can be applied either in a literal or in a numerical form, or any combination of both, but they are especially designed for use on a large scale digital computer with standard Poisson series programs. No usage is made of Newcomb operators or derivatives of Laplace coefficients.
Implementation of a quantum adiabatic algorithm for factorization on two qudits
Zobov, V. E. Ermilov, A. S.
2012-06-15
Implementation of an adiabatic quantum algorithm for factorization on two qudits with the number of levels d{sub 1} and d{sub 2} is considered. A method is proposed for obtaining a time-dependent effective Hamiltonian by means of a sequence of rotation operators that are selective with respect to the transitions between neighboring levels of a qudit. A sequence of RF magnetic field pulses is obtained, and a factorization of the numbers 35, 21, and 15 is numerically simulated on two quadrupole nuclei with spins 3/2 (d{sub 1} = 4) and 1 (d{sub 2} = 3).
Zhang, Z; Duan, L-M
2013-11-01
We propose a method to generate massive entanglement in a spinor Bose-Einstein condensate from an initial product state through an adiabatic sweep of the magnetic field across a quantum phase transition induced by competition between the spin-dependent collision interaction and the quadratic Zeeman effect. The generated many-body entanglement is characterized by the experimentally measurable entanglement depth in the proximity of the Dicke state. We show that the scheme is robust to practical noise and experimental imperfection and under realistic conditions it is possible to generate genuine entanglement for hundreds of atoms. PMID:24237490
Zhang, Z; Duan, L-M
2013-11-01
We propose a method to generate massive entanglement in a spinor Bose-Einstein condensate from an initial product state through an adiabatic sweep of the magnetic field across a quantum phase transition induced by competition between the spin-dependent collision interaction and the quadratic Zeeman effect. The generated many-body entanglement is characterized by the experimentally measurable entanglement depth in the proximity of the Dicke state. We show that the scheme is robust to practical noise and experimental imperfection and under realistic conditions it is possible to generate genuine entanglement for hundreds of atoms.
Chaotic jumps in the generalized first adiabatic invariant in current sheets
NASA Technical Reports Server (NTRS)
Brittnacher, M. J.; Whipple, E. C.
1991-01-01
The present study examines how the changes in the generalized first adiabatic invariant J derived from the separatrix crossing theory can be incorporated into the drift variable approach to generating distribution functions. A method is proposed for determining distribution functions for an ensemble of particles following interaction with the tail current sheet by treating the interaction as a scattering problem characterized by changes in the invariant. Generalized drift velocities are obtained for a 1D tail configuration by using the generalized first invariant. The invariant remained constant except for the discrete changes caused by chaotic scattering as the particles cross the separatrix.