Collective excitations of harmonically trapped ideal gases
Van Schaeybroeck, B.; Lazarides, A.
2009-01-01
We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show
Haddad, L. H.; Carr, Lincoln D.
2015-11-01
We analyze the vortex solution space of the (2+1)-dimensional nonlinear Dirac equation for bosons in a honeycomb optical lattice at length scales much larger than the lattice spacing. Dirac point relativistic covariance combined with s-wave scattering for bosons leads to a large number of vortex solutions characterized by different functional forms for the internal spin and overall phase of the order parameter. We present a detailed derivation of these solutions which include skyrmions, half-quantum vortices, Mermin-Ho and Anderson-Toulouse vortices for vortex winding {\\ell }=1. For {\\ell }≥slant 2 we obtain topological as well as non-topological solutions defined by the asymptotic radial dependence. For arbitrary values of ℓ the non-topological solutions include bright ring-vortices which explicitly demonstrate the confining effects of the Dirac operator. We arrive at solutions through an asymptotic Bessel series, algebraic closed-forms, and using standard numerical shooting methods. By including a harmonic potential to simulate a finite trap we compute the discrete spectra associated with radially quantized modes. We demonstrate the continuous spectral mapping between the vortex and free particle limits for all of our solutions.
Component separation in harmonically trapped boson-fermion mixtures
DEFF Research Database (Denmark)
Nygaard, Nicolai; Mølmer, Klaus
1999-01-01
We present a numerical study of mixed boson-fermion systems at zero temperature in isotropic and anise tropic harmonic traps. We investigate the phenomenon of component separation as a function of the strength ut the interparticle interaction. While solving a Gross-Pitaevskii mean-field equation ...... for the boson distribution in the trap, we utilize two different methods to extract the density profile of the fermion component; a semiclassical Thomas-Fermi approximation and a quantum-mechanical Slater determinant Schrodinger equation....
Higher order harmonics of reactor neutron equation
International Nuclear Information System (INIS)
Li Fu; Hu Yongming; Luo Zhengpei
1996-01-01
The flux mapping method using the higher order harmonics of the neutron equation is proposed. Based on the bi-orthogonality of the higher order harmonics, the process and formulas for higher order harmonics calculation are derived via the source iteration method with source correction. For the first time, not only any order harmonics for up-to-3-dimensional geometry are achieved, but also the preliminary verification to the capability for flux mapping have been carried out
Variational Integrals of a Class of Nonhomogeneous -Harmonic Equations
Directory of Open Access Journals (Sweden)
Guanfeng Li
2014-01-01
Full Text Available We introduce a class of variational integrals whose Euler equations are nonhomogeneous -harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous -harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.
First exit times of harmonically trapped particles: a didactic review
International Nuclear Information System (INIS)
Grebenkov, Denis S
2015-01-01
We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by a one- or multidimensional Ornstein–Uhlenbeck process. We start by recalling the main derivation steps of a propagator using Langevin and Fokker–Planck equations. The mean exit time, the moment-generating function and the survival probability are then expressed through confluent hypergeometric functions and thoroughly analyzed. We also present a rapidly converging series representation of confluent hypergeometric functions that is particularly well suited for numerical computation of eigenvalues and eigenfunctions of the governing Fokker–Planck operator. We discuss several applications of first exit times, such as the detection of time intervals during which motor proteins exert a constant force onto a tracer in optical tweezers single-particle tracking experiments; adhesion bond dissociation under mechanical stress; characterization of active periods of trend-following and mean-reverting strategies in algorithmic trading on stock markets; relation to the distribution of first crossing times of a moving boundary by Brownian motion. Some extensions are described, including diffusion under quadratic double-well potential and anomalous diffusion. (topical review)
A modular spherical harmonics approach to the neutron transport equation
International Nuclear Information System (INIS)
Inanc, F.; Rohach, A.F.
1989-01-01
A modular nodal method was developed for solving the neutron transport equation in 2-D xy coordinates. The spherical harmonic expansion was used for approximating the second-order even-parity form of the neutron transport equation. The boundary conditions of the spherical harmonics approximation were derived in a form to have forms analogous to the partial currents in the neutron diffusion equation. Relations were developed for generating both the second-order spherical harmonic equations and the boundary conditions in an automated computational algorithm. Nodes using different orders of the spherical harmonics approximation to the transport equation were interfaced through mixed-type boundary conditions. The determination of spherical harmonic orders implemented in the nodes were determined by the scheme in an automated manner. Results of the method compared favorably to benchmark problems. (author)
Automatic computation and solution of generalized harmonic balance equations
Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.
2018-02-01
Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.
Universal few-body physics in a harmonic trap
International Nuclear Information System (INIS)
Tolle, S.; Hammer, H.W.; Metsch, B.Ch.
2011-01-01
Few-body systems with resonant short-range interactions display universal properties that do not depend on the details of their structure or their interactions at short distances. In the three-body system, these properties include the existence of a geometric spectrum of three-body Efimov states and a discrete scaling symmetry. Similar universal properties appear in 4-body and possibly higher-body systems as well. We set up an effective theory for few-body systems in a harmonic trap and study the modification of universal physics for 3- and 4-particle systems in external confinement. In particular, we focus on systems where the Efimov effect can occur and investigate the dependence of the 4-body spectrum on the experimental tuning parameters. (authors)
First and second sound of a unitary Fermi gas in highly oblate harmonic traps
International Nuclear Information System (INIS)
Hu, Hui; Dyke, Paul; Vale, Chris J; Liu, Xia-Ji
2014-01-01
We theoretically investigate first and second sound modes of a unitary Fermi gas trapped in a highly oblate harmonic trap at finite temperatures. Following the idea by Stringari and co-workers (2010 Phys. Rev. Lett. 105 150402), we argue that these modes can be described by the simplified two-dimensional two-fluid hydrodynamic equations. Two possible schemes—sound wave propagation and breathing mode excitation—are considered. We calculate the sound wave velocities and discretized sound mode frequencies, as a function of temperature. We find that in both schemes, the coupling between first and second sound modes is large enough to induce significant density fluctuations, suggesting that second sound can be directly observed by measuring in situ density profiles. The frequency of the second sound breathing mode is found to be highly sensitive to the superfluid density. (paper)
Maximal Regularity of the Discrete Harmonic Oscillator Equation
Directory of Open Access Journals (Sweden)
Airton Castro
2009-01-01
Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.
A nonlinear bounce kinetic equation for trapped electrons
International Nuclear Information System (INIS)
Gang, F.Y.
1990-03-01
A nonlinear bounce averaged drift kinetic equation for trapped electrons is derived. This equation enables one to compute the nonlinear response of the trapped electron distribution function in terms of the field-line projection of a potential fluctuation left-angle e -inqθ φ n right-angle b . It is useful for both analytical and computational studies of the nonlinear evolution of short wavelength (n much-gt 1) trapped electron mode-driven turbulence. 7 refs
Using "Tracker" to Prove the Simple Harmonic Motion Equation
Kinchin, John
2016-01-01
Simple harmonic motion (SHM) is a common topic for many students to study. Using the free, though versatile, motion tracking software; "Tracker", we can extend the students experience and show that the general equation for SHM does lead to the correct period of a simple pendulum.
Inhomogeneous critical nonlinear Schroedinger equations with a harmonic potential
International Nuclear Information System (INIS)
Cao Daomin; Han Pigong
2010-01-01
In this paper, we study the Cauchy problem of the inhomogeneous nonlinear Schroedinger equation with a harmonic potential: i∂ t u=-div(f(x)∇u)+|x| 2 u-k(x)|u| 4/N u, x is an element of R N , N≥1, which models the remarkable Bose-Einstein condensation. We discuss the existence and nonexistence results and investigate the limiting profile of blow-up solutions with critical mass.
Bose gases in one-dimensional harmonic trap
Indian Academy of Sciences (India)
dimensional Bose gas confined by a harmonic potential are studied using different ensemble approaches. Combining number theory methods, a new approach is presented to calculate the occupation numbers of different energy levels in ...
A method of solving simple harmonic oscillator Schroedinger equation
Maury, Juan Carlos F.
1995-01-01
A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu
2016-02-01
The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.
Bose gases in one-dimensional harmonic trap
Indian Academy of Sciences (India)
MS received 10 June 2015; revised 27 November 2015; accepted 22 December 2015; published online 21 September 2016 ... trap can be easily adjusted by Feshbach resonance tech- ... For convenience, the ground-state energy level is set.
Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach
Energy Technology Data Exchange (ETDEWEB)
Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae
2015-02-15
This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.
International Nuclear Information System (INIS)
Klimas, A.J.
1990-01-01
Trapping saturation of the bump-on-tail instability is discussed using electron plasma Vlasov simulation results. The role of electrostatic harmonic excitation is considered in detail and shown to play a decisive role in the saturation of the instability. An extensive discussion of the simulation results is given to show that the results are not significantly limited by the finite number of Fourier modes used nor by the discrete distribution of those modes in wave number. It is argued that in the leading edge of Earth's electron foreshock a narrow wave number band of unstable field modes leads to trapping saturation of the bump-on-tail instability while simultaneously exciting electrostatic plasma waves at harmonics of the plasma frequency in simialr narrow bands of shorter wavelengths. The argument is based (1) on the observations of Lacombe et al. (1985), who found intense plasma waves at the leading edge of the foreshock with a spectral distribution sufficiently narrow to trap particles in resonance with the waves, and (2) on numerical simulations of the foreshock electron plasma which indicate that trapping saturation of the bump-on-tail instability leads to phase space vortex formation with consequent excitation of electrostatic harmonics. Thus it is suggested that observations of electrostatic harmonics in the leading edge of the foreshock would strongly implicate trapping as the saturation mechanism for the bump-on-tail instability in that region
Self-driven particles in linear flows and trapped in a harmonic potential
Sandoval, Mario; Hidalgo-Gonzalez, Julio C.; Jimenez-Aquino, Jose I.
2018-03-01
We present analytical expressions for the mean-square displacement of self-driven particles in general linear flows and trapped in a harmonic potential. The general expressions are applied to three types of linear flows, namely, shear flow, solid-body rotation flow, and extensional flow. By using Brownian dynamics simulations, the effect of trapping and external linear flows on the particles' distribution is also elucidated. These simulations also enabled us to validate our theoretical results.
Freely floating structures trapping time-harmonic water waves (revisited)
Kuznetsov, Nikolay; Motygin, Oleg
2014-01-01
We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite number of surface-piercing bodies floating freely. The mathematical model of time-harmonic motion is a spectral problem in which the frequency of oscillations serves as the spectral parameter. It is proved that there exist axisymmetric structures consisting of ...
Correlation properties of a three-body bosonic mixture in a harmonic trap
DEFF Research Database (Denmark)
Barfknecht, R. E.; Salami Dehkharghani, Amin; Foerster, A.
2016-01-01
We make use of a simple pair correlated wave function approach to obtain results for the ground-state densities and momentum distribution of a one-dimensional three-body bosonic system with different interactions in a harmonic trap. For equal interactions this approach is able to reproduce the kn...
Harmonically trapped dipolar fermions in a two-dimensional square lattice
DEFF Research Database (Denmark)
Larsen, Anne-Louise G.; Bruun, Georg
2012-01-01
We consider dipolar fermions in a two-dimensional square lattice and a harmonic trapping potential. The anisotropy of the dipolar interaction combined with the lattice leads to transitions between phases with density order of different symmetries. We show that the attractive part of the dipolar...
Daily, Kevin Michael
Underlying the many-body effects of ultracold atomic gases are the few-body dynamics and interparticle interactions. Moreover, the study of few-body systems on their own has accelerated due to confining few atoms in each well of a deep optical lattice or in a single microtrap. This thesis studies the microscopic properties of few-body systems under external spherically symmetric harmonic confinement and how the few-body properties translate to the many-body system. Bosonic and fermionic few-body systems are considered and the dependence of the energetics and other quantities are investigated as functions of the s-wave scattering length, the mass ratio and the temperature. It is found that the condensate fraction of a weakly-interacting trapped Bose gas depletes quadratically with the s-wave scattering length. The next order term in the depletion depends not only, as might be expected naively, on the s-wave scattering length and the effective range but additionally on a two-body parameter that is not needed to reproduce the energy of weakly-interacting trapped Bose gases. This finding has important implications for effective field theory treatments of the system. Weakly-interacting atomic and molecular two-component Fermi gases with equal masses are described using perturbative approaches. The energy shifts are tabulated and interpreted, and a measure of the molecular condensate fraction is developed. We develop a measure of the molecular condensate fraction using the two-body density matrix and we develop a model of the spherical component of the momentum distribution that agrees well with stochastic variational calculations. We establish the existence of intersystem degeneracies for equal mass two-component Fermi gases with zero-range interactions, where the eigen energies of the spin-imbalanced system are degenerate with a subset of the eigen energies of the more spin-balanced system and the same total number of fermions. For unequal mass two-component Fermi
Spinor monopole harmonics and the Pauli spin equation
International Nuclear Information System (INIS)
Pereira, J.G.; Ferreira, P.L.
1982-01-01
In the framework of Wu and Yang theory of U(1) magnetic monopoles, two problems are revisited: (i) the binding of spin-0 monopole to a spin-1/2 particle possessing an arbitrary magnetic dipole moment, and (ii) the energy levels and properties of the electron-dyon system. In both problems, the spin-1/2 particle is assumed to obey the Pauli spin equation. Spin-orbit and other higher order terms are treated as a perturbation, in connection with the second mentioned problem. Wu and Yang's spinor monopole harmonics allow an elegant and simplified treatment of those problems. The results obtained are in good agreement with those obtained in older papers. (Author) [pt
International Nuclear Information System (INIS)
Leznov, A.N.
1994-01-01
A general method for the construction of solutions of the d'Alamberian and double d'Alamberian (harmonic and bi-harmonic) equations with local dependence of arbitrary functions upon two independent arguments is proposed. The connection between solutions of this kind and self-dual configurations of gauge fields having no singularities is established. 5 refs
Klimas, Alexander J.
1990-01-01
The Vlasov simulation is used to examine the trapping saturation of the bump-on-tail instability both with and without mode-mode coupling and subsequent harmonic excitation. It is found that adding the pumped harmonic modes leads to a significant difference in the behavior of the phase-space distribution function near the unstable bump at the saturation time of the instability. The pumped modes permit rapid plateau formation on the space-averaged velocity distribution, in effect preventing the onset of the quasi-linear velocity-diffusion saturation mechanism.
Dziekonski, Eric T; Johnson, Joshua T; McLuckey, Scott A
2017-04-18
Mass resolution (M/ΔM fwhm) is observed to linearly increase with harmonic order in a Fourier transform electrostatic linear ion trap (ELIT) mass spectrometer. This behavior was predicted by Grosshans and Marshall for frequency-multiple detection in a Fourier transform ion cyclotron resonance mass spectrometer only for situations when the prominent mechanism for signal decay is ion ejection from the trap. As the analyzer pressure in our ELIT chamber is relatively high, such that collisional scattering and collision-induced dissociation are expected to underlie much of the ion loss, we sought to explore the relationship between harmonic order and mass resolution. Mass resolutions of 36 900 (fundamental), 75 850 (2nd harmonic), and 108 200 (3rd harmonic) were obtained for GdO + (avg. m/z 173.919) with a transient length of 300 ms. To demonstrate that the mass resolution was truly increasing with harmonic order, the unresolved isotopes at the fundamental distribution of cytochrome c +8 (m/z ∼ 1549) were nearly baseline, resolved at the third harmonic (mass resolution ≈ 23 000) with a transient length of only 200 ms. This experiment demonstrates that, when the ion density is sufficiently low, ions with frequency differences of less than 4 Hz remain uncoalesced. Higher harmonics can be used to increase the effective mass resolution for a fixed transient length and thereby may enable the resolution of closely spaced masses, determination of a protein ion's charge state, and study of the onset of peak coalescence when the resolution at the fundamental frequency is insufficient.
The Spectrum of Particles with Short-Ranged Interactions in a Harmonic Trap
Directory of Open Access Journals (Sweden)
Metsch B. Ch.
2010-04-01
Full Text Available The possibility to control short-ranged interactions of cold gases in optical traps by Feshbachresonances makes these systems ideal candidates to study universal scaling properties and Eﬁmov physics. The spectrum of particles in a trap, idealised by a harmonic oscillator potential, in the zero range limit with 2- and 3-particle contact interactions is studied numerically. The Hamiltonian is regularised by restricting the oscillator basis and the coupling constants are tuned such that the ground state energies of the 2- and 3-particle sector are reproduced [1],[2]. Results for 2-, 3-, and 4 particle systems are presented and compared to exact results [3],[4].
International Nuclear Information System (INIS)
Glasser, M.L.; March, N.H.; Nieto, L.M.
2010-01-01
This study is motivated by the very recent work on correlation energy as approximated by the Thomas-Fermi (TF) semiclassical limit [B.R. Landry, et al., Phys. Rev. Lett. 103 (2009) 066401]. In contrast, and motivated by the Hohenberg-Kohn theorem, our work is focussed primarily on the correlated TF ground-state density. We invoke directly the Holas et al. result that for two-fermion systems with harmonic trapping, the fermion-fermion interaction u simply adds to the trapping potential. We conclude this report with some results on correlation kinetic energy for two-fermion systems.
A new iterative solver for the time-harmonic wave equation
Riyanti, C.D.; Erlangga, Y.A.; Plessix, R.E.; Mulder, W.A.; Vuik, C.; Oosterlee, C.
2006-01-01
The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can
Disk-shaped Bose-Einstein condensates in the presence of an harmonic trap and an optical lattice
International Nuclear Information System (INIS)
Kapitula, Todd; Kevrekidis, Panayotis G.; Frantzeskakis, D. J.
2008-01-01
We study the existence and stability of solutions of the two-dimensional nonlinear Schroedinger equation in the combined presence of a parabolic and a periodic potential. The motivating physical example consists of Bose-Einstein condensates confined in an harmonic (e.g., magnetic) trap and an optical lattice. By connecting the nonlinear problem with the underlying linear spectrum, we examine the bifurcation of nonlinear modes out of the linear ones for both focusing and defocusing nonlinearities. In particular, we find real-valued solutions (such as multipoles) and complex-valued ones (such as vortices). A primary motivation of the present work is to develop ''rules of thumb'' about what waveforms to expect emerging in the nonlinear problem and about the stability of those modes. As a case example of the latter, we find that among the real-valued solutions, the one with larger norm for a fixed value of the chemical potential is expected to be unstable
Harmonically trapped attractive and repulsive spin–orbit and Rabi coupled Bose–Einstein condensates
International Nuclear Information System (INIS)
Chiquillo, Emerson
2017-01-01
Numerically we investigate the ground state of effective one-dimensional spin–orbit (SO) and Rabi coupled two pseudo-spinor Bose–Einstein condensates (BECs) under the effect of harmonic traps. For both signs of the interaction, density profiles of SO and Rabi coupled BECs in harmonic potentials, which simulate a real experimental situation are obtained. The harmonic trap causes a strong reduction of the multi-peak nature of the condensate and it increases its density. For repulsive interactions, the increase of SO coupling results in an uncompressed less dense condensate and with increased multi-peak nature of the density. The increase of Rabi coupling leads to a density increase with an almost constant number of multi-peaks. For both signs of the interaction and negative values of Rabi coupling, the condensate develops a notch in the central point and it seems to a dark-in-bright soliton. In the case of the attractive nonlinearity, an interesting result is the increase of the collapse threshold under the action of the SO and Rabi couplings. (paper)
Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap
Scopa, Stefano; Unterberger, Jéremie; Karevski, Dragi
2018-05-01
We study the unitary dynamics of a 1D gas of hard-core bosons trapped into a harmonic potential which varies periodically in time with frequency . Such periodic systems can be classified into orbits of different monodromies corresponding to two different physical situations, namely the case in which the bosonic cloud remains stable during the time-evolution and the case where it turns out to be unstable. In the present work we derive in the large particle number limit exact results for the stroboscopic evolution of the energy and particle densities in both physical situations.
Correlation properties of a three-body bosonic mixture in a harmonic trap
International Nuclear Information System (INIS)
Barfknecht, R E; Foerster, A; Dehkharghani, A S; Zinner, N T
2016-01-01
We make use of a simple pair correlated wave function approach to obtain results for the ground-state densities and momentum distribution of a one-dimensional three-body bosonic system with different interactions in a harmonic trap. For equal interactions this approach is able to reproduce the known analytical cases of zero and infinite repulsion. We show that our results for the correlations agree with the exact diagonalization in all interaction regimes and with analytical results for the strongly repulsive impurity. This method also enables us to access the more complicated cases of mixed interactions, and the probability densities of these systems are analyzed. (paper)
High-harmonic generation in a quantum electron gas trapped in a nonparabolic and anisotropic well
Hurst, Jérôme; Lévêque-Simon, Kévin; Hervieux, Paul-Antoine; Manfredi, Giovanni; Haas, Fernando
2016-05-01
An effective self-consistent model is derived and used to study the dynamics of an electron gas confined in a nonparabolic and anisotropic quantum well. This approach is based on the equations of quantum hydrodynamics, which incorporate quantum and nonlinear effects in an approximate fashion. The effective model consists of a set of six coupled differential equations (dynamical system) for the electric dipole and the size of the electron gas. Using this model we show that: (i) high harmonic generation is related to the appearance of chaos in the phase space, as attested to by related Poincaré sections; (ii) higher order harmonics can be excited efficiently and with relatively weak driving fields by making use of chirped electromagnetic waves.
Gia, Quoc; Mayeli, Azita; Mhaskar, Hrushikesh; Zhou, Ding-Xuan
2017-01-01
The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such a...
Modified harmonic balance method for the solution of nonlinear jerk equations
Rahman, M. Saifur; Hasan, A. S. M. Z.
2018-03-01
In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.
Low-altitude trapped protons at the geomagnetic equator
Guzik, T. G.; Miah, M. A.; Mitchell, J. M.; Wefel, J. P.
1989-01-01
Geomagnetically trapped protons in the 0.6- to 9-MeV energy range were measured at latitudes near the geomagnetic equator by the Phoenix 1 experiment on board the S81-1 mission from May to November 1982. The protons show a distribution in latitude along the line of minimum magnetic field strength with a full width at half maximum of about 10 deg but with no appreciable longitudinal variation. Between 170 and 290 Km the peak proton flux shows a fifth-power altitude dependence, in contrast to previous measurements at higher altitudes, possibly demonstrating source attenuation. The efficiency of the telescope is calculated as a function of particle pitch angle and used to investigate the time dependence (1969-1982) of the intensity.
Low-altitude trapped protons at the geomagnetic equator
International Nuclear Information System (INIS)
Guzik, T.G.; Miah, M.A.; Mitchell, J.W.; Wefel, J.P.
1989-01-01
Geomagnetically trapped protons in the 0.6- to 9-MeV energy range were measured at latitudes near the geomagnetic equator by the Phoenix 1 experiment on board the S81-1 mission from May to November 1982. The protons show a distribution in latitude along the line of minimum magnetic field strength with a full width at half maximum of ∼10 0 but with no appreciable longitudinal variation. Between 170 and 290 km the peak proton flux shows a fifth-power altitude dependence, in contrast to previous measurements at higher altitudes, possibly demonstrating source attenuation. The efficiency of the telescope is calculated as a function of particle pitch angle and used to investigate the time dependence (1969--1982) of the intensity. copyright American Geophysical Union 1989
The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps
International Nuclear Information System (INIS)
Guo Boling; Hong Minchun.
1992-05-01
We prove a global existence of solutions for the Landau-Lifshitz equation of the ferromagnetic spin chain from an m-dimensional manifold M into the unit sphere S 2 of R 3 and establish some new links between harmonic maps and the solutions of the Landau-Lifshitz equation. (author). 25 refs
Mistakidis, Simeon; Koutentakis, Georgios; Schmelcher, Peter; Theory Group of Fundamental Processes in Quantum Physics Team
2016-05-01
Recent experimental advances have introduced an interplay in the trapping length scales of the lattice and the harmonic confinement. This fact motivates the investigation to prepare atomic gases at certain quantum states by utilizing a composite atomic trap consisting of a lattice potential that is embedded inside an overlying harmonic trap. In the present work, we examine how frequency modulations of the overlying harmonic trap stimulate the dynamics of an 1D few-boson gas. The gas is initially prepared at a highly confined state, and the subsequent dynamics induced by a quench of the harmonic trap frequency to a lower value is examined. It is shown that a non-interacting gas always diffuses to the outer sites. In contrast the response of the interacting system is more involved and is dominated by a resonance, which is induced by the bifurcation of the low-lying eigenstates. Our study reveals that the position of the resonance depends both on the atom number and the interaction coupling, manifesting its many body nature. The corresponding mean field treatment as well as the single-band approximation have been found to be inadequate for the description of the tunneling dynamics in the interacting case. Deutsche Forschungsgemeinschaft, SFB 925 ``Light induced dynamics and control of correlated quantum systems''.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
2011-11-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.
Density functional theory investigation of two-dimensional dipolar fermions in a harmonic trap
International Nuclear Information System (INIS)
Ustunel, Hande; Abedinpour, Saeed H; Tanatar, B
2014-01-01
We investigate the behavior of polarized dipolar fermions in a two-dimensional harmonic trap in the framework of the density functional theory (DFT) formalism using the local density approximation. We treat only a few particles interacting moderately. Important results were deduced concerning key characteristics of the system such as total energy and particle density. Our results indicate that, at variance with Coulombic systems, the exchange- correlation component was found to provide a large contribution to the total energy for a large range of interaction strengths and particle numbers. In addition, the density profiles of the dipoles are shown to display important features around the origin that is not possible to capture by earlier, simpler treatments of such systems
Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps
DEFF Research Database (Denmark)
Salami Dehkharghani, Amin; Volosniev, A. G.; Zinner, N. T.
2016-01-01
Strongly interacting particles in one dimension subject to external confinement have become a topic of considerable interest due to recent experimental advances and the development of new theoretical methods to attack such systems. In the case of equal mass fermions or bosons with two or more...... internal degrees of freedom, one can map the problem onto the well-known Heisenberg spin models. However, many interesting physical systems contain mixtures of particles with different masses. Therefore, a generalization of the recent strong-coupling techniques would be highly desirable....... This is particularly important since such problems are generally considered non-integrable and thus the hugely successful Bethe ansatz approach cannot be applied. Here we discuss some initial steps towards this goal by investigating small ensembles of one-dimensional harmonically trapped particles where pairwise...
Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
Muruganandam, P.; Adhikari, S. K.
2009-10-01
Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation describing the properties of Bose-Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all). Program summaryProgram title: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial Catalogue identifier: AEDU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data
Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential
Directory of Open Access Journals (Sweden)
Runzhang Xu
2012-11-01
Full Text Available This article studies a nonlinear Schodinger equation with harmonic potential by constructing different cross-constrained problems. By comparing the different cross-constrained problems, we derive different sharp criterion and different invariant manifolds that separate the global solutions and blowup solutions. Moreover, we conclude that some manifolds are empty due to the essence of the cross-constrained problems. Besides, we compare the three cross-constrained problems and the three depths of the potential wells. In this way, we explain the gaps in [J. Shu and J. Zhang, Nonlinear Shrodinger equation with harmonic potential, Journal of Mathematical Physics, 47, 063503 (2006], which was pointed out in [R. Xu and Y. Liu, Remarks on nonlinear Schrodinger equation with harmonic potential, Journal of Mathematical Physics, 49, 043512 (2008].
Maddix, Danielle C.; Sampaio, Luiz; Gerritsen, Margot
2018-05-01
The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable k (p) with respect to p, namely the Porous Medium Equation (PME) and the superslow diffusion equation. Spurious temporal oscillations, and nonphysical locking and lagging have been reported in the literature. These issues have been attributed to harmonic averaging of the coefficient k (p) for small p, and arithmetic averaging has been suggested as an alternative. We show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues. Here, we investigate the causes of these numerical artifacts using modified equation analysis. The modified equation framework can be used for any type of discretization. We show results for the second order finite volume method. The observed problems with harmonic averaging can be traced to two leading error terms in its modified equation. This is also illustrated numerically through a Modified Harmonic Method (MHM) that can locally modify the critical terms to remove the aforementioned numerical artifacts.
Dynamics and decoherence of two cold bosons in a one-dimensional harmonic trap
International Nuclear Information System (INIS)
Sowinski, Tomasz; Brewczyk, Miroslaw; Gajda, Mariusz; RzaPzewski, Kazimierz
2010-01-01
We study dynamics of two interacting ultracold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the δ-like potential, we study the time evolution of an initially separable state of two particles. The corresponding time-dependent single-particle density matrix is obtained and diagonalized, and single-particle orbitals are found. This allows us to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared to the evolution according to the Gross-Pitaevskii equation. We show that if initially the center of mass and relative degrees of freedom are entangled, then the Gross-Pitaevskii equation fails to reproduce the exact dynamics and entanglement is produced dynamically. We stress that predictions of our study can be verified experimentally in an optical lattice in the low-tunneling limit.
DEFF Research Database (Denmark)
Loft, Niels Jakob; Salami Dehkharghani, Amin; Mehta, N. P.
2015-01-01
We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the particles have equal masses. For this case the system in t...
Improved harmonic balance approach to periodic solutions of non-linear jerk equations
International Nuclear Information System (INIS)
Wu, B.S.; Lim, C.W.; Sun, W.P.
2006-01-01
An analytical approximate approach for determining periodic solutions of non-linear jerk equations involving third-order time-derivative is presented. This approach incorporates salient features of both Newton's method and the method of harmonic balance. By appropriately imposing the method of harmonic balance to the linearized equation, the approach requires only one or two iterations to predict very accurate analytical approximate solutions for a large range of initial velocity amplitude. One typical example is used to verify and illustrate the usefulness and effectiveness of the proposed approach
International Nuclear Information System (INIS)
Morales, J.; Ovando, G.; Pena, J. J.
2010-01-01
One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.
Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations
Energy Technology Data Exchange (ETDEWEB)
Seiler, Jennifer; Szilagyi, Bela; Pollney, Denis; Rezzolla, Luciano [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany)
2008-09-07
We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions.
Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations
International Nuclear Information System (INIS)
Seiler, Jennifer; Szilagyi, Bela; Pollney, Denis; Rezzolla, Luciano
2008-01-01
We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions
SU(N ) fermions in a one-dimensional harmonic trap
Laird, E. K.; Shi, Z.-Y.; Parish, M. M.; Levinsen, J.
2017-09-01
We conduct a theoretical study of SU (N ) fermions confined by a one-dimensional harmonic potential. First, we introduce a numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU (N ) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz—derived for a Heisenberg SU(2) spin chain—is extendable to these N -component systems. Lastly, we consider balanced SU (N ) Fermi gases that have an equal number of particles in each spin state for N =2 ,3 ,4 . In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N -component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles.
International Nuclear Information System (INIS)
Paraan, Francis N. C.; Korepin, Vladimir E.
2010-01-01
We calculate the first-order perturbation correction to the ground-state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the infinite repulsion Tonks-Girardeau limit. With c denoting the interaction strength, we find that, for a large number of particles N, the 1/c correction to the ground-state energy increases as N 5/2 , in contrast to the unperturbed Tonks-Girardeau value that is proportional to N 2 . We describe a thermodynamic scaling limit for the trapping frequency that yields an extensive ground-state energy and reproduces the zero temperature thermodynamics obtained by a local-density approximation.
International Nuclear Information System (INIS)
Lizuain, I.; Muga, J. G.
2007-01-01
We investigate laser-driven vibronic transitions of a single two-level atomic ion in harmonic and hard-wall traps. In the Lamb-Dicke regime, for tuned or detuned lasers with respect to the internal frequency of the ion, and weak or strong laser intensities, the vibronic transitions occur at well-isolated Rabi resonances, where the detuning-adapted Rabi frequency coincides with the transition frequency between vibrational modes. These vibronic resonances are characterized as avoided crossings of the dressed levels (eigenvalues of the full Hamiltonian). Their peculiarities due to symmetry constraints and trapping potential are also examined
International Nuclear Information System (INIS)
Mukhtarova, M.I.
1988-01-01
Comparative analysis of approximations, used in the methods of Faddeev equations and hyperspherical harmonics (MHH) was conducted. The differences in solutions of these methods, related with introduction of approximation of sufficient partial states into the three-nucleon problem, is shown. MHH method is preferred. It is shown that MHH advantage can be manifested clearly when studying new classes of interactions: three-particle, Δ-isobar, nonlocal and other interactions
Energy Technology Data Exchange (ETDEWEB)
Shao, Yan-Lin, E-mail: yanlin.shao@dnvgl.com; Faltinsen, Odd M.
2014-10-01
We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods, e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.
A negative-norm least-squares method for time-harmonic Maxwell equations
Copeland, Dylan M.
2012-04-01
This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.
On the Gross–Pitaevskii equation for trapped dipolar quantum gases
Carles, Ré mi; Markowich, Peter A; Sparber, Christof
2008-01-01
We study the time-dependent Gross-Pitaevskii equation describing Bose-Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension reduction for this nonlinear and nonlocal Schrödinger equation. © 2008 IOP Publishing Ltd and London Mathematical Society.
Trapped surfaces in monopole-like Cauchy data of Einstein-Yang-Mills-Higgs equations
International Nuclear Information System (INIS)
Malec, E.; Koc, P.
1989-08-01
We choose the nonabelian monopole solution of Bogomolny, Prasad and Sommerfield as a part of Cauchy data for the evolution of Einstein-Yang-Mills-Higgs equations. Momentarily static spherically symmetric data for gravitational fields are obtained numerically via the Lichnerowicz equation. In the case of generic scaling of fields we have found initial data with trapped surfaces. (author). 13 refs
On the Gross–Pitaevskii equation for trapped dipolar quantum gases
Carles, Rémi
2008-09-29
We study the time-dependent Gross-Pitaevskii equation describing Bose-Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension reduction for this nonlinear and nonlocal Schrödinger equation. © 2008 IOP Publishing Ltd and London Mathematical Society.
Galilo, Bogdan; Lee, Derek K K; Barnett, Ryan
2017-11-17
In this Letter, it is shown that interactions can facilitate the emergence of topological edge states of quantum-degenerate bosonic systems in the presence of a harmonic potential. This effect is demonstrated with the concrete model of a hexagonal lattice populated by spin-one bosons under a synthetic gauge field. In fermionic or noninteracting systems, the presence of a harmonic trap can obscure the observation of edge states. For our system with weakly interacting bosons in the Thomas-Fermi regime, we can clearly see a topological band structure with a band gap traversed by edge states. We also find that the number of edge states crossing the gap is increased in the presence of a harmonic trap, and the edge modes experience an energy shift while traversing the first Brillouin zone which is related to the topological properties of the system. We find an analytical expression for the edge-state energies and our comparison with numerical computation shows excellent agreement.
Galilo, Bogdan; Lee, Derek K. K.; Barnett, Ryan
2017-11-01
In this Letter, it is shown that interactions can facilitate the emergence of topological edge states of quantum-degenerate bosonic systems in the presence of a harmonic potential. This effect is demonstrated with the concrete model of a hexagonal lattice populated by spin-one bosons under a synthetic gauge field. In fermionic or noninteracting systems, the presence of a harmonic trap can obscure the observation of edge states. For our system with weakly interacting bosons in the Thomas-Fermi regime, we can clearly see a topological band structure with a band gap traversed by edge states. We also find that the number of edge states crossing the gap is increased in the presence of a harmonic trap, and the edge modes experience an energy shift while traversing the first Brillouin zone which is related to the topological properties of the system. We find an analytical expression for the edge-state energies and our comparison with numerical computation shows excellent agreement.
Energy Technology Data Exchange (ETDEWEB)
Cari, C., E-mail: carinln@yahoo.com; Suparmi, A., E-mail: carinln@yahoo.com [Physics Department, Sebelas Maret University, Jl. Ir. Sutami no 36A Kentingan Surakarta 57126 (Indonesia)
2014-09-30
Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1977-01-01
A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)
Harmonic analysis, partial differential equations and applications in honor of Richard L. Wheeden
Franchi, Bruno; Lu, Guozhen; Perez, Carlos; Sawyer, Eric
2017-01-01
This is a collection of contributed papers by many eminent Harmonic Analysts and specialists of Partial Differential equations. The papers focus on weighted norm equalities for singular integrals, focusing wave equations, degenerate elliptic equations, Navier-Stokes flow in two dimensions and Poincare-Sobolev inequalities in the setting of metric spaces equipped with measures among others. Many topics considered in this volume stem from the interests of Richard L. Wheeden whose contributions to Potential Theory, singular integral theory and degenerate elliptic PDE theory this volume honors. Luis Caffarelli, Sagun Chanillo, Bruno Franchi, Cristian Guttierez, Xiaojun Huang, Carlos Kenig, Ermanno Lanconelli, Eric Sawyer and Alexander Volberg, are some of the many contributors to this volume. .
International Nuclear Information System (INIS)
Wonneberger, W.
2006-01-01
The problem of the Kohn mode in bosonized theories of one-dimensional interacting fermions in the harmonic trap is investigated and a suitable modification of the interaction is proposed which preserves the Kohn mode. The modified theory is used to calculate exactly the inhomogeneous linear mobility μ(z,z 0 ;ω) at position z in response to a spatial force pulse at position z 0 . It is found that the inhomogeneous particle mobility exhibits resonances not only at the trap frequency ω - bar but also at multiples mε-bar , m=2,3,... of a new renormalized collective mode frequency which depends on the strength of the interaction. In contrast, the homogeneous response obtained by an average over z 0 remains that of the non-interacting system
Trapping of a particle in a short-range harmonic potential well
Castro, L. B.; de Castro, A. S.
2012-01-01
Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed.
Partial Fourier analysis of time-harmonic Maxwell's equations in axisymmetric domains
International Nuclear Information System (INIS)
Nkemzi, Boniface
2003-01-01
We analyze the Fourier method for treating time-harmonic Maxwell's equations in three-dimensional axisymmetric domains with non-axisymmetric data. The Fourier method reduces the three-dimensional boundary value problem to a system of decoupled two-dimensional boundary value problems on the plane meridian domain of the axisymmetric domain. The reduction process is fully described and suitable weighted spaces are introduced on the meridian domain to characterize the two-dimensional solutions. In particular, existence and uniqueness of solutions of the two-dimensional problems is proved and a priori estimates for the solutions are given. (author)
Spherical harmonics and energy polynomial solution of the Boltzmann equation for neutrons, 1
International Nuclear Information System (INIS)
Toledo, P.S. de
1974-01-01
The approximate solution of the source-free energy-dependent Boltzmann transport equation for neutrons in plane geometry and isotropic scattering case was given by Leonard and Ferziger using a truncated development in a series of energy-polynomials for the energy dependent neutron flux and solving exactly for the angular dependence. The presence in the general solution of eigenfunctions belonging to a continuous spectrum gives rise to difficult analytical problems in the application of their method even to simple problems. To avoid such difficulties, the angular dependence is treated by a spherical harmonics method and a general solution of the energy-dependent transport equation in plane geometry and isotropic scattering is obtained, in spite of the appearance of matrices as argument of the angular polynomials [pt
The solution of the multigroup neutron transport equation using spherical harmonics
International Nuclear Information System (INIS)
Fletcher, K.
1981-01-01
A solution of the multi-group neutron transport equation in up to three space dimensions is presented. The flux is expanded in a series of unnormalised spherical harmonics. Using the various recurrence formulae a linked set of first order differential equations is obtained for the moments psisup(g)sub(lm)(r), γsup(g)sub(lm)(r). Terms with odd l are eliminated resulting in a second order system which is solved by two methods. The first is a finite difference formulation using an iterative procedure, secondly, in XYZ and XY geometry a finite element solution is given. Results for a test problem using both methods are exhibited and compared. (orig./RW) [de
Hybrid simplified spherical harmonics with diffusion equation for light propagation in tissues
International Nuclear Information System (INIS)
Chen, Xueli; Sun, Fangfang; Yang, Defu; Ren, Shenghan; Liang, Jimin; Zhang, Qian
2015-01-01
Aiming at the limitations of the simplified spherical harmonics approximation (SP N ) and diffusion equation (DE) in describing the light propagation in tissues, a hybrid simplified spherical harmonics with diffusion equation (HSDE) based diffuse light transport model is proposed. In the HSDE model, the living body is first segmented into several major organs, and then the organs are divided into high scattering tissues and other tissues. DE and SP N are employed to describe the light propagation in these two kinds of tissues respectively, which are finally coupled using the established boundary coupling condition. The HSDE model makes full use of the advantages of SP N and DE, and abandons their disadvantages, so that it can provide a perfect balance between accuracy and computation time. Using the finite element method, the HSDE is solved for light flux density map on body surface. The accuracy and efficiency of the HSDE are validated with both regular geometries and digital mouse model based simulations. Corresponding results reveal that a comparable accuracy and much less computation time are achieved compared with the SP N model as well as a much better accuracy compared with the DE one. (paper)
Hybrid simplified spherical harmonics with diffusion equation for light propagation in tissues.
Chen, Xueli; Sun, Fangfang; Yang, Defu; Ren, Shenghan; Zhang, Qian; Liang, Jimin
2015-08-21
Aiming at the limitations of the simplified spherical harmonics approximation (SPN) and diffusion equation (DE) in describing the light propagation in tissues, a hybrid simplified spherical harmonics with diffusion equation (HSDE) based diffuse light transport model is proposed. In the HSDE model, the living body is first segmented into several major organs, and then the organs are divided into high scattering tissues and other tissues. DE and SPN are employed to describe the light propagation in these two kinds of tissues respectively, which are finally coupled using the established boundary coupling condition. The HSDE model makes full use of the advantages of SPN and DE, and abandons their disadvantages, so that it can provide a perfect balance between accuracy and computation time. Using the finite element method, the HSDE is solved for light flux density map on body surface. The accuracy and efficiency of the HSDE are validated with both regular geometries and digital mouse model based simulations. Corresponding results reveal that a comparable accuracy and much less computation time are achieved compared with the SPN model as well as a much better accuracy compared with the DE one.
Universal Two-Body Spectra of Ultracold Harmonically Trapped Atoms in Two and Three Dimensions
DEFF Research Database (Denmark)
Zinner, Nikolaj Thomas
2012-01-01
of the short-range interaction. The results in three dimensions are examplified for narrow s-wave Feshbach resonances and we show how effective range corrections can modify the rearrangement of the level structure. However, this requires extremely narrow resonances or very tight traps that are not currently...
General solution of the multigroup spherical harmonics equations in R-Z geometry
International Nuclear Information System (INIS)
Matausek, M.
1983-01-01
In the present paper the generalization is performed of the procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed foe one-dimensional systems in cylindrical or spherical geometry, and later extended for special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r and z directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. The analysis is performed of the possibilities to satisfy the boundary conditions in the case when the system considered represents an elementary reactor lattice cell and in the case when the system represents a reactor as a whole. The computational effort is estimated for system of a given configuration. (author)
Macroscopic rate equation modeling of trapping/detrapping of hydrogen isotopes in tungsten materials
Energy Technology Data Exchange (ETDEWEB)
Hodille, E.A., E-mail: etienne.hodille@cea.fr [CEA, IRFM, F-13108 Saint Paul lez Durance (France); Bonnin, X. [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, F-93430 Villetaneuse (France); Bisson, R.; Angot, T. [Aix-Marseille Université, PIIM, CNRS, UMR 7345, 13397 Marseille (France); Becquart, C.S. [Université Lille I, UMET, UMR 8207, 59655 Villeneuve d’Ascq cédex France (France); Layet, J.M. [Aix-Marseille Université, PIIM, CNRS, UMR 7345, 13397 Marseille (France); Grisolia, C. [CEA, IRFM, F-13108 Saint Paul lez Durance (France)
2015-12-15
Relevant parameters for trapping of Hydrogen Isotopes (HIs) in polycrystalline tungsten are determined with the MHIMS code (Migration of Hydrogen Isotopes in MaterialS) which is used to reproduce Thermal Desorption Spectrometry experiments. Three types of traps are found: two intrinsic traps (detrapping energy of 0.87 eV and 1.00 eV) and one extrinsic trap created by ion irradiation (detrapping energy of 1.50 eV). Then MHIMS is used to simulate HIs retention at different fluences and different implantation temperatures. Simulation results agree well with experimental data. It is shown that at 300 K the retention is limited by diffusion in the bulk. For implantation temperatures above 500 K, the retention is limited by trap creation processes. Above 600 K, the retention drops by two orders of magnitude as compared to the retention at 300 K. With the determined detrapping energies, HIs outgassing at room temperature is predicted. After ions implantation at 300 K, 45% of the initial retention is lost to vacuum in 300 000 s while during this time the remaining trapped HIs diffuse twice as deep into the bulk. - Highlights: • Code development to solve numerically the model equations of diffusion and trapping of hydrogen in metals. • Parametrization of the model trapping parameters (detrapping energies and density): fitting of experimental TDS spectrum. • Confrontation model/experiment: evolution of retention with fluence and implantation temperature. • Investigation of period of rest between implantation and TDS on retention and depth profile.
Trions in bulk and monolayer materials: Faddeev equations and hyperspherical harmonics.
Filikhin, I; Kezerashvili, R Ya; Tsiklauri, Sh M; Vlahovic, B
2018-03-23
The negatively T - and positively T + charged trions in bulk and monolayer semiconductors are studied in the effective mass approximation within the framework of a potential model. The binding energies of trions in various semiconductors are calculated by employing the Faddeev equation with the Coulomb potential in 3D configuration space. Results of calculations of the binding energies for T - are consistent with previous computational studies, while the T + is unbound for all considered cases. The binding energies of trions in monolayer semiconductors are calculated using the method of hyperspherical harmonics by employing the Keldysh potential. It is shown that 2D T - and T + trions are bound and the binding energy of the positive trion is always greater than for the negative trion due to the heavier effective mass of holes. Our calculations demonstrate that screening effects play an important role in the formation of bound states of trions in 2D semiconductors.
Emission spectrum of a harmonically trapped Λ-type three-level atom
International Nuclear Information System (INIS)
Guo Hong; Tang Pei
2013-01-01
We theoretically investigate the emission spectrum for a Λ-type three-level atom trapped in the node of a standing wave. We show that the atomic center-of-mass motion not only directly affects the peak number, peak position, and peak height in the atomic emission spectrum, but also influences the effects of the cavity field and the atomic initial state on atomic emission spectrum. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap
DEFF Research Database (Denmark)
Salami Dehkharghani, Amin; Bellotti, Filipe Furlan; Zinner, Nikolaj Thomas
2017-01-01
are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using...... a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different...
An Active Trap Filter for Switching Harmonics Attenuation of Low-Pulse-Ratio Inverters
DEFF Research Database (Denmark)
Bai, Haofeng; Wang, Xiongfei; Loh, Poh Chiang
2017-01-01
method has also been proposed for the ATF to better enforce its active switching harmonic bypassing ability. Compared with conventional schemes for controlling active power filters, the proposed method is more readily implemented, since it requires neither current reference generation nor high......-bandwidth current control loop. Moreover, the use of a series LC-filter at its ac-side helps the ATF to reduce its inverter voltage and power ratings. Compensated frequency range of the ATF can hence be enlarged by using a comparably higher switching frequency and a proper step-by-step design procedure...
Application of Fokker-Planck equation in positron diffusion trapping model
International Nuclear Information System (INIS)
Bartosova, I.; Ballo, P.
2015-01-01
This paper is a theoretical prelude to future work involving positron diffusion in solids for the purpose of positron annihilation lifetime spectroscopy (PALS). PALS is a powerful tool used to study defects present in materials. However, the behavior of positrons in solids is a process hard to describe. Various models have been established to undertake this task. Our preliminary model is based on the Diffusion Trapping Model (DTM) described by partial differential Fokker-Planck equation and is solved via time discretization. Fokker-Planck equation describes the time evolution of the probability density function of velocity of a particle under the influence of various forces. (authors)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Repulsive atomic gas in a harmonic trap on the border of itinerant ferromagnetism.
Conduit, G J; Simons, B D
2009-11-13
Alongside superfluidity, itinerant (Stoner) ferromagnetism remains one of the most well-characterized phases of correlated Fermi systems. A recent experiment has reported the first evidence for novel phase behavior on the repulsive side of the Feshbach resonance in a two-component ultracold Fermi gas. By adapting recent theoretical studies to the atomic trap geometry, we show that an adiabatic ferromagnetic transition would take place at a weaker interaction strength than is observed in experiment. This discrepancy motivates a simple nonequilibrium theory that takes account of the dynamics of magnetic defects and three-body losses. The formalism developed displays good quantitative agreement with experiment.
Chen, Xi; Jiang, Ruan-Lei; Li, Jing; Ban, Yue; Sherman, E. Ya.
2018-01-01
We investigate fast transport and spin manipulation of tunable spin-orbit-coupled Bose-Einstein condensates in a moving harmonic trap. Motivated by the concept of shortcuts to adiabaticity, we design inversely the time-dependent trap position and spin-orbit-coupling strength. By choosing appropriate boundary conditions we obtain fast transport and spin flip simultaneously. The nonadiabatic transport and relevant spin dynamics are illustrated with numerical examples and compared with the adiabatic transport with constant spin-orbit-coupling strength and velocity. Moreover, the influence of nonlinearity induced by interatomic interaction is discussed in terms of the Gross-Pitaevskii approach, showing the robustness of the proposed protocols. With the state-of-the-art experiments, such an inverse engineering technique paves the way for coherent control of spin-orbit-coupled Bose-Einstein condensates in harmonic traps.
Statistical properties of spectra in harmonically trapped spin-orbit coupled systems
DEFF Research Database (Denmark)
V. Marchukov, O.; G. Volosniev, A.; V. Fedorov, D.
2014-01-01
We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin......-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner...... distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding...
Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap
Dehkharghani, A. S.; Bellotti, F. F.; Zinner, N. T.
2017-07-01
In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose-Bose and the Fermi-Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose-Fermi mixtures we find pronounced odd-even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Kikuchi, Hirohiko; Tsutsuguchi, Ken
1993-01-01
A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for x-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method. (author)
Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential
Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.
2018-03-01
We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p > 0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.
International Nuclear Information System (INIS)
Surya Mohan, P.; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon R.
2011-01-01
Highlights: → We developed a variable order global basis scheme to solve light transport in 3D. → Based on finite elements, the method can be applied to a wide class of geometries. → It is computationally cheap when compared to the fixed order scheme. → Comparisons with local basis method and other models demonstrate its accuracy. → Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.
International Nuclear Information System (INIS)
Filho, Victo S.; Tomio, Lauro; Frederico, T.; Gammal, Arnaldo
2002-01-01
The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean-field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions, where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments
Energy Technology Data Exchange (ETDEWEB)
Barvik, I [International Centre for Theoretical Physics, Trieste (Italy); Polasek, M [Charles Univ., Prague (Czech Republic). Inst. of Physics; Herman, P [Pedagogical Univ., Hradec Kralove (Czech Republic)
1995-08-01
We used the formal stochastic Liouville equations within Haken-Strobl-Reineker parametrization for the description of the influence of the bath on the memory functions entering the GME for a dimer and a linear trimer with a trap (here modeled as a sink). The often used inclusion of the noncoherent regime in the MF by an exponentially damped prefactor (after Kenkre`s prescription) does not hold for finite systems. The analytical form of the MF is changed more pronouncely and the influence of the sink in the center of the trimer runs parallel with the influence of the bath in destroying the coherence. (author). 60 refs.
Energy Technology Data Exchange (ETDEWEB)
Garcia-Ravelo, J.; Trujillo, A. L. [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Unidad Profesional Adolfo Lopez Mateos, Zacatenco, 07738 Mexico D.F. (Mexico); Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2012-10-15
We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schroedinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.
International Nuclear Information System (INIS)
García-Ravelo, J.; Trujillo, A. L.; Schulze-Halberg, A.
2012-01-01
We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schrödinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.
Sorokin, Sergey V
2011-03-01
Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America
International Nuclear Information System (INIS)
Zhang Mincang; Sun Guohua; Dong Shihai
2010-01-01
A spherically harmonic oscillatory ring-shaped potential is proposed and its exactly complete solutions are presented by the Nikiforov-Uvarov method. The effect of the angle-dependent part on the radial solutions is discussed.
International Nuclear Information System (INIS)
Pirouzmand, Ahmad; Hadad, Kamal
2012-01-01
Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.
Trapped waves on the mid-latitude β-plane
Paldor, Nathan; Sigalov, Andrey
2008-08-01
A new type of approximate solutions of the Linearized Shallow Water Equations (LSWE) on the mid-latitude β-plane, zonally propagating trapped waves with Airy-like latitude-dependent amplitude, is constructed in this work, for sufficiently small radius of deformation. In contrast to harmonic Poincare and Rossby waves, these newly found trapped waves vanish fast in the positive half-axis, and their zonal phase speed is larger than that of the corresponding harmonic waves for sufficiently large meridional domains. Our analysis implies that due to the smaller radius of deformation in the ocean compared with that in the atmosphere, the trapped waves are relevant to observations in the ocean whereas harmonic waves typify atmospheric observations. The increase in the zonal phase speed of trapped Rossby waves compared with that of harmonic ones is consistent with recent observations that showed that Sea Surface Height features propagated westwards faster than the phase speed of harmonic Rossby waves.
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1986-01-01
In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)
Ichinose, T
2004-01-01
We study the special values at $s=2$ and $3$ of the spectral zeta function $\\zeta_Q(s)$ of the non-commutative harmonic oscillator $Q(x,D_x)$ introduced in \\cite{PW1, 2}. It is shown that the series defining $\\zeta_Q(s)$ converges absolutely for Re $s>1$ and further the respective values $\\zeta_Q(2)$ and $\\zeta_Q(3)$ are represented essentially by contour integrals of the solutions, respectively, of a singly confluent Heun's ordinary differential equation and of exactly the same but an inhomogeneous equation. As a by-product of these results, we obtain integral representations of the solutions of these equations by rational functions. \\par\
Xu, H.; Kevrekidis, P. G.; Kapitula, T.
2017-06-01
In the present work, we consider a variety of two-component, one-dimensional states in nonlinear Schrödinger equations in the presence of a parabolic trap, inspired by the atomic physics context of Bose-Einstein condensates. The use of Lyapunov-Schmidt reduction methods allows us to identify persistence criteria for the different families of solutions which we classify as (m, n), in accordance with the number of zeros in each component. Upon developing the existence theory, we turn to a stability analysis of the different configurations, using the Krein signature and the Hamiltonian-Krein index as topological tools identifying the number of potentially unstable eigendirections for each branch. A perturbation expansion for the eigenvalue problems associated with nonlinear states found near the linear limit permits us to obtain explicit asymptotic expressions for the eigenvalues. Finally, when the states are found to be unstable, typically by virtue of Hamiltonian Hopf bifurcations, their dynamics is studied in order to identify the nature of the respective instability. The dynamics is generally found to lead to a vibrational evolution over long time scales.
Kim, Yeong E.; Zubarev, Alexander L.
2006-02-01
A mixture of two different species of positively charged bosons in harmonic traps is considered in the mean-field approximation. It is shown that depending on the ratio of parameters, the two components may coexist in same regions of space, in spite of the Coulomb repulsion between the two species. Application of this result is discussed for the generalization of the Bose-Einstein condensation mechanism for low-energy nuclear reaction (LENR) and transmutation processes in condensed matters. For the case of deutron-lithium (d + Li) LENR, the result indicates that (d + 6Li) reactions may dominate over (d + d) reactions in LENR experiments.
Energy Technology Data Exchange (ETDEWEB)
Yeong, E. Kim; Zubarev, Alexander L. [Purdue Nuclear and Many-Body Theory Group (PNMBTG) Department of Physics, Purdue University, West Lafayette, IN 47907 (United States)
2006-07-01
A mixture of two different species of positively charged bosons in harmonic traps is considered in the mean-field approximation. It is shown that depending on the ratio of parameters, the two components may coexist in some regions of space, in spite of the Coulomb repulsion between the two species. Application of this result is discussed for the generalization of the Bose-Einstein condensation mechanism for low-energy nuclear reaction (LENR) and transmutation processes in condensed matters. For the case of deuteron-lithium (d + Li) LENR, the result indicates that (d + {sup 6}Li) reactions may dominate over (d + d) reactions in LENR experiments. (authors)
International Nuclear Information System (INIS)
Yeong, E. Kim; Zubarev, Alexander L.
2006-01-01
A mixture of two different species of positively charged bosons in harmonic traps is considered in the mean-field approximation. It is shown that depending on the ratio of parameters, the two components may coexist in some regions of space, in spite of the Coulomb repulsion between the two species. Application of this result is discussed for the generalization of the Bose-Einstein condensation mechanism for low-energy nuclear reaction (LENR) and transmutation processes in condensed matters. For the case of deuteron-lithium (d + Li) LENR, the result indicates that (d + 6 Li) reactions may dominate over (d + d) reactions in LENR experiments. (authors)
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Farouq, S.; Neytcheva, M.
2017-01-01
Roč. 310, January 2017 (2017), s. 5-18 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : optimal control * time-harmonic Stokes problem * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://www. science direct.com/ science /article/pii/S0377042716302631?via%3Dihub
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Farouq, S.; Neytcheva, M.
2017-01-01
Roč. 310, January 2017 (2017), s. 5-18 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : optimal control * time-harmonic Stokes problem * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://www.sciencedirect.com/science/article/pii/S0377042716302631?via%3Dihub
Arminjon, Mayeul
2005-10-01
The asymptotic scheme of post-Newtonian approximation defined for general relativity in the harmonic gauge by Futamase & Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg’s (1972) expansion of the metric and his general expansion of the energy-momentum tensor T, as well as his expanded equations for the gravitational field and his general form of the expanded dynamical equations, apply naturally to this family. Then, following the asymptotic scheme, we derive the explicit form of the expansion of T for a perfect fluid, and the expanded fluid-dynamical equations. (These differ from those written by Weinberg.) By integrating these equations in the domain occupied by a body, we obtain a general form of the translational equations of motion for a 1PN perfect-fluid system in general relativity. To put them into a tractable form, we use an asymptotic framework for the separation parameter η, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order η3 included. To calculate the 1PN correction part, we assume that the Newtonian motion of each body is a rigid one, and that the family is quasispherical, in the sense that in all bodies the inertia tensor comes close to being spherical as η→0. Apart from corrections that cancel for exact spherical symmetry, there is in the final equations of motion one additional term, as compared with the Lorentz-Droste (Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the body and on its internal structure.
One dimension harmonic oscillator
International Nuclear Information System (INIS)
Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Franck.
1977-01-01
The importance of harmonic oscillator in classical and quantum physics, eigenvalues and eigenstates of hamiltonian operator are discussed. In complement are presented: study of some physical examples of harmonic oscillators; study of stationnary states in the /x> representation; Hermite polynomials; resolution of eigenvalue equation of harmonic oscillator by polynomial method; isotope harmonic oscillator with three dimensions; charged harmonic oscillator in uniform electric field; quasi classical coherent states of harmonic oscillator; eigenmodes of vibration of two coupled harmonic oscillators; vibration modus of a continuous physical system (application to radiation: photons); vibration modus of indefinite linear chain of coupled harmonic oscillators (phonons); one-dimensional harmonic oscillator in thermodynamic equilibrium at temperature T [fr
International Nuclear Information System (INIS)
Wang Qing; Hou Yu-Long; Jing Jian; Long Zheng-Wen
2014-01-01
In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed. (general)
International Nuclear Information System (INIS)
Fenstermacher, T.E.
1981-01-01
The solution of the neutron transport equation has long been a subject of intense interest to nuclear engineers. Present computer codes for the solution of this equation, however, are expensive to run for large, multidimensional problems, and also suffer from computational problems such as the ray effect. A method has been developed which eliminates many of these problems. It consists of transforming the transport equation into a set of linear partial differential equations by the use of spherical harmonics. The problem volume is divided into mesh boxes, and the flux components are approximated within each mesh box by spatially orthogonal quadratic polynomials, which need not be continuous at mesh box interfaces. A variational principle is developed, and used to solve for the unknown coefficients of these polynomials. Both one dimensional and two dimensional computer codes using this method have been written. The codes have each been tested on several test cases, and the solutions checked against solutions obtained by other methods. While the codes have some difficulty in modeling sharp transients, they produce excellent results on problems where the characteristic lengths are many mean free paths. On one test case, the two dimensional code, SHOP/2D, required only one-fourth the computer time required by the finite difference, discrete ordinates code TWOTRAN to produce a solution. In addition, SHOP/2D converged much better than TWOTRAN and produced more physical-appearing results
International Nuclear Information System (INIS)
Matausek, M.
1972-01-01
A new proposed method for solving the space-energy dependent spherical harmonics equations represents a methodological contribution to neutron transport theory. The proposed method was applied for solving the problem of spec-energy transport of fast and resonance neutrons in multi-zone, cylindrical y symmetric infinite reactor cell and is related to previously developed procedure for treating the thermal energy region. The advantages of this method are as follows: a unique algorithm was obtained for detailed determination of spatial and energy distribution of neutrons (from thermal to fast) in the reactor cell; these detailed distributions enable more precise calculations of criticality conditions, obtaining adequate multigroup data and better interpretation of experimental data; computing time is rather short
International Nuclear Information System (INIS)
Takahashi, Hiroaki; Watanabe, Ryosuke; Miyauchi, Yoshihiro; Mizutani, Goro
2011-01-01
In this report, local electronic structures of steps and terraces on rutile TiO 2 single crystal faces were studied by second harmonic and sum frequency generation (SHG/SFG) spectroscopy. We attained selective measurement of the local electronic states of the step bunches formed on the vicinal (17 18 1) and (15 13 0) surfaces using a recently developed step-selective probing technique. The electronic structures of the flat (110)-(1x1) (the terrace face of the vicinal surfaces) and (011)-(2x1) surfaces were also discussed. The SHG/SFG spectra showed that step structures are mainly responsible for the formation of trap states, since significant resonances from the trap states were observed only from the vicinal surfaces. We detected deep hole trap (DHT) states and shallow electron trap (SET) states selectively from the step bunches on the vicinal surfaces. Detailed analysis of the SHG/SFG spectra showed that the DHT and SET states are more likely to be induced at the top edges of the step bunches than on their hillsides. Unlike the SET states, the DHT states were observed only at the step bunches parallel to [1 1 1][equivalent to the step bunches formed on the (17 18 1) surface]. Photocatalytic activity for each TiO 2 sample was also measured through methylene blue photodegradation reactions and was found to follow the sequence: (110) < (17 18 1) < (15 13 0) < (011), indicating that steps along [0 0 1] are more reactive than steps along [1 1 1]. This result implies that the presence of the DHT states observed from the step bunches parallel to [1 1 1] did not effectively contribute to the methylene blue photodegradation reactions.
International Nuclear Information System (INIS)
Liu, F.-Q.; Lim, T.K.
1988-01-01
The Faddeev and Faddeev-Yakubovsky equations for three- and four-body systems are solved by applying the hyperspherical-harmonics expansion to them in momentum space. This coupling of two popular approaches to the few-body problem together with the use of the so-called Raynal-Revai transformation, which relates hyperspherical functions, allows the few-body equations to be written as one-dimensional coupled integral equations. Numerical solutions for these are achieved through standard matrix methods; these are made straightforward, because a second transformation renders potential multipoles easily calculable. For sample potentials and a restricted size of matrix in each case, the binding energies extracted match those previously obtained in solving the Schroedinger equation through the hyperspherical-harmonics expansion in coordinate space. 9 refs
International Nuclear Information System (INIS)
Cari, C; Suparmi, A
2013-01-01
The energy eigenvalues and eigenfunctions of Schrodinger equation for three dimensional harmonic oscillator potential plus Rosen-Morse non-central potential are investigated using NU method and Romanovski polynomial. The bound state energy eigenvalues are given in a closed form and corresponding radial wave functions are expressed in associated Laguerre polynomials while angular eigen functions are given in terms of Romanovski polynomials. The Rosen-Morse potential is considered to be a perturbation factor to the three dimensional harmonic oscillator potential that causes the increase of radial wave function amplitude and decrease of angular momentum length. Keywords: Schrodinger Equation, Three dimensional Harmonic Oscillator potential, Rosen-morse non-central potential, NU method, Romanovski Polynomials
Zhukovsky, K.; Oskolkov, D.
2018-03-01
A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.
International Nuclear Information System (INIS)
Fernandes, A.; Maiorino, J.R.
1989-01-01
This work presents a method to solve the neutron transport equation in thre space dimensions. The angular flux is aproximated by spherical harmonics and the finite element method is applied to the space component. The program originated by the analytical development is being tested and some results are presented. (author) [pt
Energy Technology Data Exchange (ETDEWEB)
Chen, Guang-Ping [Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi' an 710600 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Zhang, Zhi-Yuan [The School of Physics and Mech-tronic Engineering, Sichuan University of Art and Science, DaZhou 635000 (China); Dong, Biao [Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi' an 710600 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Wang, Lin-Xue [College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070 (China); Zhang, Xiao-Fei, E-mail: xfzhang@ntsc.ac.cn [Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi' an 710600 (China); Zhang, Shou-Gang, E-mail: szhang@ntsc.ac.cn [Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi' an 710600 (China)
2015-10-02
We consider a two-component Bose–Einstein condensate under extreme elongation in a harmonic plus quartic trap. The ground-state and rotational properties of such a system are numerically studied as a function of intra- and inter-component contact interactions, and of the rotational frequency. For the nonrotational case, we obtain the exact phase diagram showing the ground-state density distributions as contact-interactions varied. For both slowly and ultrarapidly rotational cases, we demonstrate that the vortex configurations depend strongly on the relative strength of the contact interactions, as well as on the rotational frequency. The controllable system may be used to investigate the interplay of interaction and rotation, and to explore more exotic quantum phases. - Highlights: • Quartic trap extends the parameter space to a fast rotating region. • Different ground state density distributions and novel vortex structures are obtained within the full parameter space. • Effects of the contact interactions and rotation are discussed in detail.
International Nuclear Information System (INIS)
Chen, Guang-Ping; Zhang, Zhi-Yuan; Dong, Biao; Wang, Lin-Xue; Zhang, Xiao-Fei; Zhang, Shou-Gang
2015-01-01
We consider a two-component Bose–Einstein condensate under extreme elongation in a harmonic plus quartic trap. The ground-state and rotational properties of such a system are numerically studied as a function of intra- and inter-component contact interactions, and of the rotational frequency. For the nonrotational case, we obtain the exact phase diagram showing the ground-state density distributions as contact-interactions varied. For both slowly and ultrarapidly rotational cases, we demonstrate that the vortex configurations depend strongly on the relative strength of the contact interactions, as well as on the rotational frequency. The controllable system may be used to investigate the interplay of interaction and rotation, and to explore more exotic quantum phases. - Highlights: • Quartic trap extends the parameter space to a fast rotating region. • Different ground state density distributions and novel vortex structures are obtained within the full parameter space. • Effects of the contact interactions and rotation are discussed in detail
International Nuclear Information System (INIS)
Capuzzi, P.; Howard, I.A.; March, N.H.; Tosi, M.P.
2007-01-01
To complement existing knowledge of the density matrix γ F (x,y) of independent fermions for N particles in one dimension under harmonic confinement, the corresponding matrix γ IB (x,y) for impenetrable bosons is given for N=2 and 3 (with the N=4 form available also). For fermions the momentum density is then obtained and illustrated numerically for N=10. The boson momentum density is studied analytically at high momentum p, the coefficients of the p -4 and p -6 terms being tabulated for N=2-5 inclusive. Their dependence on powers of N is exhibited numerically. Finally, the functional relationship between γ IB (x,y) and γ F (x,y) is formally set out and illustrated
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il
2017-05-15
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.
International Nuclear Information System (INIS)
Eliazar, Iddo
2017-01-01
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.
International Nuclear Information System (INIS)
Kobayashi, K.
1995-01-01
A simple formulation to derive second order differential equations of the spherical harmonics method is described, and it is shown that there is difficulty in deriving finite difference equations for these differential equations at material interfaces, because the second order differential terms of higher order moments must be expressed by the values in a mesh box. On the other hand, it is shown that there is no such difficulty, if the author uses the finite Fourier transformation method, since the differential equations are transformed into integral equations and the differentiation corresponds simply to a multiplication by the transformation parameter. Solution can be obtained in the form of Fourier series without making use of the inversion integral
International Nuclear Information System (INIS)
Sotnikov, Andrii
2016-01-01
We study theoretically potential advantages of two-component mixtures in optical lattices with state-dependent tunneling for approaching long-range-order phases and detecting easy-axis antiferromagnetic correlations. While we do not find additional advantages of mixtures with large hopping imbalance for approaching quantum magnetism in a harmonic trap, it is shown that a nonzero difference in hopping amplitudes remains highly important for a proper symmetry breaking in the pseudospin space for the single-site-resolution imaging and can be advantageously used for a significant increase of the signal-to-noise ratio and thus detecting long-range easy-axis antiferromagnetic correlations in the corresponding experiments. - Highlights: • The most optimal ways to observe magnetic correlations in a quantum-gas microscope are presented. • Importance of a controlled symmetry breaking for antiferromagnetism is studied. • A quantitative theoretical analysis for the entropy in ultracold fermionic mixtures is performed. • No advantages from realizations with the strong hopping asymmetry are found.
International Nuclear Information System (INIS)
Khazanov, G.V.; Koen, M.A.; Burenkov, S.I.
1979-01-01
Considered is the dinamics of photoelectron fluxes formation in the Earth plasmasphere with account of zone interaction of free and trapped photoelectrons. An algorithm and the results of numerical solution of the equation are presented. The problem of boundary condition choice is discussed. The angular distribution of 10 eV energy photoelectrons at different altitudes of plasmasphere is presented as an example. It is shown that the changes of photoelectron distribution function from bottom of plasmasphere to the top of a force line of the geomagnetic field are within the 1.6 limits. Presented is the estimate of plasmasphere transmittance value and its comparison with the experiment for Mc Ilwain parameter L=2
Energy Technology Data Exchange (ETDEWEB)
Van Criekingen, S. [Commissariat a l' energie atomique (CEA-Saclay), DEN/DM2S/SERMA/LENR (Bat 470), 91191 Gif-sur-Yvette Cedex (France)]. E-mail: serge.van-criekingen@cea.fr
2006-05-15
The Raviart-Thomas finite elements provide an appropriate spatial discretization of the mixed-dual form of the diffusion equation. This discretization can then be coupled to an efficient solution method. The high performances achieved by such an approach triggered research on its possible generalization to the transport equation using a spherical harmonic (or P {sub N}) angular approximation. In view of the difficulty of developing a straightforward generalization within the mixed-dual framework, we here consider 2D non-conforming (i.e., allowing interface discontinuities) finite elements coupled to the second-order form of the transport equation. This non-conforming approach keeps the mixed-dual property of the relaxation of the flux interface continuity constraint. We investigate different non-conforming elements and compare them to the well-known Lagrangian conforming elements.
International Nuclear Information System (INIS)
Van Criekingen, S.
2006-01-01
The Raviart-Thomas finite elements provide an appropriate spatial discretization of the mixed-dual form of the diffusion equation. This discretization can then be coupled to an efficient solution method. The high performances achieved by such an approach triggered research on its possible generalization to the transport equation using a spherical harmonic (or P N ) angular approximation. In view of the difficulty of developing a straightforward generalization within the mixed-dual framework, we here consider 2D non-conforming (i.e., allowing interface discontinuities) finite elements coupled to the second-order form of the transport equation. This non-conforming approach keeps the mixed-dual property of the relaxation of the flux interface continuity constraint. We investigate different non-conforming elements and compare them to the well-known Lagrangian conforming elements
International Nuclear Information System (INIS)
Kretzschmar, Martin
1999-01-01
When a Penning trap is operated with an additional quadrupole driving field with a frequency that equals a suitable combination (sum or difference) of the frequencies of the fundamental modes of motion (modified cyclotron, magnetron and axial frequency), then a periodic conversion of the participating modes into each other is observed, strongly resembling the Rabi oscillations in a 2-level atom driven by a laser field tuned to the transition frequency. This investigation attempts to understand on a fundamental level how and why the motion of a classical particle in a macroscopic apparatus can be truely analogous to the oscillations of states of quantum mechanical 2-level systems (2-level atom or magnetic resonance). Ion motion in a Penning trap with an additional quadrupole driving field is described in a quantum mechanical frame work. The Heisenberg equations of motion for the creation and annihilation operators of the interacting oscillators have been explicitly solved, the time development operator of the Schroedinger picture has been determined. The driving field provides for two types of intermode interaction: Type I preserves the total number of excitation quanta present in the two interacting modes, the system oscillates between the modes with a frequency corresponding to the Rabi frequency in two-level systems. Type II preserves the difference of the numbers of excitation quanta present in the two interacting modes, it causes the ion motion to become unbounded. The two types of interaction are associated in a natural way with a SU(2) and a SU(1,1) Lie algebra. The three generators of these algebras form a vector operator that we denote as the Bloch vector operator. The Hilbert space decomposes in a natural way into invariant subspaces, finite dimensional in the case of type I interaction (SU(2)-algebra) and infinite dimensional in the case of type II interaction (SU(1,1)-algebra). The physics of the 2-level atom in the laser field can be described in the 2
International Nuclear Information System (INIS)
Pirouzmand, Ahmad; Hadad, Kamal
2011-01-01
Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with P N method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P N ) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.
Green, David L.; Berry, Lee A.; Simpson, Adam B.; Younkin, Timothy R.
2018-04-01
We present the KINETIC-J code, a computational kernel for evaluating the linearized Vlasov equation with application to calculating the kinetic plasma response (current) to an applied time harmonic wave electric field. This code addresses the need for a configuration space evaluation of the plasma current to enable kinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourier spectral methods. We benchmark the kernel via comparison with the standard k →-space forms of the hot plasma conductivity tensor.
International Nuclear Information System (INIS)
Chen Qianyong; Kevrekidis, Panayotis G; Malomed, Boris A
2012-01-01
We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schrödinger equation, which includes the harmonic oscillator potential and a random potential. The equation models experimentally relevant spatially disordered settings in Bose-Einstein condensates (BECs) and nonlinear optics. First, the generation of soliton arrays from a broad initial quasi-uniform state by the modulational instability (MI) is considered following a sudden switch of the nonlinearity from repulsive to attractive. Then, we study oscillations of a single soliton in this setting, which models a recently conducted experiment in a BEC. The basic characteristics of the MI-generated array, such as the number of solitons and their mobility, are reported as functions of the strength and correlation length of the disorder, and of the total norm. For the single oscillating soliton, its survival rate is found. The main features of these dependences are explained qualitatively. (paper)
Energy Technology Data Exchange (ETDEWEB)
Lim, Eunju, E-mail: elim@dankook.ac.kr, E-mail: taguchi.d.aa@m.titech.ac.jp, E-mail: iwamoto@pe.titech.ac.jp [Department of Applied Physics, Institute of Nanosensor and Biotechnology, Dankook University, Jukjeon-dong, Gyeonggi-do 448-701 (Korea, Republic of); Taguchi, Dai, E-mail: elim@dankook.ac.kr, E-mail: taguchi.d.aa@m.titech.ac.jp, E-mail: iwamoto@pe.titech.ac.jp; Iwamoto, Mitsumasa, E-mail: elim@dankook.ac.kr, E-mail: taguchi.d.aa@m.titech.ac.jp, E-mail: iwamoto@pe.titech.ac.jp [Department of Physical Electronics, Tokyo Institute of Technology 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8552 (Japan)
2014-08-18
We studied the carrier transport and carrier trapping in indium tin oxide/polyimide (PI)/6,13-Bis(triisopropylsilylethynyl)pentacene (TIPS-pentacene)/Au diodes by using charge modulation spectroscopy (CMS) and time-resolved electric field induced optical second harmonic generation (TR-EFISHG) measurements. TR-EFISHG directly probes the spatial carrier behaviors in the diodes, and CMS is useful in explaining the carrier motion with respect to energy. The results clearly indicate that the injected carriers move across TIPS-pentacene thorough the molecular energy states of TIPS-pentacene and accumulate at the PI/TIPS-pentacene interface. However, some carriers are trapped in the PI layers. These findings take into account the capacitance-voltage and current-voltage characteristics of the diodes.
International Nuclear Information System (INIS)
Nazari-Golshan, A.; Nourazar, S. S.
2013-01-01
The time fractional modified Korteweg-de Vries (TFMKdV) equation is solved to study the nonlinear propagation of small but finite amplitude dust ion-acoustic (DIA) solitary waves in un-magnetized dusty plasma with trapped electrons. The plasma is composed of a cold ion fluid, stationary dust grains, and hot electrons obeying a trapped electron distribution. The TFMKdV equation is derived by using the semi-inverse and Agrawal's methods and then solved by the Laplace Adomian decomposition method. Our results show that the amplitude of the DIA solitary waves increases with the increase of time fractional order β, the wave velocity v 0 , and the population of the background free electrons λ. However, it is vice-versa for the deviation from isothermality parameter b, which is in agreement with the result obtained previously
International Nuclear Information System (INIS)
Polivanskij, V.P.
1989-01-01
The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs
Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.
Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene
2017-08-01
Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)
2016-07-01
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.
Mean-field model for the interference of matter-waves from a three-dimensional optical trap
International Nuclear Information System (INIS)
Adhikari, Sadhan K.; Muruganandam, Paulsamy
2003-01-01
Using the mean-field time-dependent Gross-Pitaevskii equation we study the formation of a repulsive Bose-Einstein condensate on a combined optical and harmonic traps in two and three dimensions and subsequent generation of the interference pattern upon the removal of the combined traps as in the experiment by Greiner et al. [Nature (London) 415 (2002) 39]. For optical traps of moderate strength, interference pattern of 27 (9) prominent bright spots is found to be formed in three (two) dimensions on a cubic (square) lattice in agreement with experiment. Similar interference pattern can also be formed upon removal of the optical lattice trap only. The pattern so formed can oscillate for a long time in the harmonic trap which can be observed experimentally
Csordás, András; Graham, Robert; Szépfalusy, Péter
1997-01-01
The Bogoliubov equations of the quasi-particle excitations in a weakly interacting trapped Bose-condensate are solved in the WKB approximation in an isotropic harmonic trap, determining the discrete quasi-particle energies and wave functions by torus (Bohr-Sommerfeld) quantization of the integrable classical quasi-particle dynamics. The results are used to calculate the position and strengths of the peaks in the dynamic structure function which can be observed by off-resonance inelastic light...
Dynamics of Bose-Einstein condensates in a time-dependent trap
International Nuclear Information System (INIS)
Kumar, V. Ramesh; Radha, R.; Panigrahi, Prasanta K.
2008-01-01
In this paper, we generate the Lax pair for the one-dimensional Gross-Pitaevskii equation with time-dependent scattering length in the presence of a confining or expulsive harmonic time-dependent trap. We then exploit the Lax pair profitably to construct multisoliton solutions using gauge transformation from a trivial input solution. In particular, we have investigated the effect of both expulsive and confining traps on soliton interaction. Even though we find that the amplitude of the bright soliton relies upon the time-dependent scattering length and the external time-dependent trap with the velocity being dictated by the external trap alone, the observation of interdependence of the scattering length on the trap shows that the bright solitons not only can be compressed into a desirable width and amplitude but also can be remote controlled and driven anywhere in the plane by suitably maneuvering the external time-dependent trap alone
Harmonically excited orbital variations
International Nuclear Information System (INIS)
Morgan, T.
1985-01-01
Rephrasing the equations of motion for orbital maneuvers in terms of Lagrangian generalized coordinates instead of Newtonian rectangular cartesian coordinates can make certain harmonic terms in the orbital angular momentum vector more readily apparent. In this formulation the equations of motion adopt the form of a damped harmonic oscillator when torques are applied to the orbit in a variationally prescribed manner. The frequencies of the oscillator equation are in some ways unexpected but can nonetheless be exploited through resonant forcing functions to achieve large secular variations in the orbital elements. Two cases are discussed using a circular orbit as the control case: (1) large changes in orbital inclination achieved by harmonic excitation rather than one impulsive velocity change, and (2) periodic and secular changes to the longitude of the ascending node using both stable and unstable excitation strategies. The implications of these equations are also discussed for both artificial satellites and natural satellites. For the former, two utilitarian orbits are suggested, each exploiting a form of harmonic excitation. 5 refs
Trapped ion mode in toroidally rotating plasmas
International Nuclear Information System (INIS)
Artun, M.; Tang, W.M.; Rewoldt, G.
1995-04-01
The influence of radially sheared toroidal flows on the Trapped Ion Mode (TIM) is investigated using a two-dimensional eigenmode code. These radially extended toroidal microinstabilities could significantly influence the interpretation of confinement scaling trends and associated fluctuation properties observed in recent tokamak experiments. In the present analysis, the electrostatic drift kinetic equation is obtained from the general nonlinear gyrokinetic equation in rotating plasmas. In the long perpendicular wavelength limit k τ ρ bi much-lt 1, where ρ bi is the average trapped-ion banana width, the resulting eigenmode equation becomes a coupled system of second order differential equations nmo for the poloidal harmonics. These equations are solved using finite element methods. Numerical results from the analysis of low and medium toroidal mode number instabilities are presented using representative TFTR L-mode input parameters. To illustrate the effects of mode coupling, a case is presented where the poloidal mode coupling is suppressed. The influence of toroidal rotation on a TFTR L-mode shot is also analyzed by including a beam species with considerable larger temperature. A discussion of the numerical results is presented
Choi, S; Dunjko, V; Zhang, Z D; Olshanii, M
2015-09-11
Using a time-dependent modified nonlinear Schrödinger equation (MNLSE)-where the conventional chemical potential proportional to the density is replaced by the one inferred from Lieb-Liniger's exact solution-we study frequencies of the collective monopole excitations of a one-dimensional Bose gas. We find that our method accurately reproduces the results of a recent experimental study [E. Haller et al., Science 325, 1224 (2009)] in the full spectrum of interaction regimes from the ideal gas, through the mean-field regime, through the mean-field Thomas-Fermi regime, all the way to the Tonks-Giradeau gas. While the former two are accessible by the standard time-dependent NLSE and inaccessible by the time-dependent local density approximation, the situation reverses in the latter case. However, the MNLSE is shown to treat all these regimes within a single numerical method.
General Criterion for Harmonicity
Proesmans, Karel; Vandebroek, Hans; Van den Broeck, Christian
2017-10-01
Inspired by Kubo-Anderson Markov processes, we introduce a new class of transfer matrices whose largest eigenvalue is determined by a simple explicit algebraic equation. Applications include the free energy calculation for various equilibrium systems and a general criterion for perfect harmonicity, i.e., a free energy that is exactly quadratic in the external field. As an illustration, we construct a "perfect spring," namely, a polymer with non-Gaussian, exponentially distributed subunits which, nevertheless, remains harmonic until it is fully stretched. This surprising discovery is confirmed by Monte Carlo and Langevin simulations.
Stationary solutions and self-trapping in discrete quadratic nonlinear systems
DEFF Research Database (Denmark)
Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev
1998-01-01
We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...... the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system...
Barlow, Stephan E.; Alexander, Michael L.; Follansbee, James C.
1997-01-01
An ion trap having two end cap electrodes disposed asymmetrically about a center of a ring electrode. The inner surface of the end cap electrodes are conformed to an asymmetric pair of equipotential lines of the harmonic formed by the application of voltages to the electrodes. The asymmetry of the end cap electrodes allows ejection of charged species through the closer of the two electrodes which in turn allows for simultaneously detecting anions and cations expelled from the ion trap through the use of two detectors charged with opposite polarity.
Control of trapped-ion quantum states with optical pulses
International Nuclear Information System (INIS)
Rangan, C.; Monroe, C.; Bucksbaum, P.H.; Bloch, A.M.
2004-01-01
We present new results on the quantum control of systems with infinitely large Hilbert spaces. A control-theoretic analysis of the control of trapped-ion quantum states via optical pulses is performed. We demonstrate how resonant bichromatic fields can be applied in two contrasting ways--one that makes the system completely uncontrollable and the other that makes the system controllable. In some interesting cases, the Hilbert space of the qubit-harmonic oscillator can be made finite, and the Schroedinger equation controllable via bichromatic resonant pulses. Extending this analysis to the quantum states of two ions, a new scheme for producing entangled qubits is discovered
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1985-01-01
This paper completes a descrption of the quantization procedure in the harmonic superspace approach. The Feynman rules for N=2 matter and Yang-Mills theories are derived and the various examples of harmonic supergraph calculations are given. Calculations appear to be not more difficult than those in the N=1 case. The integration over harmonic variables does not lead to any troubles, a non-locality in these disappears on-shell. The important property is that the quantum corrections are always writen as integrals over the full harmonic superspace even though the initial action is an integral over the analytic subspace. As a by-product our results imply a very simple proof of finiteness of a wide class of the N=4, d=2 non-linear Σ-models. The most general self-couplings of hypermultiplets including those with broken SU(2) are considered.The duality relations among the N=2 linear multiplet and both kinds of hypermultiplet are established
First and second sound in cylindrically trapped gases.
Bertaina, G; Pitaevskii, L; Stringari, S
2010-10-08
We investigate the propagation of density and temperature waves in a cylindrically trapped gas with radial harmonic confinement. Starting from two-fluid hydrodynamic theory we derive effective 1D equations for the chemical potential and the temperature which explicitly account for the effects of viscosity and thermal conductivity. Differently from quantum fluids confined by rigid walls, the harmonic confinement allows for the propagation of both first and second sound in the long wavelength limit. We provide quantitative predictions for the two sound velocities of a superfluid Fermi gas at unitarity. For shorter wavelengths we discover a new surprising class of excitations continuously spread over a finite interval of frequencies. This results in a nondissipative damping in the response function which is analytically calculated in the limiting case of a classical ideal gas.
The rate of plasma heating by harmonic ion cyclotron waves in tokamaks
International Nuclear Information System (INIS)
Moslehi-Fard, M.; Sobhanian, S.; Solati-Kia, F.
2002-01-01
In tokamaks, the toroidal magnetic field, B φ , is due to the current in coils around plasma, and the poloidal magnetic field B p results from the plasma itself. Usually B φ p , and the combination of these two fields forms a nested set of toroidal magnetic surfaces. The equilibrium Grad-Shafranov equation is investigated and it is shown that the particle products of fusion with different pitch angles on these surfaces have different orbital shapes. In the JET tokamak, the α particles with pitch angle θ smaller than 54.8 deg are passing, those with θ between 54.8 deg and 65.1 deg have trapping-passing orbits but for θ greater than 65.1 deg the orbit has a banana form. Other tokamaks such as Alcator and ITER are also considered. The passing, trapping-passing and banana orbits in these tokamaks are traced. The results obtained from this calculation are analyzed. The wave damping has been investigated produced from interaction with particles, particularly α particles, and the rate of heating for l = 1 to 8 harmonics is plotted. The results of calculation show that heating at the fourth harmonic reaches a maximum. For higher harmonics, the heating does not change much from the fourth harmonic. (author)
Bennett, Charles L [Livermore, CA
2009-10-20
A high efficiency harmonic engine based on a resonantly reciprocating piston expander that extracts work from heat and pressurizes working fluid in a reciprocating piston compressor. The engine preferably includes harmonic oscillator valves capable of oscillating at a resonant frequency for controlling the flow of working fluid into and out of the expander, and also preferably includes a shunt line connecting an expansion chamber of the expander to a buffer chamber of the expander for minimizing pressure variations in the fluidic circuit of the engine. The engine is especially designed to operate with very high temperature input to the expander and very low temperature input to the compressor, to produce very high thermal conversion efficiency.
Classical and multilinear harmonic analysis
Muscalu, Camil
2013-01-01
This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this vo...
The relativistic harmonic oscillator reconsidered
International Nuclear Information System (INIS)
Hofsaess, T.
1978-01-01
The bound states of scalar quarks interacting through a scalar harmonic oscillator are investigated. In the presence of this interaction the dressed quark propagator differs substantially from the free one. This leads to a Bethe Salpeter equation which does not allow for any stable bound states of positive mass. (orig.) [de
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
Harmonic mappings into manifolds with boundary
International Nuclear Information System (INIS)
Chen Yunmei; Musina, R.
1989-08-01
In this paper we deal with harmonic maps from a compact Riemannian manifold into a manifold with boundary. In this case, a weak harmonic map is by definition a solution to a differential inclusion. In the first part of the paper we investigate the general properties of weak harmonic maps, which can be seen as solutions to a system of elliptic differential equations. In the second part we concentrate our attention on the heat flow method for harmonic maps. The result we achieve in this context extends a result by Chen and Struwe. (author). 21 refs
Helson, Henry
2010-01-01
This second edition has been enlarged and considerably rewritten. Among the new topics are infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl's theorems on equidistribution. Topics that have continued from the first edition include Minkowski's theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem. Readers of the book should have studied the Lebesgue integral, the elementary theory of analytic and harmonic functions, and the basic theory of Banach spaces. The treatment is classical and as simple as possible. This is an instructional book, not a treatise. Mathematics students interested in analysis will find here what they need to know about Fourier analysis. Physicists and others can use the book as a reference for more advanced topics.
A Look at Damped Harmonic Oscillators through the Phase Plane
Daneshbod, Yousef; Latulippe, Joe
2011-01-01
Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…
Computer model for harmonic ultrasound imaging.
Li, Y; Zagzebski, J A
2000-01-01
Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. In this paper, we present a computer model that can generate realistic harmonic images. In this model, the incident ultrasound is modeled after the "KZK" equation, and the echo signal is modeled using linear propagation theory because the echo signal is much weaker than the incident pulse. Both time domain and frequency domain numerical solutions to the "KZK" equation were studied. Realistic harmonic images of spherical lesion phantoms were generated for scans by a circular transducer. This model can be a very useful tool for studying the harmonic buildup and dissipation processes in a nonlinear medium, and it can be used to investigate a wide variety of topics related to B-mode harmonic imaging.
Conformal invariance in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1987-01-01
In the present paper we show how the N = 2 superconformal group is realised in harmonic superspace and examine conformal invariance of N = 2 off-shell theories. We believe that the example of N = O self-dual Yang-Mills equations can serve as an instructive introduction to the subject of harmonic superspace and this is examined. The rigid N = 2 conformal supersymmetry and its local version, i.e. N = 2 conformal supergravity is also discussed. The paper is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. (author)
International Nuclear Information System (INIS)
Sudakov, M.Yu.
2000-01-01
One studied theoretically the mode of mass-selective unstable output of ions from three-dimensional quadrupole ion trap. One developed a method represent coordinates of ions per one period of supplying HF voltage with regard to nonlinear distortions of quadrupole potential. One derived equation for an envelope of ion oscillations in the form of motion equation of mass point in the efficient force field. One explained the effect of output delay of ions at presence of the field negative even harmonics. One proved that the positive even distortions of quadrupole potential favored realization of that mode and studied the dynamics of ions in the course of output [ru
Modified semiclassical approximation for trapped Bose gases
International Nuclear Information System (INIS)
Yukalov, V.I.
2005-01-01
A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The result of the modified approach is shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. The effective thermodynamic limit is defined for any confining dimension. The behavior of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed
Landau damping in trapped Bose condensed gases
Energy Technology Data Exchange (ETDEWEB)
Jackson, B; Zaremba, E [Department of Physics, Queen' s University, Kingston, ON K7L 3N6 (Canada)
2003-07-01
We study Landau damping in dilute Bose-Einstein condensed gases in both spherical and prolate ellipsoidal harmonic traps. We solve the Bogoliubov equations for the mode spectrum in both of these cases, and calculate the damping by summing over transitions between excited quasiparticle states. The results for the spherical case are compared to those obtained in the Hartree-Fock (HF) approximation, where the excitations take on a single-particle character, and excellent agreement between the two approaches is found. We have also taken the semiclassical limit of the HF approximation and obtain a novel expression for the Landau damping rate involving the time-dependent self-diffusion function of the thermal cloud. As a final approach, we study the decay of a condensate mode by making use of dynamical simulations in which both the condensate and thermal cloud are evolved explicitly as a function of time. A detailed comparison of all these methods over a wide range of sample sizes and trap geometries is presented.
Active stabilization of ion trap radiofrequency potentials
Energy Technology Data Exchange (ETDEWEB)
Johnson, K. G.; Wong-Campos, J. D.; Restelli, A.; Landsman, K. A.; Neyenhuis, B.; Mizrahi, J.; Monroe, C. [Joint Quantum Institute and University of Maryland Department of Physics, College Park, Maryland 20742 (United States)
2016-05-15
We actively stabilize the harmonic oscillation frequency of a laser-cooled atomic ion confined in a radiofrequency (rf) Paul trap by sampling and rectifying the high voltage rf applied to the trap electrodes. We are able to stabilize the 1 MHz atomic oscillation frequency to be better than 10 Hz or 10 ppm. This represents a suppression of ambient noise on the rf circuit by 34 dB. This technique could impact the sensitivity of ion trap mass spectrometry and the fidelity of quantum operations in ion trap quantum information applications.
Directory of Open Access Journals (Sweden)
Piotr FOLĘGA
2014-03-01
Full Text Available The variety of types and sizes currently in production harmonic drive is a problem in their rational choice. Properly selected harmonic drive must meet certain requirements during operation, and achieve the anticipated service life. The paper discusses the problems associated with the selection of the harmonic drive. It also presents the algorithm correct choice of harmonic drive. The main objective of this study was to develop a computer program that allows the correct choice of harmonic drive by developed algorithm.
Born-Oppenheimer description of two atoms in a combined oscillator and lattice trap
DEFF Research Database (Denmark)
Sørensen, Ole Søe; Mølmer, Klaus
2012-01-01
We analyze the quantum states of two identical bosons in a combined harmonic oscillator and periodic lattice trap in one spatial dimension. In the case of tight-binding and only nearest-neighbor tunneling, the equations of motion are conveniently represented in the momentum representation. We sho...... that in the case of strong attraction between the particles, the different time scales of relative and center-of-mass motions validate a separation of the problem similar to the Born-Oppenheimer approximation applied in the description of electronic and nuclear motions in molecules....
Harmonic generation with a dual frequency pulse.
Keravnou, Christina P; Averkiou, Michalakis A
2014-05-01
Nonlinear imaging was implemented in commercial ultrasound systems over the last 15 years offering major advantages in many clinical applications. In this work, pulsing schemes coupled with a dual frequency pulse are presented. The pulsing schemes considered were pulse inversion, power modulation, and power modulated pulse inversion. The pulse contains a fundamental frequency f and a specified amount of its second harmonic 2f. The advantages and limitations of this method were evaluated with both acoustic measurements of harmonic generation and theoretical simulations based on the KZK equation. The use of two frequencies in a pulse results in the generation of the sum and difference frequency components in addition to the other harmonic components. While with single frequency pulses, only power modulation and power modulated pulse inversion contained odd harmonic components, with the dual frequency pulse, pulse inversion now also contains odd harmonic components.
International Nuclear Information System (INIS)
Klimas, A.J.
1983-01-01
A bump-on-tail unstable reduced velocity distribution has been constructed from data obtained at the upstream boundary of the electron foreshock by the GSFC electron spectrometer experiment on the ISEE 1 satellite. This distribution is used as the initial plasma state for a numerical integration of the one-dimensional Vlasov-Maxwell system of equations. The integration is carried through the growth of the instability, beyond its saturation, and well into the stabilized plasma regime. A power spectrum for the electric field of the stabilized plasma is computed. The spectrum is dominated by a narrow peak at the Bohm-Gross frequency of the unstable field mode but it also contain significant power at the harmonics of the Bohm-Gross frequency. The harmonic power is in sharp peaks which are split into closely spaced doublets. The fundamental peak at the Bohm-Gross frequency is also split, in this case into a closely space triplet. The fundamental peak at the Bohm-Gross frequency is also split, in this case into a closely space triplet. The splitting is due to slow modulations of the stabilized electric field oscillations which, it is thought, are caused by wave-particle trapping. The wavelength of mth harmonic of the Bohm-Gross frequency is given by lambda/sub u//m, where lambda/sub u/ is the wavelength of the unstable mode. The mechanism for excitation of the second harmonic is shwn to be second-order wave-wave coupling which takes place during that period in the evolution of the instability which would otherwise be called the linear growth phase. It is conjectured that the higher harmonics are excited by the same mechanism. It is further argued that harmonic excitation at the boundary of the electron foreshock should be a common occurrence
Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method
Directory of Open Access Journals (Sweden)
Ying Wang
2014-06-01
Full Text Available We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.
International Nuclear Information System (INIS)
Theodorakis, Stavros
2003-01-01
We emulate the cubic term Ψ 3 in the nonlinear Schroedinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a δ function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Ψ 3 one. In particular, it can be used for the nonlinear Schroedinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions
A Landau fluid model for dissipative trapped electron modes
International Nuclear Information System (INIS)
Hedrick, C.L.; Leboeuf, J.N.; Sidikman, K.L.
1995-09-01
A Landau fluid model for dissipative trapped electron modes is developed which focuses on an improved description of the ion dynamics. The model is simple enough to allow nonlinear calculations with many harmonics for the times necessary to reach saturation. The model is motivated by a discussion that starts with the gyro-kinetic equation and emphasizes the importance of simultaneously including particular features of magnetic drift resonance, shear, and Landau effects. To ensure that these features are simultaneously incorporated in a Landau fluid model with only two evolution equations, a new approach to determining the closure coefficients is employed. The effect of this technique is to reduce the matching of fluid and kinetic responses to a single variable, rather than two, and to allow focusing on essential features of the fluctuations in question, rather than features that are only important for other types of fluctuations. Radially resolved nonlinear calculations of this model, advanced in time to reach saturation, are presented to partially illustrate its intended use. These calculations have a large number of poloidal and toroidal harmonics to represent the nonlinear dynamics in a converged steady state which includes cascading of energy to both short and long wavelengths
Local density approximation for a perturbative equation of state
International Nuclear Information System (INIS)
Astrakharchik, G. E.
2005-01-01
Knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic 'perturbative' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size, and density profile of a trapped system in three-, two-, and one-dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high-precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. The physical meaning of the expansion terms in a number of systems is discussed
Energy Technology Data Exchange (ETDEWEB)
Butler, E., E-mail: eoin.butler@cern.ch [CERN, Physics Department (Switzerland); Andresen, G. B. [Aarhus University, Department of Physics and Astronomy (Denmark); Ashkezari, M. D. [Simon Fraser University, Department of Physics (Canada); Baquero-Ruiz, M. [University of California, Department of Physics (United States); Bertsche, W. [Swansea University, Department of Physics (United Kingdom); Bowe, P. D. [Aarhus University, Department of Physics and Astronomy (Denmark); Cesar, C. L. [Universidade Federal do Rio de Janeiro, Instituto de Fisica (Brazil); Chapman, S. [University of California, Department of Physics (United States); Charlton, M.; Deller, A.; Eriksson, S. [Swansea University, Department of Physics (United Kingdom); Fajans, J. [University of California, Department of Physics (United States); Friesen, T.; Fujiwara, M. C. [University of Calgary, Department of Physics and Astronomy (Canada); Gill, D. R. [TRIUMF (Canada); Gutierrez, A. [University of British Columbia, Department of Physics and Astronomy (Canada); Hangst, J. S. [Aarhus University, Department of Physics and Astronomy (Denmark); Hardy, W. N. [University of British Columbia, Department of Physics and Astronomy (Canada); Hayden, M. E. [Simon Fraser University, Department of Physics (Canada); Humphries, A. J. [Swansea University, Department of Physics (United Kingdom); Collaboration: ALPHA Collaboration; and others
2012-12-15
Precision spectroscopic comparison of hydrogen and antihydrogen holds the promise of a sensitive test of the Charge-Parity-Time theorem and matter-antimatter equivalence. The clearest path towards realising this goal is to hold a sample of antihydrogen in an atomic trap for interrogation by electromagnetic radiation. Achieving this poses a huge experimental challenge, as state-of-the-art magnetic-minimum atom traps have well depths of only {approx}1 T ({approx}0.5 K for ground state antihydrogen atoms). The atoms annihilate on contact with matter and must be 'born' inside the magnetic trap with low kinetic energies. At the ALPHA experiment, antihydrogen atoms are produced from antiprotons and positrons stored in the form of non-neutral plasmas, where the typical electrostatic potential energy per particle is on the order of electronvolts, more than 10{sup 4} times the maximum trappable kinetic energy. In November 2010, ALPHA published the observation of 38 antiproton annihilations due to antihydrogen atoms that had been trapped for at least 172 ms and then released-the first instance of a purely antimatter atomic system confined for any length of time (Andresen et al., Nature 468:673, 2010). We present a description of the main components of the ALPHA traps and detectors that were key to realising this result. We discuss how the antihydrogen atoms were identified and how they were discriminated from the background processes. Since the results published in Andresen et al. (Nature 468:673, 2010), refinements in the antihydrogen production technique have allowed many more antihydrogen atoms to be trapped, and held for much longer times. We have identified antihydrogen atoms that have been trapped for at least 1,000 s in the apparatus (Andresen et al., Nature Physics 7:558, 2011). This is more than sufficient time to interrogate the atoms spectroscopically, as well as to ensure that they have relaxed to their ground state.
International Nuclear Information System (INIS)
Adhikari, Sadhan K
2003-01-01
We study the expansion of a Bose-Einstein condensate trapped in a combined optical-lattice and axially-symmetric harmonic potential using the numerical solution of the mean-field Gross-Pitaevskii equation. First, we consider the expansion of such a condensate under the action of the optical-lattice potential alone. In this case the result of numerical simulation for the axial and radial sizes during expansion is in agreement with two experiments by Morsch et al (2002 Phys. Rev. A 66 021601(R) and 2003 Laser Phys. 13 594). Finally, we consider the expansion under the action of the harmonic potential alone. In this case the oscillation, and the disappearance and revival of the resultant interference pattern is in agreement with the experiment by Mueller et al (2003 J. Opt. B: Quantum Semiclass. Opt. 5 S38)
Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle
International Nuclear Information System (INIS)
Salazar, Domingos S P; Lira, Sérgio A
2016-01-01
In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system’s energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of N noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions. (paper)
Klaiman, S.; Streltsov, A. I.; Alon, O. E.
2018-04-01
A solvable model of a generic trapped bosonic mixture, N 1 bosons of mass m 1 and N 2 bosons of mass m 2 trapped in an harmonic potential of frequency ω and interacting by harmonic inter-particle interactions of strengths λ 1, λ 2, and λ 12, is discussed. It has recently been shown for the ground state [J. Phys. A 50, 295002 (2017)] that in the infinite-particle limit, when the interaction parameters λ 1(N 1 ‑ 1), λ 2(N 2 ‑ 1), λ 12 N 1, λ 12 N 2 are held fixed, each of the species is 100% condensed and its density per particle as well as the total energy per particle are given by the solution of the coupled Gross-Pitaevskii equations of the mixture. In the present work we investigate properties of the trapped generic mixture at the infinite-particle limit, and find differences between the many-body and mean-field descriptions of the mixture, despite each species being 100%. We compute analytically and analyze, both for the mixture and for each species, the center-of-mass position and momentum variances, their uncertainty product, the angular-momentum variance, as well as the overlap of the exact and Gross-Pitaevskii wavefunctions of the mixture. The results obtained in this work can be considered as a step forward in characterizing how important are many-body effects in a fully condensed trapped bosonic mixture at the infinite-particle limit.
Spectral intensity distribution of trapped fermions
Indian Academy of Sciences (India)
Trapped fermions; local density approximation; spectral intensity distribution function. ... Thus, cold atomic systems allow us to study interesting ... In fermions, synthetic non-Abelian gauge ... energy eigenstates of the isotropic harmonic oscillator [26–28]. ... d i=1. (ni + 1. 2. )ω0. In calculating the SIDF exactly these eigenfunc-.
Unlocking higher harmonics in atomic force microscopy with gentle interactions.
Santos, Sergio; Barcons, Victor; Font, Josep; Verdaguer, Albert
2014-01-01
In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.
Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.
2013-06-01
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions
An explicit harmonic code for black-hole evolution using excision
International Nuclear Information System (INIS)
Szilagyi, Bela; Pollney, Denis; Rezzolla, Luciano; Thornburg, Jonathan; Winicour, Jeffrey
2007-01-01
We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the well-posedness and numerical stability of the initial-boundary problem for the quasilinear wave equation. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code. Such tests range from the evolution of isolated black holes to the head-on collision of two black holes and then to a binary black hole inspiral and merger. Besides assessing the accuracy of the code, the inspiral and merger test has revealed that the marginally trapped surfaces contained within the common apparent horizon of the merged black hole can touch and even intersect. This novel feature in the dynamics of the marginally trapped surfaces is unexpected but consistent with theorems on the properties of these surfaces
An explicit harmonic code for black-hole evolution using excision
Energy Technology Data Exchange (ETDEWEB)
Szilagyi, Bela [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany); Pollney, Denis [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany); Rezzolla, Luciano [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany); Thornburg, Jonathan [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany); Winicour, Jeffrey [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany)
2007-06-21
We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the well-posedness and numerical stability of the initial-boundary problem for the quasilinear wave equation. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code. Such tests range from the evolution of isolated black holes to the head-on collision of two black holes and then to a binary black hole inspiral and merger. Besides assessing the accuracy of the code, the inspiral and merger test has revealed that the marginally trapped surfaces contained within the common apparent horizon of the merged black hole can touch and even intersect. This novel feature in the dynamics of the marginally trapped surfaces is unexpected but consistent with theorems on the properties of these surfaces.
Harmonics and energy management
International Nuclear Information System (INIS)
Andresen, M.
1993-01-01
To summarize what this paper has presented: Voltage and current non-sinusoidal wave shapes exist in our power system. These harmonics result from the prolific use of non-linear loads. The use of these types of loads is increasing dramatically, partly due to the push to implement energy management techniques involving harmonic generating equipment. Harmonic analysis can identify specific harmonics, their frequency, magnitude, and phase shift referenced to the fundamental. Harmonic distortion forces the use of true RMS multimeters for measurement accuracy. High levels of neutral current and N-G voltages are now possible. Transformers may overheat and fail even though they are below rated capacity. Low power factors due to harmonics cannot be corrected by the installation of capacitors, and knowledge of the fundamental VARs or the displacement power factor is needed to use capacitors alone for power factor correction. The harmonic related problems presented are by no means an exhaustive list. Many other concerns arise when harmonics are involved in the power system. The critical issue behind these problems is that many of the devices being recommended from an energy management point of view are contributing to the harmonic levels, and thus to the potential for harmonic problems. We can no longer live in the sinusoidal mentality if we are to be effective in saving energy and reducing costs
Some remarks on geodesics in gauge groups and harmonic maps
International Nuclear Information System (INIS)
Valli, G.
1987-08-01
The following topics are discussed: Euler's equations for geodesics in the gauge groups and in gauge orbits of connections, conserved quantities and moment map, existence and uniqueness of solutions for the Cauchy problem, stationary solutions and harmonic bundles, harmonic gauges on Riemann surfaces and Lax pairs, low geodesics in gauge groups over Riemann surfaces produce, by Hodge decomposition, paths of holomorphic differentials. 19 refs
Higher-order harmonics of limited diffraction Bessel beams
Ding; Lu
2000-03-01
We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.
Solving Nonlinear Coupled Differential Equations
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
Sobolev Spaces Associated to the Harmonic Oscillator
Indian Academy of Sciences (India)
We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator H = − + | x | 2 . Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.
2006-01-01
3 April 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows the margin of a lava flow on a cratered plain in the Athabasca Vallis region of Mars. Remarkably, the cratered plain in this scene is essentially free of bright, windblown ripples. Conversely, the lava flow apparently acted as a trap for windblown materials, illustrated by the presence of the light-toned, wave-like texture over much of the flow. That the lava flow surface trapped windblown sand and granules better than the cratered plain indicates that the flow surface has a rougher texture at a scale too small to resolve in this image. Location near: 10.7oN, 204.5oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Northern Winter
Omega-Harmonic Functions and Inverse Conductivity Problems on Networks
National Research Council Canada - National Science Library
Berenstein, Carlos A; Chung, Soon-Yeong
2003-01-01
.... To do this, they introduce an elliptic operator DELTA omega and an omega-harmonic function on the graph, with its physical interpretation being the diffusion equation on the graph, which models an electric network...
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle- n-hole) configurations, deformations, excitation energies, or angular momenta. Similarly, Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean-field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: [J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166]. Reasons for new version: Version 2.49s of HFODD provides a number of new options such as the isospin mixing and projection of the Skyrme functional, the finite-temperature HF and HFB formalism and optimized methods to perform multi-constrained calculations. It is also the first version of HFODD to contain threading and parallel capabilities. Summary of revisions: Isospin mixing and projection of the HF states has been implemented. The finite-temperature formalism for the HFB equations has been implemented. The Lipkin translational energy correction method has been implemented. Calculation of the shell correction has been implemented. The two-basis method for the solution to the HFB equations has been implemented. The Augmented Lagrangian Method (ALM) for calculations with multiple constraints has been implemented. The linear constraint method based on the cranking approximation of the RPA matrix has been implemented. An
Butler, E; Ashkezari, M D; Baquero-Ruiz, M; Bertsche, W; Bowe, P D; Cesar, C L; Chapman, S; Charlton, M; Deller, A; Eriksson, S; Fajans, J; Friesen, T; Fujiwara, M C; Gill, D R; Gutierrez, A; Hangst, J S; Hardy, W N; Hayden, M E; Humphries, A J; Hydomako, R; Jenkins, M J; Jonsell, S; Jørgensen, L V; Kemp, S L; Kurchaninov, L; Madsen, N; Menary, S; Nolan, P; Olchanski, K; Olin, A; Povilus, A; Pusa, P; Rasmussen, C Ø; Robicheaux, F; Sarid, E; Seif el Nasr, S; Silveira, D M; So, C; Storey, J W; Thompson, R I; van der Werf, D P; Wurtele, J S; Yamazaki,Y
2012-01-01
Precision spectroscopic comparison of hydrogen and antihydrogen holds the promise of a sensitive test of the Charge-Parity-Time theorem and matter-antimatter equivalence. The clearest path towards realising this goal is to hold a sample of antihydrogen in an atomic trap for interrogation by electromagnetic radiation. Achieving this poses a huge experimental challenge, as state-of-the-art magnetic-minimum atom traps have well depths of only ∼1 T (∼0.5 K for ground state antihydrogen atoms). The atoms annihilate on contact with matter and must be ‘born’ inside the magnetic trap with low kinetic energies. At the ALPHA experiment, antihydrogen atoms are produced from antiprotons and positrons stored in the form of non-neutral plasmas, where the typical electrostatic potential energy per particle is on the order of electronvolts, more than 104 times the maximum trappable kinetic energy. In November 2010, ALPHA published the observation of 38 antiproton annihilations due to antihydrogen atoms that had been ...
Stability and nonlinear dynamics of gyrotrons at cyclotron harmonics
International Nuclear Information System (INIS)
Saraph, G.P.; Nusinovich, G.S.; Antonsen, T.M. Jr.; Levush, B.
1992-01-01
Gyrotrons operating at higher harmonics of the cyclotron frequency can overcome the frequency limitations caused by achievable strength of the magnetic field. However, the excitation of modes at the fundamental frequency exhibit a major problem for stable operation of harmonic gyrotron at high power with high efficiency. Therefore the issues of stability of gyrotron operation at the cyclotron harmonics and nonlinear dynamics of mode interaction are of great importance. The results of the authors stability analysis and multimode simulation are presented here. A detailed nonlinear theory of steady state single mode operation at cyclotron harmonics has been presented previously, taking into account beam-wave coupling and nonlinear gain function at cyclotron harmonics. A set of equations describing low gain regime interaction of modes resonant at different cyclotron harmonics was studied before. The multifrequency time-dependent nonlinear analysis presented here is based on previous gyrotron studies and beam-wave interaction at cyclotron harmonics. The authors have determined the parameter space for stable single mode operation at the second harmonic. The nonlinear dynamics of mode evolution and mode interaction for a harmonic gyrotron is presented. A new nonlinear effect in which the parasite at the fundamental harmonic helps excite the operating mode at the second harmonic has been demonstrated
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
International Nuclear Information System (INIS)
Belendez, Augusto; Pascual, Carolina
2007-01-01
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A
Rotational states of Bose gases with attractive interactions in anharmonic traps
International Nuclear Information System (INIS)
Lundh, Emil; Collin, Anssi; Suominen, Kalle-Antti
2004-01-01
A rotated and harmonically trapped Bose gas with attractive interactions is expected to either remain stationary or escape from the trap. Here we report that, on the contrary, in an anharmonic trapping potential the Bose gas with attractive interactions responds to external rotation very differently, namely, through center-of-mass motion or by formation of vortices
The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection
Franzen, J.
1994-01-01
The superposition of higher order multipole fields on the basic quadrupole field in ion traps generates a non-harmonic oscillator system for the ions. Fourier analyses of simulated secular oscillations in non-linear ion traps, therefore, not only reveal the sideband frequencies, well-known from the Mathieu theory, but additionally a commonwealth of multipole-specific overtones (or higher harmonics), and corresponding sidebands of overtones. Non-linear resonances occur when the overtone frequencies match sideband frequencies. It can be shown that in each of the resonance conditions, not just one overtone matches one sideband, instead, groups of overtones match groups of sidebands. The generation of overtones is studied by Fourier analysis of computed ion oscillations in the direction of thez axis. Even multipoles (octopole, dodecapole, etc.) generate only odd orders of higher harmonics (3, 5, etc.) of the secular frequency, explainable by the symmetry with regard to the planez = 0. In contrast, odd multipoles (hexapole, decapole, etc.) generate all orders of higher harmonics. For all multipoles, the lowest higher harmonics are found to be strongest. With multipoles of higher orders, the strength of the overtones decreases weaker with the order of the harmonics. Forz direction resonances in stationary trapping fields, the function governing the amplitude growth is investigated by computer simulations. The ejection in thez direction, as a function of timet, follows, at least in good approximation, the equation wheren is the order of multipole, andC is a constant. This equation is strictly valid for the electrically applied dipole field (n = 1), matching the secular frequency or one of its sidebands, resulting in a linear increase of the amplitude. It is valid also for the basic quadrupole field (n = 2) outside the stability area, giving an exponential increase. It is at least approximately valid for the non-linear resonances by weak superpositions of all higher odd
Bounce-harmonic Landau Damping of Plasma Waves
Anderegg, Francois
2015-11-01
We present measurement of plasma wave damping, spanning the temperature regimes of direct Landau damping, bounce-harmonic Landau damping, inter-species drag damping, and viscous damping. Direct Landau damping is dominant at high temperatures, but becomes negligible as v vph / 5 . The measurements are conducted in trapped pure ion plasmas contained in Penning-Malmberg trap, with wave-coherent LIF diagnostics of particle velocities. Our focus is on bounce harmonics damping, controlled by an applied ``squeeze'' potential, which generates harmonics in the wave potential and in the particle dynamics. A particle moving in z experiences a non-sinusoidal mode potential caused by the squeeze, producing high spatial harmonics with lower phase velocity. These harmonics are Landau damped even when the mode phase velocity vph is large compared to the thermal velocity v , since the nth harmonic is resonant with a particle bouncing at velocity vb =vph / n . Here we increase the bounce harmonics through applied squeeze potential; but some harmonics are always present in finite length systems. For our centered squeeze geometry, theory shows that only odd harmonics are generated, and predicts the Landau damping rate from vph / n . Experimentally, the squeeze potential increases the wave damping and reduces its frequency. The frequency shift occurs because the squeeze potential reduces the number of particle where the mode velocity is the largest, therefore reducing the mode frequency. We observe an increase in the damping proportional to Vs2,and a frequency reduction proportional to Vs , in quantitative agreement with theory. Wave-coherent laser induced fluorescence allows direct observation of bounce resonances on the particle distribution, here predominantly at vph / 3 . A clear increase of the bounce harmonics is visible on the particle distribution when the squeeze potential is applied. Supported by NSF Grant PHY-1414570, and DOE Grants DE-SC0002451 and DE-SC0008693.
Analysing harmonic motions with an iPhone’s magnetometer
Yavuz, Ahmet; Kağan Temiz, Burak
2016-05-01
In this paper, we propose an experiment for analysing harmonic motion using an iPhone’s (or iPad’s) magnetometer. This experiment consists of the detection of magnetic field variations obtained from an iPhone’s magnetometer sensor. A graph of harmonic motion is directly displayed on the iPhone’s screen using the Sensor Kinetics application. Data from this application was analysed with Eureqa software to establish the equation of the harmonic motion. Analyses show that the use of an iPhone’s magnetometer to analyse harmonic motion is a practical and effective method for small oscillations and frequencies less than 15-20 Hz.
Effect of trapping on transport coherence
International Nuclear Information System (INIS)
Barvik, I.; Herman, P.
1990-10-01
Influence of a trap (sink) on an exciton transfer in molecular aggregates is investigated. Memory functions entering the generalized master equations are calculated. The presence of the sink changes their analytical form. We used the sink in trimer as example to show that for large trapping rate parameters the rest of the system is decoupled from the sink. (author). 8 refs, 2 figs
Electromagnetic cyclotron harmonic waves
International Nuclear Information System (INIS)
Ohnuma, T.; Watanabe, T.; Hamamatsu, K.
1981-09-01
Electromagnetic electron cyclotron harmonic waves just below the electron cyclotron harmonics are investigated numerically and experimentally. Backward waves which are observed to propagate nearly perpendicular to the magnetic field just below the electron cyclotron frequency in a high density magnetoplasma are confirmed to be in accord with the theoretical electromagnetic cyclotron waves. (author)
Sakhel, Asaad R.; Sakhel, Roger R.
2018-02-01
We examine the dynamics of a one-dimensional harmonically trapped Bose-Einstein condensate (BEC), induced by the addition of a dimple trap whose depth oscillates with time. For this purpose, the Lagrangian variational method (LVM) is applied to provide the required analytical equations. The goal is to provide an analytical explanation for the quasiperiodic oscillations of the BEC size at resonance, that is additional to the one given by Adhikari (J Phys B At Mol Opt Phys 36:1109, 2003). It is shown that LVM is able to reproduce instabilities in the dynamics along the same lines outlined by Lellouch et al. (Phys Rev X 7:021015, 2017). Moreover, it is found that at resonance the energy dynamics display ordered oscillations, whereas at off-resonance they tend to be chaotic. Further, by using the Poincare-Lindstedt method to solve the LVM equation of motion, the resulting solution is able to reproduce the quasiperiodic oscillations of the BEC.
Laser-induced blurring of molecular structure information in high harmonic spectroscopy
DEFF Research Database (Denmark)
Risoud, Francois; Leveque, Camille; Labeye, Marie
2017-01-01
High harmonic spectroscopy gives access to molecular structure with Angstrom resolution. Such information is encoded in the destructive interferences occurring between the harmonic emissions from the different parts of the molecule. By solving the time-dependent Schrodinger equation, either....... These findings have important consequences for molecular imaging and orbital tomography using high harmonic spectroscopy....
Canonical harmonic tracking of charged particles in circular accelerators
International Nuclear Information System (INIS)
Kvardakov, V.; Levichev, E.
2006-01-01
Harmonic tracking is a method used to study non-linear particle dynamics in a circular accelerator. The tracking algorithm is based on numerical solution of the Hamilton equations of motion. An essential feature of the method is the approximation of Hamiltonian perturbation terms by a finite number of azimuthal harmonics, which provides an effective tool for optimization of non-linear particle motion. The equations of motion are solved canonically, with the first-order prediction made using the explicit Lie transformation. The major features of harmonic tracking are presented and examples of its application are discussed
Canonical harmonic tracking of charged particles in circular accelerators
Kvardakov, V.; Levichev, E.
2006-03-01
Harmonic tracking is a method used to study non-linear particle dynamics in a circular accelerator. The tracking algorithm is based on numerical solution of the Hamilton equations of motion. An essential feature of the method is the approximation of Hamiltonian perturbation terms by a finite number of azimuthal harmonics, which provides an effective tool for optimization of non-linear particle motion. The equations of motion are solved canonically, with the first-order prediction made using the explicit Lie transformation. The major features of harmonic tracking are presented and examples of its application are discussed.
Linear spin waves in a trapped Bose gas
International Nuclear Information System (INIS)
Nikuni, T.; Williams, J.E.; Clark, C.W.
2002-01-01
An ultracold Bose gas of two-level atoms can be thought of as a spin-1/2 Bose gas. It supports spin-wave collective modes due to the exchange mean field. Such collective spin oscillations have been observed in recent experiments at JILA with 87 Rb atoms confined in a harmonic trap. We present a theory of the spin-wave collective modes based on the moment method for trapped gases. In the collisionless and hydrodynamic limits, we derive analytic expressions for the frequencies and damping rates of modes with dipole and quadrupole symmetry. We find that the frequency for a given mode is given by a temperature-independent function of the peak density n, and falls off as 1/n. We also find that, to a very good approximation, excitations in the radial and axial directions are decoupled. We compare our model to the numerical integration of a one-dimensional version of the kinetic equation and find very good qualitative agreement. The damping rates, however, show the largest deviation for intermediate densities, where one expects Landau damping--which is unaccounted for in our moment approach--to play a significant role
Thermal motion of a holographically trapped SPM-like probe
International Nuclear Information System (INIS)
Simpson, Stephen H; Hanna, Simon
2009-01-01
By holding a complex object in multiple optical traps, it may be harmonically bound with respect to both its position and its orientation. In this way a small probe, or nanotool, can be manipulated in three dimensions and used to measure and apply directed forces, in the manner of a scanning probe microscope. In this paper we evaluate the thermal motion of such a probe held in holographic optical tweezers, by solving the Langevin equation for the general case of a set of spherical vertices linked by cylindrical rods. The concept of a corner frequency, familiar from the case of an optically trapped sphere, is appropriately extended to represent a set of characteristic frequencies given by the eigenvalues of the product of the stiffness matrix and the inverse hydrodynamic resistance matrix of the tool. These eigenvalues may alternatively be interpreted as inverses of a set of characteristic relaxation times for the system. The approach is illustrated by reference to a hypothetical tool consisting of a triangular arrangement of spheres with a lateral probe. The characteristic frequencies and theoretical resolution of the device are derived; variations of these quantities with tool size and orientation and with the optical power distribution, are also considered.
New macroscopic theory of anamalous diffusion induced by the dissipative trapped-ion instability
International Nuclear Information System (INIS)
Wimmel, H.K.
1975-03-01
For an axisymmetric toroidal plasma of the TOKAMAK type a new set of dissipative trapped-fluid equations is established. In addition to E vector x B vector drifts and collisions of the trapped particles, these equations take full account of the effect of Esub(//) (of the trapped ion modes) on free and trapped particles, and of the effect of grad delta 0 (delta 0 = equilibrium fraction of trapped particles). From the new equations the linear-mode properties of the dissipative trapped-ion instability and the anomalous diffusion flux of the trapped particles are derived. (orig.) [de
Quality of potential harmonics expansion method for dilute Bose ...
Indian Academy of Sciences (India)
Abstract. We present and examine an approximate but ab initio many-body approach, viz., potential harmonics expansion method (PHEM), which includes two-body correla- tions for dilute Bose–Einstein condensates. Comparing the total ground state energy for three trapped interacting bosons calculated in PHEM with the ...
Energy Technology Data Exchange (ETDEWEB)
Schneidmiller, E.A.; Yurkov, M.V.
2012-05-15
Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed) might be a cheap and efficient way of extension of wavelength ranges of existing and planned X-ray FEL facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of X-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust than usually thought, and can be widely used in the existing or planned X-ray FEL facilities. In particular, LCLS after a minor modification can lase to saturation at the 3rd harmonic up to the photon energy of 25-30 keV providing multi-gigawatt power level and narrow bandwidth. As for the European XFEL, harmonic lasing would allow to extend operating range (ultimately up to 100 keV), to reduce FEL bandwidth and to increase brilliance, to enable two-color operation for pump-probe experiments, and to provide more flexible operation at different electron energies. Similar improvements can be realized in other X-ray FEL facilities with gap-tunable undulators like FLASH II, SACLA, LCLS II, etc. Harmonic lasing can be an attractive option for compact X-ray FELs (driven by electron beams with a relatively low energy), allowing the use of the standard undulator technology instead of small-gap in-vacuum devices. Finally, in this paper we discover that in a part of the
Degenerate Fermi gas in a combined harmonic-lattice potential
International Nuclear Information System (INIS)
Blakie, P. B.; Bezett, A.; Buonsante, P.
2007-01-01
In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used in current experiments with quantum degenerate gases. We compare this analytic density of states to numerical solutions and demonstrate its validity regime. Our work explicitly considers the role of higher bands and when they are important in quantitative analysis of this system. Applying our density of states to a degenerate Fermi gas, we consider how adiabatic loading from a harmonic trap into the combined harmonic-lattice potential affects the degeneracy temperature. Our results suggest that occupation of excited bands during loading should lead to more favorable conditions for realizing degenerate Fermi gases in optical lattices
International Nuclear Information System (INIS)
Fei Xiang; Snow, W.M.
1999-01-01
Harmonic potentials can be produced in cylindrical ion traps by means of dynamic orthogonalized anharmonicity compensation with use of two (or multiple) sets of compensation electrodes. One special example is for traps with multiple identical electrodes which are not only easy to construct and allow access to the center region of the trap for particle loading and releasing, laser beams, and microwaves, but also flexible in forming harmonic potential wells in many locations. The nested trap configuration and the side-by-side trap configuration are readily available in this special scheme. Analytical solutions for cylindrical traps with multiple sets of compensation potentials are presented. This work will be useful for studies involving Penning trap diagnostics, atomic and molecular interactions (including the production of antihydrogen atoms), accurate mass measurements of exotic particles, and precision measurements of the spin precession frequencies of trapped particles
Fei Xiang
1999-01-01
Harmonic potentials can be produced in cylindrical ion traps by means of dynamic orthogonalized anharmonicity compensation with use of two (or multiple) sets of compensation electrodes. One special example is for traps with multiple identical electrodes which are not only easy to construct and allow access to the center region of the trap for particle loading and releasing, laser beams, and microwaves, but also flexible in forming harmonic potential wells in many locations. The nested trap configuration and the side-by-side trap configuration are readily available in this special scheme. Analytical solutions for cylindrical traps with multiple sets of compensation potentials are presented. This work will be useful for studies involving Penning trap diagnostics, atomic and molecular interactions (including the production of antihydrogen atoms), accurate mass measurements of exotic particles, and precision measurements of the spin precession frequencies of trapped particles.
International Nuclear Information System (INIS)
Lin, Qui-xun; Van Wechel, T.D.
1987-01-01
A single gap harmonic buncher has been constructed as a pretandem buncher. Over 85% of a proton dc beam has been bunched into pulses. The width (fwhm) of the pulses is 0.7 ns. The buncher is based on that built at Argonne. Changes were made to the buncher's configuration so that the buncher could be tuned to the desired four harmonic frequencies. A method of calibrating and setting the relative phases and amplitudes of the four harmonic frequencies has been used to obtain an optimum sawtooth-like bunching waveform
Harmonic supergraphs. Green functions
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Gievetsky, V.; Sokatchev, E.
1985-01-01
The quantization procedure in the harmonic superspace approach is worked out. Harmonic distributions are introduced and are used to construct the analytic superspace delta-functions and the Green functions for the hypermultiplet and the N=2 Yang-Mills superfields. The gauge fixing is described and the relevant Faddeev-Popov ghosts are defined. The corresponding BRST transformations are found. The harmonic superspace quantization of the N=2 gauge theory turns out to be rather simple and has many parallels with that for the standard (N=0) Yang-Mills theory. In particular, no ghosts-forghosts are needed
Harmonic analysis from Fourier to wavelets
Pereyra, Maria Cristina
2012-01-01
In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...
Faddeev wave function decomposition using bipolar harmonics
International Nuclear Information System (INIS)
Friar, J.L.; Tomusiak, E.L.; Gibson, B.F.; Payne, G.L.
1981-01-01
The standard partial wave (channel) representation for the Faddeev solution to the Schroedinger equation for the ground state of 3 nucleons is written in terms of functions which couple the interacting pair and spectator angular momenta to give S, P, and D waves. For each such coupling there are three terms, one for each of the three cyclic permutations of the nucleon coordinates. A series of spherical harmonic identities is developed which allows writing the Faddeev solution in terms of a basis set of 5 bipolar harmonics: 1 for S waves; 1 for P waves; and 3 for D waves. The choice of a D-wave basis is largely arbitrary, and specific choices correspond to the decomposition schemes of Derrick and Blatt, Sachs, Gibson and Schiff, and Bolsterli and Jezak. The bipolar harmonic form greatly simplifies applications which utilize the wave function, and we specifically discuss the isoscalar charge (or mass) density and the 3 He Coulomb energy
Single and dual fiber nano-tip optical tweezers: trapping and analysis
Decombe , Jean-Baptiste; Huant , Serge; Fick , Jochen
2013-01-01
International audience; An original optical tweezers using one or two chemically etched fiber nano-tips is developed. We demonstrate optical trapping of 1 micrometer polystyrene spheres at optical powers down to 2 mW. Harmonic trap potentials were found in the case of dual fiber tweezers by analyzing the trapped particle position fluctuations. The trap stiffness was deduced using three different models. Consistent values of up to 1 fN/nm were found. The stiffness linearly decreases with decre...
Superstrings and harmonic superspace
International Nuclear Information System (INIS)
Kallosh, R.E.; AN SSSR, Moscow. Fizicheskij Inst.)
1987-01-01
The paper on superstrings and harmonic superspace is a contribution to the book dedicated to E.S. Fradkin on his sixtieth birthday. The purpose of the paper is to propose a description of N = 2,3 superspace which could be used for the investigation of the effective d = 10 harmonic superspace corresponding to the heterotic superstring. A description is given of the structure of semi-simple Lie algebras in the Cartan-Weyl basis, as well as the general properties of the even, compact part of harmonic superspace. The main properties of the four-dimensional N = 2 SYM theory are discussed, along with the N = 3, d = 4 super Yang-Mills theory. Finally the relation between the harmonic superspace and the heterotic E 8 x E 8 superstring is examined. (U.K.)
Harmonic excitations in quasicrystals
International Nuclear Information System (INIS)
Luck, J.M.
1986-03-01
The harmonic excitations (phonons) of quasicrystals are studied in a simple one-dimensional model. The spectrum is a Cantor set, which exhibits selfsimilarity properties. The eigenstates are generically ''critical'', i.e. neither extended nor localized
Multidimensional high harmonic spectroscopy
International Nuclear Information System (INIS)
Bruner, Barry D; Soifer, Hadas; Shafir, Dror; Dudovich, Nirit; Serbinenko, Valeria; Smirnova, Olga
2015-01-01
High harmonic generation (HHG) has opened up a new frontier in ultrafast science where attosecond time resolution and Angstrom spatial resolution are accessible in a single measurement. However, reconstructing the dynamics under study is limited by the multiple degrees of freedom involved in strong field interactions. In this paper we describe a new class of measurement schemes for resolving attosecond dynamics, integrating perturbative nonlinear optics with strong-field physics. These approaches serve as a basis for multidimensional high harmonic spectroscopy. Specifically, we show that multidimensional high harmonic spectroscopy can measure tunnel ionization dynamics with high precision, and resolves the interference between multiple ionization channels. In addition, we show how multidimensional HHG can function as a type of lock-in amplifier measurement. Similar to multi-dimensional approaches in nonlinear optical spectroscopy that have resolved correlated femtosecond dynamics, multi-dimensional high harmonic spectroscopy reveals the underlying complex dynamics behind attosecond scale phenomena. (paper)
Quasilinear ion distribution function during first harmonic ion cyclotron heating
International Nuclear Information System (INIS)
Brambilla, M.
1993-12-01
The quasilinear modification of the ion distribution function during first harmonic ion cyclotron (FHIC) heating is investigated both with a simple already well established analytic one-dimensional approach, and with a new two dimensional steady state solver of the quasilinear kinetic equation, SSFPQL. By accepting to disregard the effects of ion trapping in banana orbits, but including finite Larmor radius effects, the latter code has been made much faster than full surface-averaged codes; yet it can provide most of the relevant information on the suprathermal ion tail produced by this heating method. With SSFPQL we confirm that the one-dimensional model gives fair approximations for global properties of the distribution function, such as the average energy content of the tail and the fusion reactivity. On the other hand the tail is found to be very anisotropic, the increase of the parallel effective temperature being a small fraction of the total energy increase. Information on the anisotropy is essential to study the feedback of the fast ion tail on wave propagation and absorption, which is quite sensitive to the distribution of parallel velocities. The insight gained in the derivation and discussion of this model can be used to build a selfconsistent description of this heating scenario, whose implementation requires only a reasonable numerical effort. (orig.)
Pairing fluctuations in trapped Fermi gases
International Nuclear Information System (INIS)
Viverit, Luciano; Bruun, Georg M.; Minguzzi, Anna; Fazio, Rosario
2004-01-01
We examine the contribution of pairing fluctuations to the superfluid order parameter for harmonically trapped atomic Fermi gases in the BCS regime. In the limit of small systems we consider, both analytically and numerically, their space and temperature dependence. We predict a parity effect, i.e., that pairing fluctuations show a maximum or a minimum at the center of the trap, depending on the value of the last occupied shell being even or odd. We propose to detect pairing fluctuations by measuring the density-density correlation function after a ballistic expansion of the gas
Nonexistence theorems for Yang-Mills fields and harmonic maps in the Schwarzschild spacetime
International Nuclear Information System (INIS)
Hu Hesheng
1987-01-01
The nonexistence of static solutions to pure Yang-Mills equations and nonconstant harmonic maps defined on the Schwarzschild spacetime outside the black hole (r>2M) is considered. Nonexistence theorems for pure Yang-Mills equations and harmonic maps in the region r≥5M and r≥3M are obtained, respectively. (orig.)
Exact solution of a quantum forced time-dependent harmonic oscillator
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
Recent Developments in Real and Harmonic Analysis In Honor of Carlos Segovia
Cabrelli, Carlos A
2008-01-01
Featuring a collection of invited chapters dedicated to Carlos Segovia, this volume examines the developments in real and harmonic analysis. It includes topics such as: Vector-valued singular integral equations; Harmonic analysis related to Hermite expansions; Gas flow in porous media; and, Global well-posedness of the KPI Equation
A simplified spherical harmonic method for coupled electron-photon transport calculations
International Nuclear Information System (INIS)
Josef, J.A.
1996-12-01
In this thesis we have developed a simplified spherical harmonic method (SP N method) and associated efficient solution techniques for 2-D multigroup electron-photon transport calculations. The SP N method has never before been applied to charged-particle transport. We have performed a first time Fourier analysis of the source iteration scheme and the P 1 diffusion synthetic acceleration (DSA) scheme applied to the 2-D SP N equations. Our theoretical analyses indicate that the source iteration and P 1 DSA schemes are as effective for the 2-D SP N equations as for the 1-D S N equations. Previous analyses have indicated that the P 1 DSA scheme is unstable (with sufficiently forward-peaked scattering and sufficiently small absorption) for the 2-D S N equations, yet is very effective for the 1-D S N equations. In addition, we have applied an angular multigrid acceleration scheme, and computationally demonstrated that it performs as well for the 2-D SP N equations as for the 1-D S N equations. It has previously been shown for 1-D S N calculations that this scheme is much more effective than the DSA scheme when scattering is highly forward-peaked. We have investigated the applicability of the SP N approximation to two different physical classes of problems: satellite electronics shielding from geomagnetically trapped electrons, and electron beam problems. In the space shielding study, the SP N method produced solutions that are accurate within 10% of the benchmark Monte Carlo solutions, and often orders of magnitude faster than Monte Carlo. We have successfully modeled quasi-void problems and have obtained excellent agreement with Monte Carlo. We have observed that the SP N method appears to be too diffusive an approximation for beam problems. This result, however, is in agreement with theoretical expectations
Directory of Open Access Journals (Sweden)
João Caraça
2017-05-01
Full Text Available The promise of making society progress through the direct applications of science was finally fulfilled in the mid-20th century. Science progressed immensely, propelled by the effects of the two world wars. The first science-based technologies saw the daylight during the 1940s and their transformative power was such that neither the military, nor subsequently the markets, allowed science to return intact to its curiosity-driven nest. Technoscience was born then and (being progressively pulled away from curiosity-driven science was able to grow enormously, erecting a formidable structure of networks of institutions that impacted decisively on the economy. It is a paradox, or maybe a trap, that the fulfillment of science’s solemn promise of ‘transforming nature’ means seeing ourselves and our Western societies entangled in crises after crises with no clear outcome in view. A redistribution of geopolitical power is under way, along with the deployment of information and communication technologies, forcing dominant structures to oscillate, as knowledge about organization and methods, marketing, design, and software begins to challenge the role of technoscience as the main vector of economic growth and wealth accumulation. What ought to be done?
Density excitations of a harmonically trapped ideal gas
Indian Academy of Sciences (India)
†Worked as a summer student fellow of the Indian Academy of Sciences for six weeks. 83 ... Motivation for calculating the dynamical structure factor is its ...... [9] J P Hansen and I R McDonald, Theory of simple liquids (Academic Press, London.
International Nuclear Information System (INIS)
Niedermayr, M.
2015-01-01
Microfabricated surface traps are a promising architecture to realize a scalable quantum computer based on trapped ions. In principle, hundreds or thousands of surface traps can be located on a single substrate in order to provide large arrays of interacting ions. To this end, trap designs and fabrication methods are required that provide scalable, stable and reproducible ion traps. This work presents a novel surface-trap design developed for cryogenic applications. Intrinsic silicon is used as the substrate material of the traps. The well-developed microfabrication and structuring methods of silicon are utilized to create simple and reproducible traps. The traps were tested and characterized in a cryogenic setup. Ions could be trapped and their life time and motional heating were investigated. Long ion lifetimes of several hours were observed and the measured heating rates were reproducibly low at around 1 phonon per second at a trap frequency of 1 MHz. (author) [de
Optical klystron and harmonic generation free electron laser
Directory of Open Access Journals (Sweden)
Qika Jia
2005-06-01
Full Text Available The optical field evolution of an optical klystron free electron laser is analytically described for both low gain and high gain cases. The harmonic optical klystron (HOK in which the second undulator is resonant on the higher harmonic of the first undulator is analyzed as a harmonic amplifier. The optical field evolution equation of the HOK is derived analytically for both the CHG mode (coherent harmonic generation, the quadratic gain regime and the HGHG mode (high gain harmonic generation, the exponential gain regime, the effects of energy spread, energy modulation, and dispersion in the whole process are taken into account. The linear theory is given and discussed for the HGHG mode. The analytical formula is given for the CHG mode.
Generalized Harmonic Functions and the Dewetting of Thin Films
International Nuclear Information System (INIS)
Auchmuty, Giles; Kloucek, Petr
2007-01-01
This paper describes the solvability of Dirichlet problems for Laplace's equation when the boundary data is not smooth enough for the existence of a weak solution in H 1 Ω. Scales of spaces of harmonic functions and of boundary traces are defined and the solutions are characterized as limits of classical harmonic functions in special norms. The generalized harmonic functions, and their norms, are defined using series expansions involving harmonic Steklov eigenfunctions on the domain. It is shown that the usual trace operator has a continuous extension to an isometric isomorphism of specific spaces. This provides a characterization of the generalized solutions of harmonic Dirichlet problems. Numerical simulations of a model problem are described. This problem is related to the dewetting of thin films and the associated phenomenology is described
Harmonization versus Mutual Recognition
DEFF Research Database (Denmark)
Jørgensen, Jan Guldager; Schröder, Philipp
The present paper examines trade liberalization driven by the coordination of product standards. For oligopolistic firms situated in separate markets that are initially sheltered by national standards, mutual recognition of standards implies entry and reduced profits at home paired with the oppor......The present paper examines trade liberalization driven by the coordination of product standards. For oligopolistic firms situated in separate markets that are initially sheltered by national standards, mutual recognition of standards implies entry and reduced profits at home paired...... countries and three firms, where firms first lobby for the policy coordination regime (harmonization versus mutual recognition), and subsequently, in case of harmonization, the global standard is auctioned among the firms. We discuss welfare effects and conclude with policy implications. In particular......, harmonized standards may fail to harvest the full pro-competitive effects from trade liberalization compared to mutual recognition; moreover, the issue is most pronounced in markets featuring price competition....
Second harmonic generation imaging
2013-01-01
Second-harmonic generation (SHG) microscopy has shown great promise for imaging live cells and tissues, with applications in basic science, medical research, and tissue engineering. Second Harmonic Generation Imaging offers a complete guide to this optical modality, from basic principles, instrumentation, methods, and image analysis to biomedical applications. The book features contributions by experts in second-harmonic imaging, including many pioneering researchers in the field. Written for researchers at all levels, it takes an in-depth look at the current state of the art and possibilities of SHG microscopy. Organized into three sections, the book: Provides an introduction to the physics of the process, step-by-step instructions on how to build an SHG microscope, and comparisons with related imaging techniques Gives an overview of the capabilities of SHG microscopy for imaging tissues and cells—including cell membranes, muscle, collagen in tissues, and microtubules in live cells—by summarizing experi...
Bennett, Charles L.
2016-03-22
A reciprocating-piston uniflow engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. When released, the inlet valve head undergoes a single oscillation past the equilibrium position to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. In other embodiments, the harmonic oscillator arrangement of the inlet valve enables the uniflow engine to be reversibly operated as a uniflow compressor.
International Nuclear Information System (INIS)
Au, R.; Fowler, M.; Hanawa, H.; Riedel, J.; Qua, Z.G.
1984-01-01
In early 1983 it was decided to mount coils on arms separated by 120 degrees and buck them out so that the third harmonic dphi/dt component would be cancelled and thus the first and second field harmonics could be very accurately measured. The original intention was to do as others had done, namely, use fast ADC's to read the voltages, and computer process the result to get the Fourier components. However, because of the 100 to 1 dynamic range of the fast ADC's and the likelihood that noise would be a problem, the authors decided to do things differently. Using a fast Fourier transform analyzer was considered, but this instrument is very expensive, so they decided to use a completely electronic analog approach: The authors decided to use active bandpass filters to render the harmonic components
Nonlinearly driven harmonics of Alfvén modes
Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.
2014-01-01
In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.
Nonlinearly driven harmonics of Alfvén modes
Energy Technology Data Exchange (ETDEWEB)
Zhang, B., E-mail: bozhang@austin.utexas.edu; Breizman, B. N.; Zheng, L. J.; Berk, H. L. [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
2014-01-15
In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.
Three-dimensional analysis of harmonic generation in high-gain free-electron lasers
International Nuclear Information System (INIS)
Huang, Zhirong; Kim, Kwang-Je
2000-01-01
In a high-gain free-electron laser (FEL) employing a planar undulator, strong bunching at the fundamental wavelength can drive substantial bunching and power levels at the harmonic frequencies. In this paper we investigate the three-dimensional evolution of harmonic radiation based on the coupled Maxwell-Klimontovich equations that take into account nonlinear harmonic interactions. Each harmonic field is a sum of a linear amplification term and a term driven by nonlinear harmonic interactions. After a certain stage of exponential growth, the dominant nonlinear term is determined by interactions of the lower nonlinear harmonics and the fundamental radiation. As a result, the gain length, transverse profile, and temporal structure of the first few harmonics are eventually governed by those of the fundamental. Transversely coherent third-harmonic radiation power is found to approach 1% of the fundamental power level for current high-gain FEL projects
Harmonic arbitrary waveform generator
Roberts, Brock Franklin
2017-11-28
High frequency arbitrary waveforms have applications in radar, communications, medical imaging, therapy, electronic warfare, and charged particle acceleration and control. State of the art arbitrary waveform generators are limited in the frequency they can operate by the speed of the Digital to Analog converters that directly create their arbitrary waveforms. The architecture of the Harmonic Arbitrary Waveform Generator allows the phase and amplitude of the high frequency content of waveforms to be controlled without taxing the Digital to Analog converters that control them. The Harmonic Arbitrary Waveform Generator converts a high frequency input, into a precision, adjustable, high frequency arbitrary waveform.
Second-harmonic generation of practical Bessel beams
Huang, Jin H.; Ding, Desheng; Hsu, Yin-Sung
2009-11-01
A fast Gaussian expansion approach is used to investigate fundamental and second-harmonic generation in practical Bessel beams of finite aperture. The analysis is based on the integral solutions of the KZK equation under the quasilinear approximation. The influence of the medium's attenuation on the beam profile is considered. Analysis results show that the absorption parameter has a significant effect on the far-field beam profile of the second harmonic. Under certain circumstances, the second harmonic of a practical Bessel beam still has the main properties of an ideal Bessel beam of infinite aperture when it propagates within its depth of field.
Higher-order harmonics of general limited diffraction Bessel beams
International Nuclear Information System (INIS)
Ding De-Sheng; Huang Jin-Huang
2016-01-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m -th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. (special topic)
Higher-order harmonics of general limited diffraction Bessel beams
Ding, De-Sheng; Huang, Jin-Huang
2016-12-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).
Incomplete Thermalization from Trap-Induced Integrability Breaking: Lessons from Classical Hard Rods
Cao, Xiangyu; Bulchandani, Vir B.; Moore, Joel E.
2018-04-01
We study a one-dimensional gas of hard rods trapped in a harmonic potential, which breaks integrability of the hard-rod interaction in a nonuniform way. We explore the consequences of such broken integrability for the dynamics of a large number of particles and find three distinct regimes: initial, chaotic, and stationary. The initial regime is captured by an evolution equation for the phase-space distribution function. For any finite number of particles, this hydrodynamics breaks down and the dynamics becomes chaotic after a characteristic timescale determined by the interparticle distance and scattering length. The system fails to thermalize over the timescale studied (1 04 natural units), but the time-averaged ensemble is a stationary state of the hydrodynamic evolution. We close by discussing logical extensions of the results to similar systems of quantum particles.
Ansatz from nonlinear optics applied to trapped Bose-Einstein condensates
International Nuclear Information System (INIS)
Keceli, Murat; Ilday, F. Oe.; Oktel, M. Oe.
2007-01-01
A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser (a laser with self-similar propagation of ultrashort pulses), is used as a variational wave function to solve the Gross-Pitaevskii equation for a wide range of interaction parameters. The variational form interpolates between the noninteracting density profile and the strongly interacting Thomas-Fermi profile smoothly. The simple form of the ansatz is modified for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground-state density profile and energy are in very good agreement with both the analytical solutions in the limiting cases of interaction and the numerical solutions in the intermediate regime
Harmonic and power balance tools for tapping-mode atomic force microscope
International Nuclear Information System (INIS)
Sebastian, A.; Salapaka, M. V.; Chen, D. J.; Cleveland, J. P.
2001-01-01
The atomic force microscope (AFM) is a powerful tool for investigating surfaces at atomic scales. Harmonic balance and power balance techniques are introduced to analyze the tapping-mode dynamics of the atomic force microscope. The harmonic balance perspective explains observations hitherto unexplained in the AFM literature. A nonconservative model for the cantilever - sample interaction is developed. The energy dissipation in the sample is studied and the resulting power balance equations combined with the harmonic balance equations are used to estimate the model parameters. Experimental results confirm that the harmonic and power balance tools can be used effectively to predict the behavior of the tapping cantilever. [copyright] 2001 American Institute of Physics
Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional spaces
International Nuclear Information System (INIS)
Oyewumi, K.A.; Bangudu, E.A.
2003-01-01
Some aspects of the N-dimensional isotropic harmonic plus inverse quadratic potential were discussed. The hyperradial equation for isotropic harmonic oscillator plus inverse quadratic potential is solved by transformation into the confluent hypergeometric equation to obtain the normalized hyperradial solution. Together with the hyperangular solutions (hyperspherical harmonics), these form the complete energy eigenfunctions of the N-dimensional isotropic harmonic oscillator plus inverse quadratic potential and the energy eigenvalues are also obtained. These are dimensionally dependent. The dependence of radial solution on the dimensions or potential strength and the degeneracy of the energy levels are discussed. (author)
Comparing Harmonic Similarity Measures
de Haas, W.B.; Robine, M.; Hanna, P.; Veltkamp, R.C.; Wiering, F.
2010-01-01
We present an overview of the most recent developments in polyphonic music retrieval and an experiment in which we compare two harmonic similarity measures. In contrast to earlier work, in this paper we specifically focus on the symbolic chord description as the primary musical representation and
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm; Jensen, Jesper Rindom
2017-01-01
-robust to noise, or very computationally inten- sive. In this paper, we propose a fast algorithm for the harmonic chirp summation method which has been demonstrated in the liter- ature to be accurate and robust to noise. The proposed algorithm is orders of magnitudes faster than previous algorithms which is also...
Pruitt, Kathryn Ringler
2012-01-01
This dissertation proposes a model of word stress in a derivational version of Optimality Theory (OT) called Harmonic Serialism (HS; Prince and Smolensky 1993/2004, McCarthy 2000, 2006, 2010a). In this model, the metrical structure of a word is derived through a series of optimizations in which the "best" metrical foot is chosen…
Gluck, P.; Krakower, Zeev
2010-01-01
We present a unit comprising theory, simulation and experiment for a body oscillating on a vertical spring, in which the simultaneous use of a force probe and an ultrasonic range finder enables one to explore quantitatively and understand many aspects of simple and damped harmonic motions. (Contains 14 figures.)
Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System
Directory of Open Access Journals (Sweden)
Salim Medjber
2016-01-01
Full Text Available The Schrödinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential are investigated. Because of the time-dependence of parameters, we cannot solve the Schrödinger solutions relying only on the conventional method of separation of variables. To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrödinger equation for the system. In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. Through this procedure, we derived exact Schrödinger solutions (wave functions of the system. It is confirmed that the wave functions are represented in terms of time-dependent radial functions, spherical harmonics, and general time-varying global phases. Such wave functions are useful for studying various quantum properties of the system. As an example, the uncertainty relations for position and momentum are derived by taking advantage of the wave functions.
Nonlinear von Neumann equations for quantum dissipative systems
International Nuclear Information System (INIS)
Messer, J.; Baumgartner, B.
1978-01-01
For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)
Nonlinear von Neumann equations for quantum dissipative systems
International Nuclear Information System (INIS)
Messer, J.; Baumgartner, B.
For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)
Young children's harmonic perception.
Costa-Giomi, Eugenia
2003-11-01
Harmony and tonality are two of the most difficult elements for young children to perceive and manipulate and are seldom taught in the schools until the end of early childhood. Children's gradual harmonic and tonal development has been attributed to their cumulative exposure to Western tonal music and their increasing experiential knowledge of its rules and principles. Two questions that are relevant to this problem are: (1) Can focused and systematic teaching accelerate the learning of the harmonic/tonal principles that seem to occur in an implicit way throughout childhood? (2) Are there cognitive constraints that make it difficult for young children to perceive and/or manipulate certain harmonic and tonal principles? A series of studies specifically addressed the first question and suggested some possible answers to the second one. Results showed that harmonic instruction has limited effects on children's perception of harmony and indicated that the drastic improvement in the perception of implied harmony noted approximately at age 9 is due to development rather than instruction. I propose that young children's difficulty in perceiving implied harmony stems from their attention behaviors. Older children have less memory constraints and more strategies to direct their attention to the relevant cues of the stimulus. Younger children focus their attention on the melody, if present in the stimulus, and specifically on its concrete elements such as rhythm, pitch, and contour rather than its abstract elements such as harmony and key. The inference of the abstract harmonic organization of a melody required in the perception of implied harmony is thus an elusive task for the young child.
Symmetries in physics and harmonics
International Nuclear Information System (INIS)
Kolk, D.
2006-01-01
In this book the symmetries of elementary particles are described in relation to the rules of harmonics in music. The selection rules are described in connections with harmonic intervals. Also symmetry breaking is considered in this framework. (HSI)
International Nuclear Information System (INIS)
Schunck, N.; Dobaczewski, J.
2017-01-01
Here, we describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree–Fock or Skyrme Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton–neutron mixing in the particle–hole channel for Skyrme functionals, (ii) the Gogny force in both particle–hole and particle–particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.
International Nuclear Information System (INIS)
Schunck, Nicolas F.; McDonnell, J.; Sheikh, J.A.; Staszczak, A.; Stoitsov, Mario; Dobaczewski, J.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.
Harmonic Patterns in Forex Trading
Nemček, Sebastian
2013-01-01
This diploma thesis is committed to examination of validity of Harmonic Patterns in Forex trading. Scott Carney described existing and introduced new Harmonic Patterns in 1999 in his book Harmonic Trader. These patterns use the Fibonacci principle to analyze price action and to provide both bullish and bearish trading signals. The goal of this thesis is to find out whether harmonic trading strategy on selected pairs is profitable in FX market, which patterns are the most profitable and what i...
Atto second high harmonic sources
International Nuclear Information System (INIS)
Nam, Chang Hee
2008-01-01
High harmonic generation is a powerful method to produce attosecond pulses. The high harmonics, emitted from atoms driven by intense femtosecond laser pulses, can from an attosecond pulse train with equally spaced harmonic spectrum or an isolated single attosecond pulse with broad continuum spectrum. Using high power femtosecond laser technology developed at CXRC, we have investigated the spectral and temporal characteristics of high harmonics obtained from gaseous atoms. The spectral structure of harmonics could be manipulated by controlling laser chirp, and continuous tuning of harmonic wavelengths was achieved. For rigorous temporal characterization of attosecond harmonic pulses a cross correlation technique was applied to the photoionization process by harmonic and IR femtosecond pulses and achieved the complete temporal reconstruction of attosecond pulse trains, revealing the detailed temporal structure of the attosecond chirp by material dispersion. The duration of attosecond high harmonic pulses is usually much longer than that of transform limited pulses due to the inherent chirp originating from the harmonic generation process. The attosecond chirp compensation in the harmonic generation medium itself was demonstrated, thereby realizing the generation of near transform limited attosecond pulses. The interference of attosecond electron wave packets, generated from an atom by attosecond harmonic pulses, will be also presented
Second harmonic inversion for ultrasound contrast harmonic imaging
Energy Technology Data Exchange (ETDEWEB)
Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico [THORAXCENTER, Department of Biomedical Engineering Ee2302, Erasmus MC, Rotterdam (Netherlands); Cachard, Christian; Basset, Olivier, E-mail: mirza.pasovic@creatis.insa-lyon.fr [CREATIS-LRMN, Universite de Lyon, INSA-Lyon, Universite Lyon 1, Inserm U630, CNRS UMR 5220 (France)
2011-06-07
Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f{sub 0} and the same amplitude P{sub 0} to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.
Second harmonic inversion for ultrasound contrast harmonic imaging
International Nuclear Information System (INIS)
Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico; Cachard, Christian; Basset, Olivier
2011-01-01
Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f 0 and the same amplitude P 0 to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.
DEFF Research Database (Denmark)
Gambalemoke, Mbalitini; Mukinzi, Itoka; Amundala, Drazo
2008-01-01
We investigated the efficiency of four trap types (pitfall, Sherman LFA, Victor snap and Museum Special snap traps) to capture shrews. This experiment was conducted in five inter-riverine forest blocks in the region of Kisangani. The total trapping effort was 6,300, 9,240, 5,280 and 5,460 trap......, our results indicate that pitfall traps are the most efficient for capturing shrews: not only do they have a higher efficiency (yield), but the taxonomic diversity of shrews is also higher when pitfall traps are used....
Coulomb crystallites from harmonically confined charged bosons in two dimensions
International Nuclear Information System (INIS)
Mese, A I; Okan, S E; Capuzzi, P; Akdeniz, Z; Tosi, M P
2008-01-01
We exploit rotational-symmetry breaking in the one-body density to examine the formation of structures in systems of N strongly coupled charged bosons with logarithmic repulsions inside isotropic two-dimensional harmonic traps, with N in the range from 2 to 7. The results serve as a map for ordered arrangements of vortices in a trapped Bose-Einstein condensate. Two types of N-body wavefunctions are assumed: (i) a permanent |ψ WM > of N identical Gaussian orbitals centred at variationally determined sites, and (ii) a permanent |ψ SM > of N orthogonal orbitals built from harmonic-oscillator energy eigenstates. With increasing coupling strength, the bosons in the |ψ WM > orbitals localize into polygonal-ringlike crystalline patterns ('Wigner molecules'), whereas the wavefunctions |ψ SM / describe low energy excited states containing delocalized bosons as in supersolid crystallites ('supermolecules'). For N = 2 at strong coupling both states describe a Wigner dimer
Influence of modulation method on using LC-traps with single-phase voltage source converters
DEFF Research Database (Denmark)
Wang, Xiongfei; Min, Huang; Bai, Haofeng
2015-01-01
The switching-frequency LC-trap filter has recently been employed with high-order passive filters for Voltage Source Inverters (VSIs). This paper investigates the influence of modulation method on using the LC-traps with single-phase VSIs. Two-level (bipolar) and three-level (unipolar) modulations...... that include phase distortion and alternative phase opposition distortion methods are analyzed. Harmonic filtering performances of four LC-trap-based filters with different locations of LC-traps are compared. It is shown that the use of parallel-LC-traps in series with filter inductors, either grid...... or converter side, has a worse harmonic filtering performance than using series-LC-trap in the shunt branch. Simulations and experimental results are presented for verifications....
Nonequilibrium Spin Dynamics in a Trapped Fermi Gas with Effective Spin-Orbit Interactions
International Nuclear Information System (INIS)
Stanescu, Tudor D.; Zhang Chuanwei; Galitski, Victor
2007-01-01
We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and nontrivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive nonequilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters
Wolff, Thomas H; Shubin, Carol
2003-01-01
This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for fu...
The Harmonization of Accounting
Directory of Open Access Journals (Sweden)
Hajnal Noémi
2017-11-01
Full Text Available The development and configuration of the regulatory framework of the accounting systems in Romania and Hungary took place in different ways. Among the reasons for the diversities in these countries’ accounting systems, the following can be certainly mentioned: different purposes of taxation, legal structure, the accountancy’s connection with the corporate law and family law, diversification on corporate financing policy, and cultural heterogeneity. Both countries quickly caught up with the international accounting harmonization standards. The adaptation of the international accounting standards has many advantages and disadvantages; these have been discussed in several previous researches. This paper aims at comparing the Romanian and Hungarian states’ accounting regulations from the early 1990s, which were implemented in order to harmonize the states’ accountancy regulations with the international standards, and their impact on the economy, based on secondary analysis.
Electrostatic ion trap and Fourier transform measurements for high-resolution mass spectrometry
International Nuclear Information System (INIS)
Bhushan, K. G.; Gadkari, S. C.; Yakhmi, J. V.; Sahni, V. C.
2007-01-01
We report on the development of an electrostatic ion trap for high-resolution mass spectrometry. The trap works on purely electrostatic fields and hence trapping and storing of ions is not mass restrictive, unlike other techniques based on Penning, Paul, or radio frequency quadrupole ion traps. It allows simultaneous trapping and studying of multiple mass species over a large mass range. Mass spectra were recorded in ''dispersive'' and ''self-bunching'' modes of ions. Storage lifetimes of about 100 ms and mass resolving power of about 20 000 could be achieved from the fifth harmonic Fourier transform spectrum of Xe ions recorded in the self-bunching mode
Simulation of Second Harmonic Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2010-01-01
A non-linear ultrasound imaging simulation software should be capable of simulating the non-linear fields for any kind of transducer, focusing, apodization, and attenuation. At present, a major issue is the overlong simulation time of the non-linear software. An Angular Spectrum Approach (ASA......) using a quasi-linear approximation for solving the Westervelt equation can simulate the second harmonic pressure at any distance. Therefore, it shortens the execution time compared with the operator splitting method. The purpose of this paper is to implement the monochromatic solution for the second...... harmonic component based on ASA and Field II, and to compare with results from the simulation program Abersim. A linear array transducer with a center frequency of 4 MHz and 64 active elements is used as the transmitting source. The initial plane is 5 mm away from the transducer surface...
[Harmonization of TSH Measurements.
Takeoka, Keiko; Hidaka, Yoh; Hishinuma, Akira; Ikeda, Katsuyoshi; Okubo, Shigeo; Tsuchiya, Tatsuyuki; Hashiguchi, Teruto; Furuta, Koh; Hotta, Taeko; Matsushita, Kazuyuki; Matsumoto, Hiroyuki; Murakami, Masami; Maekawa, Masato
2016-05-01
The measured concentration of thyroid stimulating hormone (TSH) differs depending on the reagents used. Harmonization of TSH is crucial because the decision limits are described in current clinical practice guide- lines as absolute values, e.g. 2.5 mIU/L in early pregnancy. In this study, we tried to harmonize the report- ed concentrations of TSH using the all-procedure trimmed mean. TSH was measured in 146 serum samples, with values ranging from 0.01 to 18.8 mIU/L, using 4 immunoassays. The concentration of TSH was highest with E test TOSOH and lowest with LUMIPULSE. The concentrations with each reagent were recalculated with the following formulas: E test TOSOH 0.855x-0.014; ECLusys 0.993x+0.079; ARCHITECT 1.041x- 0.010; and LUMIPULSE 1.096x-0.015. Recalculation eliminated the between-assay discrepancy. These formulas may be used until harmonization of TSH is achieved by the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC).
A Series-LC-Filtered Active Trap Filter for High Power Voltage Source Inverter
DEFF Research Database (Denmark)
Bai, Haofeng; Wang, Xiongfei; Loh, Poh Chiang
2016-01-01
Passive trap filters are widely used in high power Voltage Source Inverters (VSI) for the switching harmonic attenuation. The usage of the passive trap filters requires clustered and fixed switching harmonic spectrum, which is not the case for low pulse-ratio or Variable Switching Frequency (VSF...... current control of the auxiliary converter, which can be challenging considering that the switching harmonics have very high orders. In this paper, an Active Trap Filter (ATF) based on output impedance shaping is proposed. It is able to bypass the switching harmonics by providing nearly zero output...... impedance. A series-LC-filter is used to reduce the power rating and synthesize the desired output impedance of the ATF. Compared with the existing approaches, the compensated frequency range is greatly enlarged. Also, the current reference is simply set to zero, which reduces the complexity of the control...
Local condensate depletion at trap center under strong interactions
Yukalov, V. I.; Yukalova, E. P.
2018-04-01
Cold trapped Bose-condensed atoms, interacting via hard-sphere repulsive potentials are considered. Simple mean-field approximations show that the condensate distribution inside a harmonic trap always has the shape of a hump with the maximum condensate density occurring at the trap center. However, Monte Carlo simulations at high density and strong interactions display the condensate depletion at the trap center. The explanation of this effect of local condensate depletion at trap center is suggested in the frame of self-consistent theory of Bose-condensed systems. The depletion is shown to be due to the existence of the anomalous average that takes into account pair correlations and appears in systems with broken gauge symmetry.
Phase diagram of a polarized Fermi gas across a Feshbach resonance in a potential trap
International Nuclear Information System (INIS)
Yi, W.; Duan, L.-M.
2006-01-01
We map out the detailed phase diagram of a trapped ultracold Fermi gas with population imbalance across a wide Feshbach resonance. We show that under the local density approximation, the properties of the atoms in any (anisotropic) harmonic traps are universally characterized by three dimensionless parameters: the normalized temperature, the dimensionless interaction strength, and the population imbalance. We then discuss the possible quantum phases in the trap, and quantitatively characterize their phase boundaries in various typical parameter regions
National Oceanic and Atmospheric Administration, Department of Commerce — The data set contains detailed information about the catch from 600 trap stations around St. Croix. Data fields include species caught, size data, trap location...
Physics of tissue harmonic imaging by ultrasound
Jing, Yuan
Tissue Harmonic Imaging (THI) is an imaging modality that is currently deployed on diagnostic ultrasound scanners. In THI the amplitude of the ultrasonic pulse that is used to probe the tissue is large enough that the pulse undergoes nonlinear distortion as it propagates into the tissue. One result of the distortion is that as the pulse propagates energy is shifted from the fundamental frequency of the source pulse into its higher harmonics. These harmonics will scatter off objects in the tissue and images formed from the scattered higher harmonics are considered to have superior quality to the images formed from the fundamental frequency. Processes that have been suggested as possibly responsible for the improved imaging in THI include: (1) reduced sensitivity to reverberation, (2) reduced sensitivity to aberration, and (3) reduction in side lobes. By using a combination of controlled experiments and numerical simulations, these three reasons have been investigated. A single element transducer and a clinical ultrasound scanner with a phased array transducer were used to image a commercial tissue-mimicking phantom with calibrated targets. The higher image quality achieved with THI was quantified in terms of spatial resolution and "clutter" signals. A three-dimensional model of the forward propagation of nonlinear sound beams in media with arbitrary spatial properties (a generalized KZK equation) was developed. A time-domain code for solving the KZK equation was validated with measurements of the acoustic field generated by the single element transducer and the phased array transducer. The code was used to investigate the impact of aberration using tissue-like media with three-dimensional variations in all acoustic properties. The three-dimensional maps of tissue properties were derived from the datasets available through the Visible Female project. The experiments and simulations demonstrated that second harmonic imaging (1) suffers less clutter associated with
Electron scattering by trapped fermionic atoms
International Nuclear Information System (INIS)
Wang Haijun; Jhe, Wonho
2002-01-01
Considering the Fermi gases of alkali-metal atoms that are trapped in a harmonic potential, we study theoretically the elastic and inelastic scattering of the electrons by the trapped Fermi atoms and present the corresponding differential cross sections. We also obtain the stopping power for the cases that the electronic state as well as the center-of-mass state are excited both separately and simultaneously. It is shown that the elastic scattering process is no longer coherent in contrast to the electron scattering by the atomic Bose-Einstein condensate (BEC). For the inelastic scattering process, on the other hand, the differential cross section is found to be proportional to the 2/3 power of the number of the trapped atoms. In particular, the trapped fermionic atoms display the effect of ''Fermi surface,'' that is, only the energy levels near the Fermi energy have dominant contributions to the scattering process. Moreover, it is found that the stopping power scales as the 7/6 power of the atomic number. These results are fundamentally different from those of the electron scattering by the atomic BEC, mainly due to the different statistics obeyed by the trapped atomic systems
Angular trap for macroparticles
International Nuclear Information System (INIS)
Aksyonov, D.S.
2013-01-01
Properties of angular macroparticle traps were investigated in this work. These properties are required to design vacuum arc plasma filters. The correlation between trap geometry parameters and its ability to absorb macroparticles were found. Calculations allow one to predict the behaviour of filtering abilities of separators which contain such traps in their design. Recommendations regarding the use of angular traps in filters of different builds are given.
Centrifugal trapping in the magnetotail
Directory of Open Access Journals (Sweden)
D. C. Delcourt
Full Text Available Particles leaving the neutral sheet in the distant magnetotail at times display adiabatic trajectory sequences characterized by an inflection toward the equator and subsequent mirroring in its vicinity. We demonstrate that this low-latitude mirroring results primarily from a centrifugal deceleration due to the fast direction-changing E×B drift. This effect which we refer to as "centrifugal trapping" appears both in guiding centre and full particle treatments. It thus does not directly relate to nonadiabatic motion. However, pitch angle scattering due to nonadiabatic neutral sheet interaction does play a role in reducing the parallel speed of the particles. We show that centrifugal trapping is an important mechanism for the confinement of the slowest (typically below the equatorial E×B drift speed plasma sheet populations to the midplane vicinity.
Centrifugal trapping in the magnetotail
Directory of Open Access Journals (Sweden)
D. C. Delcourt
1995-03-01
Full Text Available Particles leaving the neutral sheet in the distant magnetotail at times display adiabatic trajectory sequences characterized by an inflection toward the equator and subsequent mirroring in its vicinity. We demonstrate that this low-latitude mirroring results primarily from a centrifugal deceleration due to the fast direction-changing E×B drift. This effect which we refer to as "centrifugal trapping" appears both in guiding centre and full particle treatments. It thus does not directly relate to nonadiabatic motion. However, pitch angle scattering due to nonadiabatic neutral sheet interaction does play a role in reducing the parallel speed of the particles. We show that centrifugal trapping is an important mechanism for the confinement of the slowest (typically below the equatorial E×B drift speed plasma sheet populations to the midplane vicinity.
High-harmonic generation in a dense medium
International Nuclear Information System (INIS)
Strelkov, V.V.; Platonenko, V.T.; Becker, A.
2005-01-01
The high-harmonic generation in a plasma or gas under conditions when the single-atom response is affected by neighboring ions or atoms of the medium is studied theoretically. We solve numerically the three-dimensional Schroedinger equation for a single-electron atom in the combined fields of the neighboring particles and the laser, and average the results over different random positions of the particles using the Monte Carlo method. Harmonic spectra are calculated for different medium densities and laser intensities. We observe a change of the harmonic properties due to a random variation of the harmonic phase induced by the field of the medium, when the medium density exceeds a certain transition density. The transition density is found to depend on the harmonic order, but it is almost independent of the fundamental intensity. It also differs for the two (shorter and longer) quantum paths. The latter effect leads for ionic densities in the transition regime to a narrowing of the harmonic lines and a shortening of the attosecond pulses generated using a group of harmonics
Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.
2017-11-01
We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton
Intelligent harmonic load model based on neural networks
Ji, Pyeong-Shik; Lee, Dae-Jong; Lee, Jong-Pil; Park, Jae-Won; Lim, Jae-Yoon
2007-12-01
In this study, we developed a RBFNs(Radial Basis Function Networks) based load modeling method with harmonic components. The developed method implemented by using harmonic information as well as fundamental frequency and voltage which are essential input factors in conventional method. Thus, the proposed method makes it possible to effectively estimate load characteristics in power lines with harmonics. The RBFNs have certain advantage such as simple structure and rapid computation ability compared with multilayer perceptron which is extensively applied for load modeling. To show the effectiveness, the proposed method has been intensively tested with various dataset acquired under the different frequency and voltage and compared it with conventional methods such as polynominal 2nd equation method, MLP and RBF without considering harmonic components.
Numerical modeling of Harmonic Imaging and Pulse Inversion fields
Humphrey, Victor F.; Duncan, Tracy M.; Duck, Francis
2003-10-01
Tissue Harmonic Imaging (THI) and Pulse Inversion (PI) Harmonic Imaging exploit the harmonics generated as a result of nonlinear propagation through tissue to improve the performance of imaging systems. A 3D finite difference model, that solves the KZK equation in the frequency domain, is used to investigate the finite amplitude fields produced by rectangular transducers driven with short pulses and their inverses, in water and homogeneous tissue. This enables the characteristic of the fields and the effective PI field to be calculated. The suppression of the fundamental field in PI is monitored, and the suppression of side lobes and a reduction in the effective beamwidth for each field are calculated. In addition, the differences between the pulse and inverse pulse spectra resulting from the use of very short pulses are noted, and the differences in the location of the fundamental and second harmonic spectral peaks observed.
Designing of a Quadrupole Paul Ion Trap
Kiyani, Abouzar; Abdollahzadeh, M.; Sadat Kiai, S. M.; Zirak, A. R.
2011-08-01
The ion motion equation in a Paul ion trap known as Mathieu differential equation has been solved for the first time by using Runge-Kutta methods with 4th, 6th, and 8th orders. The first stability regions in az - qz plane and the corresponding qmax values were determined and compared. Also, the first stability regions of , , , ions in the Vdc - Vac plane were drown, and the threshold voltages for the ion separation was investigated.
Spherical Harmonics Treatment of Epithermal Neutron Spectra in Reactor lattices
International Nuclear Information System (INIS)
Matausek, M.V.
1972-04-01
A procedure has been developed to solve the slowing down transport equation for neutrons in a cylindrized reactor lattice cell. Treating the anisotropy of the epithermal neutron flux by the spherical harmonics formalism, which reduces the space-angle-lethargy-dependent transport equation to the matrix integrodifferential equation in space and lethargy, and replacing the lethargy transfer integrals by finite-difference forms, a set of matrix ordinary differential equations, with lethargy and space dependent coefficients, is obtained. In the resonance region this set takes a lower block triangular form and can be directly solved by forward block substitution; in the lethargy range, where the fast fission effects have to be considered, the iterative procedure is introduced. A simple and efficient approximation is then proposed, making possible the analytical solution for the spatial dependence of the spherical harmonics flux moments. The proposed procedure has been numerically examined and approved. Some typical results are presented and discussed. (author)
Cubic Invariant Spherical Surface Harmonics in Conjunction With Diffraction Strain Pole-Figures
Brakman, C.M.
1986-01-01
Four kinds of cubic invariant spherical surface harmonics are introduced. It has been shown previously that these harmonics occur in the equations relating measured diffraction (line-shift) elastic strain and macro-stresses generating these strains for the case of textured cubic materials. As a
Feynman integrals and difference equations
International Nuclear Information System (INIS)
Moch, S.; Schneider, C.
2007-09-01
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Feynman integrals and difference equations
Energy Technology Data Exchange (ETDEWEB)
Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2007-09-15
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Next generation data harmonization
Armstrong, Chandler; Brown, Ryan M.; Chaves, Jillian; Czerniejewski, Adam; Del Vecchio, Justin; Perkins, Timothy K.; Rudnicki, Ron; Tauer, Greg
2015-05-01
Analysts are presented with a never ending stream of data sources. Often, subsets of data sources to solve problems are easily identified but the process to align data sets is time consuming. However, many semantic technologies do allow for fast harmonization of data to overcome these problems. These include ontologies that serve as alignment targets, visual tools and natural language processing that generate semantic graphs in terms of the ontologies, and analytics that leverage these graphs. This research reviews a developed prototype that employs all these approaches to perform analysis across disparate data sources documenting violent, extremist events.
Hyperchaotic circuit with damped harmonic oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
2001-01-01
A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance, two ideal...... capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...... by means of numerical integration of the appropriate differential equations....
An introduction to non-harmonic Fourier series
Young, Robert M
2001-01-01
An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.
Quantum theory of damped harmonic oscillator | Antia | Global ...
African Journals Online (AJOL)
The exact solutions of the Schrödinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle ...
The resonating group method in an harmonic oscillator basis
International Nuclear Information System (INIS)
Silvestre-Brac, B.; Gignoux, C.; Ayant, Y.
1987-05-01
The scattering states for a general many body system is formulated within the resonating group method. The resulting Lippman-Schwinger equation is solved in an harmonic oscillator basis for which a number of advantages are emphasized. The analytical formula giving the free propagator in that basis is fully derived
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...
The essential harmony in the classical equations of mathematical physics
Nucci, M C
2001-01-01
The possibility to transform any system of linear ordinary differential equations into a system of constant coefficient equations is demonstrated using Lie theory. Some examples relate the classical equations of mathematical physics to the simple harmonic oscillator. The roles of the third order form of the Ermakov-Pinney equation and of Fleischen-von Weltunter systems are explained.
On the spherical harmonic expansion of the neutron angular distribution function
Energy Technology Data Exchange (ETDEWEB)
Depken, Sven
1959-03-15
The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases.
On the spherical harmonic expansion of the neutron angular distribution function
International Nuclear Information System (INIS)
Depken, Sven
1959-03-01
The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases
Solid neutron matter the energy density in the relativistic harmonic approximation
International Nuclear Information System (INIS)
Cattani, M.; Fernandes, N.C.
A relativistic expression for the energy density as a function of particle density for solid neutron matter is obtained using Dirac's equation with a truncated harmonic potential. Ultrabaric and superluminous effects are not found in our approach [pt
Tissue Harmonic Synthetic Aperture Imaging
DEFF Research Database (Denmark)
Rasmussen, Joachim
The main purpose of this PhD project is to develop an ultrasonic method for tissue harmonic synthetic aperture imaging. The motivation is to advance the field of synthetic aperture imaging in ultrasound, which has shown great potentials in the clinic. Suggestions for synthetic aperture tissue...... system complexity compared to conventional synthetic aperture techniques. In this project, SASB is sought combined with a pulse inversion technique for 2nd harmonic tissue harmonic imaging. The advantages in tissue harmonic imaging (THI) are expected to further improve the image quality of SASB...
Potential harmonic expansion for atomic wave functions
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.; Larsen, S.Y.
1991-01-01
One way to reduce the large degeneracy of the Hyperspherical Harmonic basis for solving few- and many-body bound state problems is to introduce an optimal basis truncation called the Potential Harmonic (PH) basis. Various PH truncation schemes are introduced, and their accuracies are evaluated in predicting the energies of the Helium and H - ground states , and the excited 2 1 S level of the Helium atom. It was found that the part of the PH basis that accounts for one-body correlations gives a better ground state energy for He than the Hartree-Fock approximation. When an orthogonal complement is introduced to the basis to account for e-e correlations, the error in the binding energy is found to be .00025 au and .00015 au for ground and excited helium, resp., and .00035 au for H - . Furthermore, the PH truncation is about 99.9% accurate in accounting for contributions coming from large values of the global angular momentum. This PH scheme is also much more accurate than previous versions based on the Faddeev equations. The present results indicate that the PH truncation can render the Hyperspherical Harmonic method useful for systems with N>3. (R.P.) 14 refs., 4 tabs
Undulator physics and coherent harmonic generation at the MAX-lab electron storage ring
International Nuclear Information System (INIS)
Werin, Sverker.
1991-01-01
This work presents the undulator and harmonic generation project at the electron storage ring MAX-lab at University of Lund. The theory of undulator radiation, laser coherent harmonic generation, optical klystron amplifiers and FELs is treated in one uniform way, with complete solutions of the necessary equations. The permanent magnet undulator is described in some detail, along with the installation of the undulator in the storage ring. Details regarding the emitted radiation, the electron beam path in the undulator and other results are analysed. Finally harmonic generation using a Nd:YAG laser and the creation of coherent photons at the third harmonic (355 nm) is described. (author)
Density profiles and collective excitations of a trapped two-component Fermi vapour
International Nuclear Information System (INIS)
Amoruso, M.; Meccoli, I.; Minguzzi, A.; Tosi, M.P.
1999-08-01
We discuss the ground state and the small-amplitude excitations of a degenerate vapour of fermionic atoms placed in two hyperfine states inside a spherical harmonic trap. An equations-of-motion approach is set up to discuss the hydrodynamic dissipation processes from the interactions between the two components of the fluid beyond mean-field theory and to emphasize analogies with spin dynamics and spin diffusion in a homogeneous Fermi liquid. The conditions for the establishment of a collisional regime via scattering against cold-atom impurities are analyzed. The equilibrium density profiles are then calculated for a two-component vapour of 40 K atoms: they are little modified by the interactions for presently relevant values of the system parameters, but spatial separation of the two components will spontaneously arise as the number of atoms in the trap is increased. The eigenmodes of collective oscillation in both the total particle number density and the concentration density are evaluated analytically in the special case of a symmetric two-component vapour in the collisional regime. The dispersion relation of the surface modes for the total particle density reduces in this case to that of a one-component Fermi vapour, whereas the frequencies of all other modes are shifted by the interactions. (author)
Efficiency enhancement of a harmonic lasing free-electron laser
International Nuclear Information System (INIS)
Salehi, E.; Maraghechi, B.; Mirian, N. S.
2015-01-01
The harmonic lasing free-electron laser amplifier, in which two wigglers is employed in order for the fundamental resonance of the second wiggler to coincide with the third harmonic of the first wiggler to generate ultraviolet radiation, is studied. A set of coupled nonlinear first-order differential equations describing the nonlinear evolution of the system, for a long electron bunch, is solved numerically by CYRUS code. Solutions for the non-averaged and averaged equations are compared. Remarkable agreement is found between the averaged and non-averaged simulations for the evolution of the third harmonic. Thermal effects in the form of longitudinal velocity spread are also investigated. For efficiency enhancement, the second wiggler field is set to decrease linearly and nonlinearly at the point where the radiation of the third harmonic saturates. The optimum starting point and the slope of the tapering of the amplitude of the wiggler are found by a successive run of the code. It is found that tapering can increase the saturated power of the third harmonic considerably. In order to reduce the length of the wiggler, the prebunched electron beam is considered
Efficiency enhancement of a harmonic lasing free-electron laser
Salehi, E.; Maraghechi, B.; Mirian, N. S.
2015-03-01
The harmonic lasing free-electron laser amplifier, in which two wigglers is employed in order for the fundamental resonance of the second wiggler to coincide with the third harmonic of the first wiggler to generate ultraviolet radiation, is studied. A set of coupled nonlinear first-order differential equations describing the nonlinear evolution of the system, for a long electron bunch, is solved numerically by CYRUS code. Solutions for the non-averaged and averaged equations are compared. Remarkable agreement is found between the averaged and non-averaged simulations for the evolution of the third harmonic. Thermal effects in the form of longitudinal velocity spread are also investigated. For efficiency enhancement, the second wiggler field is set to decrease linearly and nonlinearly at the point where the radiation of the third harmonic saturates. The optimum starting point and the slope of the tapering of the amplitude of the wiggler are found by a successive run of the code. It is found that tapering can increase the saturated power of the third harmonic considerably. In order to reduce the length of the wiggler, the prebunched electron beam is considered.
Efficiency enhancement of a harmonic lasing free-electron laser
Energy Technology Data Exchange (ETDEWEB)
Salehi, E.; Maraghechi, B., E-mail: behrouz@aut.ac.ir [Department of Physics, Amirkabir University of Technology, 15875-4413 Tehran (Iran, Islamic Republic of); Mirian, N. S. [School of Particle and Accelerator Physics, Institute for Research in Fundamental Sciences (IPM), 19395-5531 Tehran (Iran, Islamic Republic of)
2015-03-15
The harmonic lasing free-electron laser amplifier, in which two wigglers is employed in order for the fundamental resonance of the second wiggler to coincide with the third harmonic of the first wiggler to generate ultraviolet radiation, is studied. A set of coupled nonlinear first-order differential equations describing the nonlinear evolution of the system, for a long electron bunch, is solved numerically by CYRUS code. Solutions for the non-averaged and averaged equations are compared. Remarkable agreement is found between the averaged and non-averaged simulations for the evolution of the third harmonic. Thermal effects in the form of longitudinal velocity spread are also investigated. For efficiency enhancement, the second wiggler field is set to decrease linearly and nonlinearly at the point where the radiation of the third harmonic saturates. The optimum starting point and the slope of the tapering of the amplitude of the wiggler are found by a successive run of the code. It is found that tapering can increase the saturated power of the third harmonic considerably. In order to reduce the length of the wiggler, the prebunched electron beam is considered.
P-adic Schroedinger type equation
International Nuclear Information System (INIS)
Vladimirov, V.S.; Volovich, I.V.
1988-12-01
In p-adic quantum mechanics a Schroedinger type equation is considered. We discuss the appropriate notion of differential operators. A solution of the Schroedinger type equation is given. A new set of vacuum states for the p-adic quantum harmonic oscillator is presented. The correspondence principle with the standard quantum mechanics is discussed. (orig.)
2011-12-01
variations of ion traps, including (1) the cylindrically symmetric 3D ring trap; (2) the linear trap with a combination of cavity QED; (#) the symmetric...concepts of quantum information. The major demonstration has been the test of a Bell inequality as demonstrated by Rowe et al. [50] and a decoherence...famous physics experiment [62]. Wolfgang Paul demonstrated a similar apparatus during his Nobel Prize speech [63]. This device is hyperbolic- parabolic
Second harmonic generation microscopy
DEFF Research Database (Denmark)
Brüggemann, Dagmar Adeline; Brewer, Jonathan R.; Risbo, Jens
2010-01-01
Myofibers and collagen show non-linear optical properties enabling imaging using second harmonic generation (SHG) microscopy. The technique is evaluated for use as a tool for real-time studies of thermally induced changes in thin samples of unfixed and unstained pork. The forward and the backward...... scattered SHG light reveal complementary features of the structures of myofibers and collagen fibers. Upon heating the myofibers show no structural changes before reaching a temperature of 53 °C. At this temperature the SHG signal becomes extinct. The extinction of the SHG at 53 °C coincides with a low......-temperature endotherm peak observable in the differential scanning calorimetry (DSC) thermograms. DSC analysis of epimysium, the connective tissue layer that enfold skeletal muscles, produces one large endotherm starting at 57 °C and peaking at 59.5 °C. SHG microscopy of collagen fibers reveals a variability of thermal...
Jorgensen, L V; Bertsche, W; Boston, A; Bowe, P D; Cesar, C L; Chapman, S; Charlton, M; Fajans, J; Fujiwara, M C; Funakoshi, R; Gill, D R; Hangst, J S; Hayano, R S; Hydomako, R; Jenkins, M J; Kurchaninov, L; Madsen, N; Nolan, P; Olchanski, K; Olin, A; Page, R D; Povilus, A; Robicheaux, F; Sarid, E; Silveira, D M; Storey, J W; Thompson, R I; van der Werf, D P; Wurtele, J S; Yamazaki, Y
2008-01-01
Substantial progress has been made in the last few years in the nascent field of antihydrogen physics. The next big step forward is expected to be the trapping of the formed antihydrogen atoms using a magnetic multipole trap. ALPHA is a new international project that started to take data in 2006 at CERN’s Antiproton Decelerator facility. The primary goal of ALPHA is stable trapping of cold antihydrogen atoms to facilitate measurements of its properties. We discuss the status of the ALPHA project and the prospects for antihydrogen trapping.
Azimuthal anisotropy: The higher harmonics
International Nuclear Information System (INIS)
Poskanzer, Arthur M.; STAR Collaboration
2004-01-01
We report the first observations of the fourth harmonic (v 4 ) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v 4 is about a factor of 10 smaller than v 2 . For the sixth (v 6 ) and eighth (v 8 ) harmonics upper limits on the magnitudes are reported
Harmonic Series Meets Fibonacci Sequence
Chen, Hongwei; Kennedy, Chris
2012-01-01
The terms of a conditionally convergent series may be rearranged to converge to any prescribed real value. What if the harmonic series is grouped into Fibonacci length blocks? Or the harmonic series is arranged in alternating Fibonacci length blocks? Or rearranged and alternated into separate blocks of even and odd terms of Fibonacci length?
Tuvan Throat Singing and Harmonics
Ruiz, Michael J.; Wilken, David
2018-01-01
Tuvan throat singing, also called overtone singing, provides for an exotic demonstration of the physics of harmonics as well as introducing an Asian musical aesthetic. A low fundamental is sung and the singer skillfully alters the resonances of the vocal system to enhance an overtone (harmonic above the fundamental). The result is that the…
SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÃ–DINGER
Directory of Open Access Journals (Sweden)
T B Prayitno
2012-02-01
Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master SchrÃ¶dinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution canâ€™t be normalized. Â Keywords : harmonic oscillator, nonlinear SchrÃ¶dinger.
Harmonic ultrasound fields through layered liquid media.
Li, Yadong; Chen, Quan; Zagzebski, James
2004-02-01
Harmonic field generation through a layered liquid media is studied experimentally and theoretically. Lateral and axial beam profiles of the fundamental to the 4th harmonic component of the field from a focused, 19-mm diameter transducer were measured using a calibrated hydrophone in a water tank. Measurements were performed before and after the insertion of a cylindrical phantom containing vegetable oil. A frequency domain numerical solution to the "KZK" equation was used to calculate the beam profile, taking into account the acoustic properties of the medium and phantom. Effects of nonlinear propagation, diffraction, attenuation, and reflection are include in the calculation. Agreement within 5% was obtained between measurements and theoretical predictions throughout the mid- and far-field of the transducer for both the uniform path and the layered media. Measurements also were carried out using an unfocused transducer as a receiver. The shape of the axial beam profile using this receiver agreed very well with the theoretical prediction using the "KZK" equation, after accounting for phase variations over the finite-sized detector in the calculated field.
Quasisymmetry equations for conventional stellarators
International Nuclear Information System (INIS)
Pustovitov, V.D.
1994-11-01
General quasisymmetry condition, which demands the independence of B 2 on one of the angular Boozer coordinates, is reduced to two equations containing only geometrical characteristics and helical field of a stellarator. The analysis is performed for conventional stellarators with a planar circular axis using standard stellarator expansion. As a basis, the invariant quasisymmetry condition is used. The quasisymmetry equations for stellarators are obtained from this condition also in an invariant form. Simplified analogs of these equations are given for the case when averaged magnetic surfaces are circular shifted torii. It is shown that quasisymmetry condition can be satisfied, in principle, in a conventional stellarator by a proper choice of two satellite harmonics of the helical field in addition to the main harmonic. Besides, there appears a restriction on the shift of magnetic surfaces. Thus, in general, the problem is closely related with that of self-consistent description of a configuration. (author)
Harmonics in transmission power systems
DEFF Research Database (Denmark)
Wiechowski, Wojciech Tomasz
. The comparison shows that results obtained used both types of the cores are the same, so it is concluded that both cores can be used for harmonic measurements. Low-inductance resistors are introduced in the secondary circuits, in series with the metering and protective relaying. On those resistors, the harmonic......Some time ago, Energinet.dk, the Transmission System Operator of the 150 kV and 400 kV transmission network in Denmark, had experienced operational malfunctions of some of the measuring and protection equipment. Also an overloading of a harmonic filter has been reported, and therefore, a need...... end only so the ground is not used as a return path. A way to reduce the capacitive coupling is to provide shielding. Harmonic currents are measured using the conventional inductive voltage transformers. Both protective and metering cores were compared if they could be used for harmonic measurements...
Tuvan throat singing and harmonics
Ruiz, Michael J.; Wilken, David
2018-05-01
Tuvan throat singing, also called overtone singing, provides for an exotic demonstration of the physics of harmonics as well as introducing an Asian musical aesthetic. A low fundamental is sung and the singer skillfully alters the resonances of the vocal system to enhance an overtone (harmonic above the fundamental). The result is that the listener hears two pitches simultaneously. Harmonics such as H8, H9, H10, and H12 form part of a pentatonic scale and are commonly selected for melody tones by Tuvan singers. A real-time spectrogram is provided in a video (Ruiz M J 2018 Video: Tuvan Throat Singing and Harmonics http://mjtruiz.com/ped/tuva/) so that Tuvan harmonics can be visualized as they are heard.
Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.
Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht
2013-09-21
The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.
Parametric Resonance in a Time-Dependent Harmonic Oscillator
Directory of Open Access Journals (Sweden)
P. N. Nesterov
2013-01-01
Full Text Available In this paper, we study the phenomenon of appearance of new resonances in a timedependent harmonic oscillator under an oscillatory decreasing force. The studied equation belongs to the class of adiabatic oscillators and arises in connection with the spectral problem for the one-dimensional Schr¨odinger equation with Wigner–von Neumann type potential. We use a specially developed method for asymptotic integration of linear systems of differential equations with oscillatory decreasing coefficients. This method uses the ideas of the averaging method to simplify the initial system. Then we apply Levinson’s fundamental theorem to get the asymptotics for its solutions. Finally, we analyze the features of a parametric resonance phenomenon. The resonant frequencies of perturbation are found and the pointwise type of the parametric resonance phenomenon is established. In conclusion, we construct an example of a time-dependent harmonic oscillator (adiabatic oscillator in which the parametric resonances, mentioned in the paper, may occur.
Phase-dependent quantum interference between different pathways in bichromatic harmonic generation
International Nuclear Information System (INIS)
Jun, Cai; Li-Ming, Wang; Hao-Xue, Qiao
2009-01-01
This paper studies the harmonic generation of the hydrogen atom subjected to a collinear bichromatic laser field by numerically solving the time-dependent Schrödinger equation using the split-operator pseudo-spectral method. By adding a frequency variation to the additional field, the contributions of different pathways to particular order harmonic generation can be isolated. The quantum interference pattern between harmonic pathways, which influences the harmonic intensity, is found to be either constructive or destructive with respect to different relative phase of the two field components. Detailed description of up to the 35th-order harmonics and the harmonic pathways for a wide range of field parameters is presented. (atomic and molecular physics)
Single and dual fiber nano-tip optical tweezers: trapping and analysis.
Decombe, Jean-Baptiste; Huant, Serge; Fick, Jochen
2013-12-16
An original optical tweezers using one or two chemically etched fiber nano-tips is developed. We demonstrate optical trapping of 1 micrometer polystyrene spheres at optical powers down to 2 mW. Harmonic trap potentials were found in the case of dual fiber tweezers by analyzing the trapped particle position fluctuations. The trap stiffness was deduced using three different models. Consistent values of up to 1 fN/nm were found. The stiffness linearly decreases with decreasing light intensity and increasing fiber tip-to-tip distance.
Standard superfields in the harmonic formalism of supergauge theories
International Nuclear Information System (INIS)
Zupnik, B.M.; Tolstonog, L.V.
1989-01-01
Connection between the standard superfield formalism and the harmonic superspace method is studied in the 6-dimensional and extended 4-dimensional supergauge theories. The action of the abelian theory is expressed in terms of the real prepotential V ik . A generalization for the non-abelian case can be performed with the help of the iterative method. Analysing the supergauge theory with the gauge group SU(2) the authors exploit the exact solution of the equations for the harmonic superfield connections which can be expressed in terms of the real prepotential V iklm in a special gauge
Effects of neutrino trapping on supernova explosions
International Nuclear Information System (INIS)
Takahara, Mariko; Sato, Katsuhiko
1982-01-01
Effects of neutrino trapping on the mass ejection from the stellar cores are investigated with the aid of a simplified equation of state under the assumption of adiabatic collapse. It is found that mass ejection becomes violent only if the ratio of the trapped leptons to baryons, Y sub(L), lies in an appropriate range. If the value of Y sub(L) lies out of this range, mass ejection is difficult. It is also shown that as the thermal stiffness of the shocked matter increases, the range necessary for the violent mass ejection becomes wider. Possibilities of supernova explosion are discussed on the basis of these results. (author)
International Nuclear Information System (INIS)
Feng-De, Zong; Jie-Fang, Zhang
2008-01-01
A model of the perturbed complex Toda chain (PCTC) to describe the dynamics of a Bose–Einstein condensate (BEC) N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential. (general)
Tightly confined atoms in optical dipole traps
International Nuclear Information System (INIS)
Schulz, M.
2002-12-01
This thesis reports on the design and setup of a new atom trap apparatus, which is developed to confine few rubidium atoms in ultrahigh vacuum and make them available for controlled manipulations. To maintain low background pressure, atoms of a vapour cell are transferred into a cold atomic beam by laser cooling techniques, and accumulated by a magneto-optic trap (MOT) in a separate part of the vacuum system. The laser cooled atoms are then transferred into dipole traps made of focused far-off-resonant laser fields in single- or crossed-beam geometry, which are superimposed with the center of the MOT. Gaussian as well as hollow Laguerre-Gaussian (LG$ ( 01)$) beam profiles are used with red-detuned or blue-detuned light, respectively. Microfabricated dielectric phase objects allow efficient and robust mode conversion of Gaussian into Laguerre-Gaussian laser beams. Trap geometries can easily be changed due to the highly flexible experimental setup. The dipole trap laser beams are focused to below 10 microns at a power of several hundred milliwatts. Typical trap parameters, at a detuning of several ten nanometers from the atomic resonance, are trag depths of few millikelvin, trap frequencies near 30-kHz, trap light scattering rates of few hundred photons per atom and second, and lifetimes of several seconds. The number of dipole-trapped atoms ranges from more than ten thousand to below ten. The dipole-trapped atoms are detected either by a photon counting system with very efficient straylight discrimination, or by recapture into the MOT, which is imaged onto a sensitive photodiode and a CCD-camera. Due to the strong AC-Stark shift imposed by the high intensity trapping light, energy-selective resonant excitation and detection of the atoms is possible. The measured energy distribution is consistent with a harmonic potential shape and allows the determination of temperatures and heating rates. In first measurements, the thermal energy is found to be about 10 % of the
van Veldhoven, J.; Bethlem, H.L.; Schnell, M.; Meijer, G.
2006-01-01
A four electrode electrostatic trap geometry is demonstrated that can be used to combine a dipole, quadrupole, and hexapole field. A cold packet of ND315 molecules is confined in both a purely quadrupolar and hexapolar trapping field and additionally, a dipole field is added to a hexapole field to
International Nuclear Information System (INIS)
Hundal, R.
1976-01-01
A cold trap assembly for removing impurities from a liquid metal is described. A hole between the incoming impure liquid metal and purified outgoing liquid metal acts as a continuous bleed means and thus prevents the accumulation of cover gases within the cold trap assembly
Capillary-gravity waves and the Navier-Stokes equation
International Nuclear Information System (INIS)
Behroozi, F.; Podolefsky, N.
2001-01-01
Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)
Deuterium trapping in tungsten
Poon, Michael
Tungsten is one of the primary material candidates being investigated for use in the first-wall of a magnetic confinement fusion reactor. An ion accelerator was used to simulate the type of ion interaction that may occur at a plasma-facing material. Thermal desorption spectroscopy (TDS) was the primary tool used to analyze the effects of the irradiation. Secondary ion mass spectroscopy (SIMS) was used to determine the distribution of trapped D in the tungsten specimen. The tritium migration analysis program (TMAP) was used to simulate thermal desorption profiles from the D depth distributions. Fitting of the simulated thermal desorption profiles with the measured TDS results provided values of the D trap energies. Deuterium trapping in single crystal tungsten was studied as a function of the incident ion fluence, ion flux, irradiation temperature, irradiation history, and surface impurity levels during irradiation. The results show that deuterium was trapped at vacancies and voids. Two deuterium atoms could be trapped at a tungsten vacancy, with trapping energies of 1.4 eV and 1.2 eV for the first and second D atoms, respectively. In a tungsten void, D is trapped as atoms adsorbed on the inner walls of the void with a trap energy of 2.1 eV, or as D2 molecules inside the void with a trap energy of 1.2 eV. Deuterium trapping in polycrystalline tungsten was also studied as a function of the incident fluence, irradiation temperature, and irradiation history. Deuterium trapping in polycrystalline tungsten also occurs primarily at vacancies and voids with the same trap energies as in single crystal tungsten; however, the presence of grain boundaries promotes the formation of large surface blisters with high fluence irradiations at 500 K. In general, D trapping is greater in polycrystalline tungsten than in single crystal tungsten. To simulate mixed materials comprising of carbon (C) and tungsten, tungsten specimens were pre-irradiated with carbon ions prior to D
Deuterium trapping in tungsten
International Nuclear Information System (INIS)
Poon, M.
2004-01-01
Tungsten is one of the primary material candidates being investigated for use in the first-wall of a magnetic confinement fusion reactor. An ion accelerator was used to simulate the type of ion interaction that may occur at a plasma-facing material. Thermal desorption spectroscopy (TDS) was the primary tool used to analyze the effects of the irradiation Secondary ion mass spectroscopy (SIMS) was used to determine the distribution of trapped D in the tungsten specimen. The tritium migration analysis program (TMAP) was used to simulate thermal desorption profiles from the D depth distributions. Fitting of the simulated thermal desorption profiles with the measured TDS results provided values of the D trap energies. . Deuterium trapping in single crystal tungsten was studied as a function of the incident ion fluence, ion flux, irradiation temperature, irradiation history, and surface impurity levels during irradiation The results show that deuterium was trapped at vacancies and voids. Two deuterium atoms could be trapped at a tungsten vacancy, with trapping energies of 1.4 eV and 1.2 eV for the first and second D atoms, respectively. In a tungsten void, D is trapped as atoms adsorbed on the inner walls of the void with a trap energy of 2.1 eV, or as D 2 molecules inside the void with a trap energy of 1.2 eV. . Deuterium trapping in polycrystalline tungsten was also studied as a function of the incident fluence, irradiation temperature, and irradiation history. Deuterium trapping in polycrystalline tungsten also occurs primarily at vacancies and voids with the same trap energies as in single crystal tungsten; however, the presence of grain boundaries promotes the formation of large surface blisters with high fluence irradiations at 500 K. In general, D trapping is greater in polycrystalline tungsten than in single crystal tungsten. To simulate mixed materials comprising of carbon (C) and tungsten, tungsten specimens were pre-irradiated with carbon ions prior to D
Deuterium trapping in tungsten
Energy Technology Data Exchange (ETDEWEB)
Poon, M
2004-07-01
Tungsten is one of the primary material candidates being investigated for use in the first-wall of a magnetic confinement fusion reactor. An ion accelerator was used to simulate the type of ion interaction that may occur at a plasma-facing material. Thermal desorption spectroscopy (TDS) was the primary tool used to analyze the effects of the irradiation Secondary ion mass spectroscopy (SIMS) was used to determine the distribution of trapped D in the tungsten specimen. The tritium migration analysis program (TMAP) was used to simulate thermal desorption profiles from the D depth distributions. Fitting of the simulated thermal desorption profiles with the measured TDS results provided values of the D trap energies. . Deuterium trapping in single crystal tungsten was studied as a function of the incident ion fluence, ion flux, irradiation temperature, irradiation history, and surface impurity levels during irradiation The results show that deuterium was trapped at vacancies and voids. Two deuterium atoms could be trapped at a tungsten vacancy, with trapping energies of 1.4 eV and 1.2 eV for the first and second D atoms, respectively. In a tungsten void, D is trapped as atoms adsorbed on the inner walls of the void with a trap energy of 2.1 eV, or as D{sub 2} molecules inside the void with a trap energy of 1.2 eV. . Deuterium trapping in polycrystalline tungsten was also studied as a function of the incident fluence, irradiation temperature, and irradiation history. Deuterium trapping in polycrystalline tungsten also occurs primarily at vacancies and voids with the same trap energies as in single crystal tungsten; however, the presence of grain boundaries promotes the formation of large surface blisters with high fluence irradiations at 500 K. In general, D trapping is greater in polycrystalline tungsten than in single crystal tungsten. To simulate mixed materials comprising of carbon (C) and tungsten, tungsten specimens were pre-irradiated with carbon ions prior to D
Kluge, Heinz-Jürgen
2004-01-01
Trapping devices for atomic and nuclear physics experiments with radioactive ions are becoming more and more important at accelerator facilities. While about ten years ago only one online Penning trap experiment existed, namely ISOLTRAP at ISOLDE/CERN, meanwhile almost every radioactive beam facility has installed or plans an ion trap setup. This article gives an overview on ion traps in the operation, construction or planing phase which will be used for fundamental studies with short-lived radioactive nuclides such as mass spectrometry, laser spectroscopy and nuclear decay spectroscopy. In addition, this article summarizes the use of gas cells and radiofrequency quadrupole (Paul) traps at different facilities as a versatile tool for ion beam manipulation like retardation, cooling, bunching, and cleaning.
International Nuclear Information System (INIS)
Kluge, H.-J.; Blaum, K.
2004-01-01
Trapping devices for atomic and nuclear physics experiments with radioactive ions are becoming more and more important at accelerator facilities. While about ten years ago only one online Penning trap experiment existed, namely ISOLTRAP at ISOLDE/CERN, meanwhile almost every radioactive beam facility has installed or plans an ion trap setup. This article gives an overview on ion traps in the operation, construction or planing phase which will be used for fundamental studies with short-lived radioactive nuclides such as mass spectrometry, laser spectroscopy and nuclear decay spectroscopy. In addition, this article summarizes the use of gas cells and radiofrequency quadrupole (Paul) traps at different facilities as a versatile tool for ion beam manipulation like retardation, cooling, bunching, and cleaning
Harmonic lasing in x-ray free electron lasers
Directory of Open Access Journals (Sweden)
E. A. Schneidmiller
2012-08-01
Full Text Available Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed might be a cheap and efficient way of extension of wavelength ranges of existing and planned x-ray free electron laser (FEL facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of x-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust than usually thought, and can be widely used in the existing or planned x-ray FEL (XFEL facilities. In particular, Linac Coherent Light Source (LCLS after a minor modification can lase to saturation at the 3rd harmonic up to the photon energy of 25–30 keV providing multigigawatt power level and narrow bandwidth. As for the European XFEL, harmonic lasing would allow one to extend operating range (ultimately up to 100 keV, to reduce FEL bandwidth and to increase brilliance, to enable two-color operation for pump-probe experiments, and to provide more flexible operation at different electron energies. Similar improvements can be realized in other x-ray FEL facilities with gap-tunable undulators like FLASH II, SACLA, LCLS II, etc. Harmonic lasing can be an attractive option for compact x-ray FELs (driven by electron beams with a relatively low energy, allowing the use of the standard undulator technology instead of
Harmonic operation of high gain harmonic generation free electron laser
International Nuclear Information System (INIS)
Deng Haixiao; Chinese Academy of Sciences, Beijing; Dai Zhimin
2008-01-01
In high gain harmonic generation (HGHG) free electron laser (FEL), with the right choice of parameters of the modulator undulator, the dispersive section and the seed laser, one may make the spatial bunching of the electron beam density distribution correspond to one of the harmonic frequencies of the radiator radiation, instead of the fundamental frequency of the radiator radiation in conventional HGHG, thus the radiator undulator is in harmonic operation (HO) mode. In this paper, we investigate HO of HGHG FEL. Theoretical analyses with universal method are derived and numerical simulations in ultraviolet and deep ultraviolet spectral regions are given. It shows that the power of the 3rd harmonic radiation in the HO of HGHG may be as high as 18.5% of the fundamental power level. Thus HO of HGHG FEL may obtain short wavelength by using lower beam energy. (authors)
Power quality issues current harmonics
Mikkili, Suresh
2015-01-01
Power Quality Issues: Current Harmonics provides solutions for the mitigation of power quality problems related to harmonics. Focusing on active power filters (APFs) due to their excellent harmonic and reactive power compensation in two-wire (single phase), three-wire (three-phase without neutral), and four-wire (three-phase with neutral) AC power networks with nonlinear loads, the text:Introduces the APF technology, describing various APF configurations and offering guidelines for the selection of APFs for specific application considerationsCompares shunt active filter (SHAF) control strategi
Canonical statistics of trapped ideal and interacting Bose gases
International Nuclear Information System (INIS)
Xiong Hongwei; Liu Shujuan; Huang Guoxiang; Xu Zaixin
2002-01-01
The mean ground-state occupation number and condensate fluctuations of interacting and noninteracting Bose gases confined in a harmonic trap are considered by using a canonical ensemble approach. To obtain the mean ground-state occupation number and the condensate fluctuations, an analytical description for the probability distribution function of the condensate is provided directly starting from the analysis of the partition function of the system. For the ideal Bose gas, the probability distribution function is found to be a Gaussian one for the case of the harmonic trap. For the interacting Bose gas, using a unified approach the condensate fluctuations are calculated based on the lowest-order perturbation method and on Bogoliubov theory. It is found that the condensate fluctuations based on the lowest-order perturbation theory follow the law 2 N 0 >∼N, while the fluctuations based on Bogoliubov theory behave as N 4/3
Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.
Humphrey, V F
2000-03-01
In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described.
Jiang, Xiangzhi; Xiang, Meichun; Liu, Xingzhong
2017-01-01
Nematode-trapping fungi are a unique and intriguing group of carnivorous microorganisms that can trap and digest nematodes by means of specialized trapping structures. They can develop diverse trapping devices, such as adhesive hyphae, adhesive knobs, adhesive networks, constricting rings, and nonconstricting rings. Nematode-trapping fungi have been found in all regions of the world, from the tropics to Antarctica, from terrestrial to aquatic ecosystems. They play an important ecological role in regulating nematode dynamics in soil. Molecular phylogenetic studies have shown that the majority of nematode-trapping fungi belong to a monophyletic group in the order Orbiliales (Ascomycota). Nematode-trapping fungi serve as an excellent model system for understanding fungal evolution and interaction between fungi and nematodes. With the development of molecular techniques and genome sequencing, their evolutionary origins and divergence, and the mechanisms underlying fungus-nematode interactions have been well studied. In recent decades, an increasing concern about the environmental hazards of using chemical nematicides has led to the application of these biological control agents as a rapidly developing component of crop protection.
solution of free harmonic vibration equation of simply supported
African Journals Online (AJOL)
user
such as bridge decks, ship decks, airplanes, machine parts, highway pavements, airport runways and floor ... to the evaluation of certain definite integrals which can be done numerically; in cases where closed .... [1] Rao, S. Vibration of Continuous Systems, John Wiley and Sons Inc. New Jersey. 2007. [2] Timoshenko, S.
Explaining the harmonic sequence paradox.
Schmidt, Ulrich; Zimper, Alexander
2012-05-01
According to the harmonic sequence paradox, an expected utility decision maker's willingness to pay for a gamble whose expected payoffs evolve according to the harmonic series is finite if and only if his marginal utility of additional income becomes zero for rather low payoff levels. Since the assumption of zero marginal utility is implausible for finite payoff levels, expected utility theory - as well as its standard generalizations such as cumulative prospect theory - are apparently unable to explain a finite willingness to pay. This paper presents first an experimental study of the harmonic sequence paradox. Additionally, it demonstrates that the theoretical argument of the harmonic sequence paradox only applies to time-patient decision makers, whereas the paradox is easily avoided if time-impatience is introduced. ©2011 The British Psychological Society.
Introduction to abstract harmonic analysis
Loomis, Lynn H
2011-01-01
Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.
Cohabiting with the harmonic pollution
International Nuclear Information System (INIS)
Garcia C, Antonio A
1999-01-01
The Norm IEEE 519 tries of the permissible limits of harmonic distortion in the point of common joining between the energy supplier company and the industry. However fulfilling these limits of distortion doesn't guarantee that the problem for the company has finished, on the contrary will have to counteract the effects created by the harmonic distortion toward the interior of its electric system and to cohabit with this distortion
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
Quantum versus semiclassical description of self-trapping: Anharmonic effects
International Nuclear Information System (INIS)
Raghavan, S.; Bishop, A.R.; Kenkre, V.M.
1999-01-01
Self-trapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of anharmonicity and nonlinearity in this context, we present below a fully quantum-mechanical analysis of a two-site system, where the oscillator is described by a tunably anharmonic potential, with a square well with infinite walls and the harmonic potential as its extreme limits, and wherein the interaction is nonlinear in the oscillator displacement. We find that even highly anharmonic polarons behave similar to their harmonic counterparts in that self-trapping is preserved for long times in the limit of strong coupling, and that the polaronic tunneling time scale depends exponentially on the polaron binding energy. Further, in agreement, with earlier results related to harmonic polarons, the semiclassical approximation agrees with the full quantum result in the massive oscillator limit of small oscillator frequency and strong quasiparticle-oscillator coupling. copyright 1999 The American Physical Society
A Coordinate Transformation for Unsteady Boundary Layer Equations
Directory of Open Access Journals (Sweden)
Paul G. A. CIZMAS
2011-12-01
Full Text Available This paper presents a new coordinate transformation for unsteady, incompressible boundary layer equations that applies to both laminar and turbulent flows. A generalization of this coordinate transformation is also proposed. The unsteady boundary layer equations are subsequently derived. In addition, the boundary layer equations are derived using a time linearization approach and assuming harmonically varying small disturbances.
Coherent harmonics generated by a super-short electron pulse
International Nuclear Information System (INIS)
Ding Wu
1996-01-01
A novel mechanism generating superradiance harmonics is found. In this superradiance harmonics, the temporal width of harmonics is extremely short, the ratio of high harmonic fundamental wave is much higher than the known superradiance harmonics
General Lp-harmonic Blaschke bodies
Indian Academy of Sciences (India)
Abstract. Lutwak introduced the harmonic Blaschke combination and the harmonic. Blaschke body of a star body. Further, Feng and Wang introduced the concept of the L p- harmonic Blaschke body of a star body. In this paper, we define the notion of general. L p-harmonic Blaschke bodies and establish some of its ...
General Lp-harmonic Blaschke bodies
Indian Academy of Sciences (India)
Lutwak introduced the harmonic Blaschke combination and the harmonic Blaschke body of a star body. Further, Feng and Wang introduced the concept of the -harmonic Blaschke body of a star body. In this paper, we define the notion of general -harmonic Blaschke bodies and establish some of its properties.
Audibility of harmonics in 'periodic white noise'
Duifhuis, H.; Tomesen, H.H.
1970-01-01
In a previous article (Duifhuis, 1970) results' concerning the audibility of harmonics in a periodic pulse have been presented. Each of the lower harmonics could be perceived separately, whereas the high harmonics were heard together as one complex signal. High harmonics, however, appeared to be
High-order harmonic conversion efficiency in helium
International Nuclear Information System (INIS)
Crane, J.K.
1992-01-01
Calculated results are presented for the energy, number of photons, and conversion efficiency for high-order harmonic generation in helium. The results show the maximum values that we should expect to achieve experimentally with our current apparatus and the important parameters for scaling this source to higher output. In the desired operating regime where the coherence length, given by L coh =πb/(q-1), is greater than the gas column length, l, the harmonic output can be summarized by a single equation: N q =[(π z n z b 3 τ q |d q | z )/4h]{(p/q)(2l/b) z }. N q - numbers of photons of q-th harmonic; n - atom density; b - laser confocal parameter; τ q - pulse width of harmonic radiation; q - harmonic order; p - effective order of nonlinearity. (Note the term in brackets, the phase-matching function, has been separated from the rest of the expression in order to be consistent with the relevant literature)
Energy Technology Data Exchange (ETDEWEB)
Mihalcea, Bogdan M., E-mail: bogdan.mihalcea@inflpr.ro; Vişan, Gina T.; Ganciu, Mihai [National Institute for Laser, Plasma and Radiation Physics (INFLPR), Atomiştilor Str. Nr. 409, 077125 Măgurele, Ilfov (Romania); Giurgiu, Liviu C. [University of Bucharest, Faculty of Physics, Atomistilor Str. Nr. 405, 077125 Măgurele (Romania); Stan, Cristina [Department of Physics, Politehnica University, 313 Splaiul Independenţei, RO-060042 Bucharest (Romania); Filinov, Vladimir; Lapitsky, Dmitry, E-mail: dmitrucho@yandex.ru; Deputatova, Lidiya; Syrovatka, Roman [Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya Str. 13, Bd. 2, 125412 Moscow (Russian Federation)
2016-03-21
Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report microparticle trapping in case of multipole linear Paul trap geometries, operating under standard ambient temperature and pressure conditions. An 8- and 12-electrode linear trap geometries have been designed and tested with an aim to achieve trapping for larger number of particles and to study microparticle dynamical stability in electrodynamic fields. We report emergence of planar and volume ordered structures of microparticles, depending on the a.c. trapping frequency and particle specific charge ratio. The electric potential within the trap is mapped using the electrolytic tank method. Particle dynamics is simulated using a stochastic Langevin equation. We emphasize extended regions of stable trapping with respect to quadrupole traps, as well as good agreement between experiment and numerical simulations.
International Nuclear Information System (INIS)
Mihalcea, Bogdan M.; Vişan, Gina T.; Ganciu, Mihai; Giurgiu, Liviu C.; Stan, Cristina; Filinov, Vladimir; Lapitsky, Dmitry; Deputatova, Lidiya; Syrovatka, Roman
2016-01-01
Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report microparticle trapping in case of multipole linear Paul trap geometries, operating under standard ambient temperature and pressure conditions. An 8- and 12-electrode linear trap geometries have been designed and tested with an aim to achieve trapping for larger number of particles and to study microparticle dynamical stability in electrodynamic fields. We report emergence of planar and volume ordered structures of microparticles, depending on the a.c. trapping frequency and particle specific charge ratio. The electric potential within the trap is mapped using the electrolytic tank method. Particle dynamics is simulated using a stochastic Langevin equation. We emphasize extended regions of stable trapping with respect to quadrupole traps, as well as good agreement between experiment and numerical simulations.
Trapping and Probing Antihydrogen
Energy Technology Data Exchange (ETDEWEB)
Wurtele, Jonathan [UC Berkeley and LBNL
2013-03-27
Precision spectroscopy of antihydrogen is a promising path to sensitive tests of CPT symmetry. The most direct route to achieve this goal is to create and probe antihydrogen in a magnetic minimum trap. Antihydrogen has been synthesized and trapped for 1000s at CERN by the ALPHA Collaboration. Some of the challenges associated with achieving these milestones will be discussed, including mixing cryogenic positron and antiproton plasmas to synthesize antihydrogen with kinetic energy less than the trap potential of .5K. Recent experiments in which hyperfine transitions were resonantly induced with microwaves will be presented. The opportunity for gravitational measurements in traps based on detailed studies of antihydrogen dynamics will be described. The talk will conclude with a discussion future antihydrogen research that will use a new experimental apparatus, ALPHA-I.
International Nuclear Information System (INIS)
Elliott, S.R.; Beck, B.; Beiersdorfer, P.; Church, D.; DeWitt, D.; Knapp, D.K.; Marrs, R.E.; Schneider, D.; Schweikhard, L.
1993-01-01
The LLNL electron beam ion trap provides the world's only source of stationary highly charged ions up to bare U. This unique capability makes many new atomic and nuclear physics experiments possible. (orig.)
Microfabricated Waveguide Atom Traps.
Energy Technology Data Exchange (ETDEWEB)
Jau, Yuan-Yu [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-09-01
A nanoscale , microfabricated waveguide structure can in - principle be used to trap atoms in well - defined locations and enable strong photon-atom interactions . A neutral - atom platform based on this microfabrication technology will be prealigned , which is especially important for quantum - control applications. At present, there is still no reported demonstration of evanescent - field atom trapping using a microfabricated waveguide structure. We described the capabilities established by our team for future development of the waveguide atom - trapping technology at SNL and report our studies to overcome the technical challenges of loading cold atoms into the waveguide atom traps, efficient and broadband optical coupling to a waveguide, and the waveguide material for high - power optical transmission. From the atomic - physics and the waveguide modeling, w e have shown that a square nano-waveguide can be utilized t o achieve better atomic spin squeezing than using a nanofiber for first time.
Martini, Ruud; Kersten, P.H.M.
1983-01-01
Using 1-1 mappings, the complete symmetry groups of contact transformations of general linear second-order ordinary differential equations are determined from two independent solutions of those equations, and applied to the harmonic oscillator with and without damping.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
International Nuclear Information System (INIS)
Chou, Chia-Chun
2016-01-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw
2016-10-15
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Geomagnetically trapped carbon, nitrogen, and oxygen nuclei.
Mogro-Campero, A.
1972-01-01
Results of measurements carried out with the University of Chicago nuclear composition telescope on the Ogo 5 satellite, establishing the presence of 13- to 33-MeV/nucleon geomagnetically trapped C and O nuclei, with some evidence for N nuclei. These trapped nuclei were found at L less than or equal to 5 and near the geomagnetic equator. The data cover the period from Mar. 3, 1968, to Dec. 31, 1969. The distribution of CNO flux as a function of L is given. No change in the intensity of the average trapped CNO flux was detected by comparing data for 1968 and 1969. The results reported set a new value for the observed high energy limit of trapping as described by the critical adiabaticity parameter. The penetration of solar flare CNO up to L = 4 was observed twice in 1968, in disagreement with Stormer theory predictions. The effects of these results on some models for the origin of the trapped radiation are discussed.
Time-dependent Hartree approximation and time-dependent harmonic oscillator model
International Nuclear Information System (INIS)
Blaizot, J.P.
1982-01-01
We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schroedinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory. (orig.)
An easy trick to a periodic solution of relativistic harmonic oscillator
Directory of Open Access Journals (Sweden)
Jafar Biazar
2014-04-01
Full Text Available In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.
Studies of harmonic generation in free electron lasers
International Nuclear Information System (INIS)
Goldammer, K.
2007-01-01
Nonlinear harmonic generation is one of the most interesting aspects of Free Electron Lasers under study today. It provides for coherent, high intensity radiation at higher harmonics of the FEL resonant frequency. The sources, numerical simulation and applications of harmonic radiation in cascaded High Gain Harmonic Generation FELs were the subject of this thesis. Harmonic emission in FELs originates from harmonic microbunching of the particles and the particular electron trajectory during FEL interaction. Numerical FEL simulation codes model these analytical equations and predict the performance of Free Electron Lasers with good accuracy. This thesis has relied heavily upon the FEL simulation code Genesis 1.3 which has been upgraded in the framework of this thesis to compute harmonic generation in a self-consistent manner. Tests against analytical predictions suggest that the harmonic power levels as well as harmonic gain lengths are simulated correctly. A benchmark with the FEL simulation code GINGER yields excellent agreement of the harmonic saturation length and saturation power. The new version of the simulation code Genesis was also tested against measurements from the VUV-FEL FLASH at DESY. The spectral power distributions of fundamental and third harmonic radiation were recorded at 25.9 nm and 8.6 nm, respectively. The relative bandwidths (FWHM) were in the range of 2 % for both the fundamental as well as the third harmonic, which was accurately reproduced by time-dependent simulations with Genesis. The new code was also used to propose and evaluate a new design for the BESSY Soft X-Ray FEL, a cascaded High Gain Harmonic Generation FEL proposed by BESSY in Berlin. The original design for the BESSY High Energy FEL line requires four HGHG stages to convert the initial seed laser wavelength of 297.5 nm down to 1.24 nm. A new scheme is proposed that makes use of fifth harmonic radiation from the first stage and reduces the number of HGHG stages to three. It
Studies of harmonic generation in free electron lasers
Energy Technology Data Exchange (ETDEWEB)
Goldammer, K.
2007-11-12
Nonlinear harmonic generation is one of the most interesting aspects of Free Electron Lasers under study today. It provides for coherent, high intensity radiation at higher harmonics of the FEL resonant frequency. The sources, numerical simulation and applications of harmonic radiation in cascaded High Gain Harmonic Generation FELs were the subject of this thesis. Harmonic emission in FELs originates from harmonic microbunching of the particles and the particular electron trajectory during FEL interaction. Numerical FEL simulation codes model these analytical equations and predict the performance of Free Electron Lasers with good accuracy. This thesis has relied heavily upon the FEL simulation code Genesis 1.3 which has been upgraded in the framework of this thesis to compute harmonic generation in a self-consistent manner. Tests against analytical predictions suggest that the harmonic power levels as well as harmonic gain lengths are simulated correctly. A benchmark with the FEL simulation code GINGER yields excellent agreement of the harmonic saturation length and saturation power. The new version of the simulation code Genesis was also tested against measurements from the VUV-FEL FLASH at DESY. The spectral power distributions of fundamental and third harmonic radiation were recorded at 25.9 nm and 8.6 nm, respectively. The relative bandwidths (FWHM) were in the range of 2 % for both the fundamental as well as the third harmonic, which was accurately reproduced by time-dependent simulations with Genesis. The new code was also used to propose and evaluate a new design for the BESSY Soft X-Ray FEL, a cascaded High Gain Harmonic Generation FEL proposed by BESSY in Berlin. The original design for the BESSY High Energy FEL line requires four HGHG stages to convert the initial seed laser wavelength of 297.5 nm down to 1.24 nm. A new scheme is proposed that makes use of fifth harmonic radiation from the first stage and reduces the number of HGHG stages to three. It
Stability criteria for neutral delay differential-algebraic equations
Directory of Open Access Journals (Sweden)
FAN Ni
2013-10-01
Full Text Available The asymptotic stability of neutral delay differential-algebraic equations is studied in this paper.Two stability criteria described by evaluating a corresponding harmonic function on the boundary of a torus region are presented.
Mixtures Equation Pilot Program to Reduce Animal Testing
EPA is announcing the start of a pilot program to evaluate the usefulness and acceptability of a mathematical tool (the GHS Mixtures Equation), which is used in the Globally Harmonized System of Classification and Labeling of Chemicals (GHS).
Search For Trapped Antihydrogen
Andresen, Gorm B.; Baquero-Ruiz, Marcelo; Bertsche, William; Bowe, Paul D.; Bray, Crystal C.; Butler, Eoin; Cesar, Claudio L.; Chapman, Steven; Charlton, Michael; Fajans, Joel; Friesen, Tim; Fujiwara, Makoto C.; Gill, David R.; Hangst, Jeffrey S.; Hardy, Walter N.; Hayano, Ryugo S.; Hayden, Michael E.; Humphries, Andrew J.; Hydomako, Richard; Jonsell, Svante; Jorgensen, Lars V.; Kurchaninov, Lenoid; Lambo, Ricardo; Madsen, Niels; Menary, Scott; Nolan, Paul; Olchanski, Konstantin; Olin, Art; Povilus, Alexander; Pusa, Petteri; Robicheaux, Francis; Sarid, Eli; Nasr, Sarah Seif El; Silveira, Daniel M.; So, Chukman; Storey, James W.; Thompson, Robert I.; van der Werf, Dirk P.; Wilding, Dean; Wurtele, Jonathan S.; Yamazaki, Yasunori
2011-01-01
We present the results of an experiment to search for trapped antihydrogen atoms with the ALPHA antihydrogen trap at the CERN Antiproton Decelerator. Sensitive diagnostics of the temperatures, sizes, and densities of the trapped antiproton and positron plasmas have been developed, which in turn permitted development of techniques to precisely and reproducibly control the initial experimental parameters. The use of a position-sensitive annihilation vertex detector, together with the capability of controllably quenching the superconducting magnetic minimum trap, enabled us to carry out a high-sensitivity and low-background search for trapped synthesised antihydrogen atoms. We aim to identify the annihilations of antihydrogen atoms held for at least 130 ms in the trap before being released over ~30 ms. After a three-week experimental run in 2009 involving mixing of 10^7 antiprotons with 1.3 10^9 positrons to produce 6 10^5 antihydrogen atoms, we have identified six antiproton annihilation events that are consist...
Transient regime in second harmonic generation
Szeftel, Jacob; Sandeau, Laure; Sandeau, Nicolas; Delezoide, Camille; Khater, Antoine
2013-09-01
The time growth of the electromagnetic field at the fundamental and double frequencies is studied from the very onset of the second harmonic generation (SHG) process for a set of dipoles lacking a symmetry centre and exhibiting a nonresonant coupling with a classical electromagnetic field. This approach consists first of solving the Schrödinger equation by applying a generalised Rabi rotation to the Hamiltonian describing the light-dipole interaction. This rotation has been devised for the resulting Hamiltonian to show up time-independent for both components of the electromagnetic field at the fundamental frequency and the second harmonic one. Then an energy conservation argument, derived from the Poynting theorem, is introduced to work out an additional relationship between the electromagnetic field and its associated electric polarisation. Finally this analysis yields the full time behaviour of all physical quantities of interest. The calculated results reproduce accurately both the observed spatial oscillations of the SHG intensity (Maker's fringes) and its power law dependence on the intensity of the incoming light at the fundamental frequency.
Harmonic Balance Computations of Fan Aeroelastic Stability
Bakhle, Milind A.; Reddy, T. S. R.
2010-01-01
A harmonic balance (HB) aeroelastic analysis, which has been recently developed, was used to determine the aeroelastic stability (flutter) characteristics of an experimental fan. To assess the numerical accuracy of this HB aeroelastic analysis, a time-domain aeroelastic analysis was also used to determine the aeroelastic stability characteristics of the same fan. Both of these three-dimensional analysis codes model the unsteady flowfield due to blade vibrations using the Reynolds-averaged Navier-Stokes (RANS) equations. In the HB analysis, the unsteady flow equations are converted to a HB form and solved using a pseudo-time marching method. In the time-domain analysis, the unsteady flow equations are solved using an implicit time-marching approach. Steady and unsteady computations for two vibration modes were carried out at two rotational speeds: 100 percent (design) and 70 percent (part-speed). The steady and unsteady results obtained from the two analysis methods compare well, thus verifying the recently developed HB aeroelastic analysis. Based on the results, the experimental fan was found to have no aeroelastic instability (flutter) at the conditions examined in this study.
Steffen, T; Tanimura, Y
The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by
Harmonic states for the free particle
International Nuclear Information System (INIS)
Guerrero, J; López-Ruiz, F F; Aldaya, V; Cossío, F
2011-01-01
Different families of states, which are solutions of the time-dependent free Schrödinger equation, are imported from the harmonic oscillator using the quantum Arnold transformation introduced in Aldaya et al (2011 J. Phys. A: Math. Theor.44 065302). Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite–Gauss and Laguerre–Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined. (paper)
Factorization Procedure for Harmonically Bound Brownian Particle
International Nuclear Information System (INIS)
Omolo, JK.
2006-01-01
The method of factorization to solve the problem of the one-dimensional harmonically bound Brownian particle was applied. Assuming the the rapidily fluctuating random force is Gaussian and has an infinitely short correlation time, explicit expressions for the position-position,velocity-velocity, and the position-velocity correlation functions, which are also use to write down appropriate distribution functions were used. The correlation and distribution functions for the complex quantity (amplititude) which provides the expressions for the position and velocity of the particle are calculated. Finally, Fokker-Planck equations for the joint probability distribution functions for the amplititude and it's complex conjugate as well as for the position and velocity of the particle are obtained. (author)
International Nuclear Information System (INIS)
Chiang, Yuan-Jen.
1989-01-01
Harmonic maps between manifolds are described as the critical maps of their associated energy functionals. By using Sampson's method [Sam1], the author constructs a Sobolev's chain on a compact V-manifold and obtain Rellich's Theorem (Theorem 3.1), Sobolev's Theorem (Theorem 3.2), the regularity theorem (Theorem 3.3), the property of the eigenspaces for the Laplacian (Theorem 3.5) and the solvability of Laplacian (Theorem 3.6). Then, with these results, he constructs the Green's functions for the Laplacian on a compact V-manifold M in Proposition 4.1; and obtain an orthonormal basis for L 2 (M) formed by the eigenfunctions of the Laplacian corresponding to the eigenvalues in Proposition 4.2. He also estimates the eigenvalues and eigenfunctions of the Laplacian in Theorem 4.3, which is used to construct the heat kernel on a compact V-manifold in Proposition 5.1. Afterwards, he compares the G-invariant heat kernel functions with the G-invariant fundamental solutions of heat equations in the finite V-charts of a compact V-manifold in Theorem 6.1, and then study two integral operators associated to the heat kernel on a compact V-manifold in section 7. With all the preceding results established, in Theorem 8.3 he uses successive approximations to prove the existence of the solutions of parabolic equations on V-manifolds. Finally, he uses Theorem 8.3 to show the existence of harmonic maps from compact V-manifolds into compact Riemannian manifolds in Theorem 9.1 which extends Eells-Sampson's results [E-S
Theory of nonlinear harmonic generation in free-electron lasers with helical wigglers
International Nuclear Information System (INIS)
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2007-05-01
CoherentHarmonicGeneration (CHG), and in particularNonlinearHarmonicGeneration (NHG), is of importance for both short wavelength Free-Electron Lasers (FELs), in relation with the achievement of shorter wavelengths with a fixed electron-beam energy, and high-average power FEL resonators, in relation with destructive effects of higher harmonics radiation on mirrors. In this paper we present a treatment of NHG from helical wigglers with particular emphasis on the second harmonic. Our study is based on an exact analytical solution of Maxwell's equations, derived with the help of a Green's function method. In particular, we demonstrate that nonlinear harmonic generation (NHG) fromhelicalwigglers vanishes on axis. Our conclusion is in open contrast with results in literature, that include a kinematical mistake in the description of the electron motion. (orig.)
Finding trap stiffness of optical tweezers using digital filters.
Almendarez-Rangel, Pedro; Morales-Cruzado, Beatriz; Sarmiento-Gómez, Erick; Pérez-Gutiérrez, Francisco G
2018-02-01
Obtaining trap stiffness and calibration of the position detection system is the basis of a force measurement using optical tweezers. Both calibration quantities can be calculated using several experimental methods available in the literature. In most cases, stiffness determination and detection system calibration are performed separately, often requiring procedures in very different conditions, and thus confidence of calibration methods is not assured due to possible changes in the environment. In this work, a new method to simultaneously obtain both the detection system calibration and trap stiffness is presented. The method is based on the calculation of the power spectral density of positions through digital filters to obtain the harmonic contributions of the position signal. This method has the advantage of calculating both trap stiffness and photodetector calibration factor from the same dataset in situ. It also provides a direct method to avoid unwanted frequencies that could greatly affect calibration procedure, such as electric noise, for example.
Generalized reduced magnetohydrodynamic equations
International Nuclear Information System (INIS)
Kruger, S.E.
1999-01-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics
Radiation of electrons in an electromagnetic axial trap
International Nuclear Information System (INIS)
Toropova, A.I.
1998-01-01
The version of a trap. wherein particles move in a homogeneous constant magnetic field and electrostatic field, formed by two equipotential planes and rotation axial surface, is proposed. The solution of canonic equations is found. It is shown that interaction of electrons with the radiation field leads to damping parametric resonance. The trap model, accounting for the finite conductivity of the resonator walls and losses by collisions with gas, is studied
Characterization of nonequilibrium states of trapped Bose–Einstein condensates
Yukalov, V. I.; Novikov, A. N.; Bagnato, V. S.
2018-06-01
The generation of different nonequilibrium states in trapped Bose–Einstein condensates is studied by numerically solving the nonlinear Schrödinger equation. Inducing nonequilibrium states by shaking a trap creates the following states: weak nonequilibrium, the state of vortex germs, the state of vortex rings, the state of straight vortex lines, the state of deformed vortices, vortex turbulence, grain turbulence, and wave turbulence. A characterization of nonequilibrium states is advanced by introducing effective temperature, Fresnel number, and Mach number.
Relativistic Bosons in Time-Harmonic Electric Fields
Buhucianu, Ovidiu; Dariescu, Marina-Aura; Dariescu, Ciprian
2012-02-01
In the present paper, we consider a bi-dimensional thin sample, placed in a strong harmonically oscillating electric field and a static magnetic induction, both directed along the normal to the sample's plane. The Klein-Gordon equation describing the relativistic bosons leads to a Mathieu's type equation for the temporal part of the wave functions. It follows that, for the electric field pulsation inside a computable range, depending on the external fields intensities, the amplitude functions are turning from oscillatory to exponentially growing modes. For ultra-relativistic particles, one can recover the periodic stationary amplitude behavior.
A non-conforming 3D spherical harmonic transport solver
Energy Technology Data Exchange (ETDEWEB)
Van Criekingen, S. [Commissariat a l' Energie Atomique CEA-Saclay, DEN/DM2S/SERMA/LENR Bat 470, 91191 Gif-sur-Yvette, Cedex (France)
2006-07-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
A non-conforming 3D spherical harmonic transport solver
International Nuclear Information System (INIS)
Van Criekingen, S.
2006-01-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
HARMONIZED EUROPE OR EUROPEAN HARMONY?
Directory of Open Access Journals (Sweden)
Cosmin Marinescu
2007-07-01
Full Text Available Recent evolutions in Europe raise questions on the viability of the present economic and social model that defines the European construction project. In this paper, the author will try to explain the viability of institutional European model that sticks between free market mechanisms and protectionism. The main challenge for the EU is about the possibility to bring together the institutional convergence and the welfare for all Europeans. This is the result of the view, still dominant, of European politics elite, according to which institutional harmonization is the solution of a more dynamic and prosper Europe. But, economic realities convince us that, more and more, a harmonized, standardized Europe is not necessarily identical with a Europe of harmony and social cooperation. If „development through integration” seems to be harmonization through „institutional transplant”, how could then be the European model one sufficiently wide open to market, which creates the prosperity so long waited for by new member countries?
Harmonic superspaces of extended supersymmetry
International Nuclear Information System (INIS)
Ivanov, E.; Kalitzin, S.; Nguyen Ai Viet; Ogievetsky, V.
1984-01-01
The main technical apparatus of the harmonic superspace approach to extended SUSY, the calculus of harmonic variables on homogeneous spaces of the SUSY automorphism groups, is presented in detail for N=2, 3, 4. The basic harmonics for the coset manifolds G/H with G=SU(2), H=U(1); G=SU(3), H=SU(2)xU(1) and H=U(1)xU(1); G=SU(4), H=SU(3)xU(1), H=SU(2)xSU(2)xU(1), H=SU(2)xU(1)xU(1) and H=U(1)xU(1)xU(1); G=USp(2), H=SU(2)xSU(2), H=SU(2)xU(1) and H=U(1)xU(1) are tabulated a number of useful relations among them
Random walk and the heat equation
Lawler, Gregory F
2010-01-01
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For exa...
Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator
Directory of Open Access Journals (Sweden)
Kunle Adegoke
2016-01-01
Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
Elements of abstract harmonic analysis
Bachman, George
2013-01-01
Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give
Harmonic modeling of induction motors
Energy Technology Data Exchange (ETDEWEB)
Pedra, J.; Sainz, L.; Corcoles, F. [Department of Electrical Engineering, ETSEIB-UPC, Av. Diagonal 647, 08028 Barcelona (Spain)
2006-07-15
The paper proposes an induction motor model for the study of harmonic load flow in balanced and unbalanced conditions. The parameters of this model are obtained from motor manufacturer data and the positive- and negative-sequence equivalent circuits of the single- and double-cage models. An approximate harmonic model based on motor manufacturer data only is also proposed. In addition, the paper includes manufacturer data and the calculated parameters of 36 induction motors of different rated powers. This database is used to analyze the proposed models. (author)
Physics with Trapped Antihydrogen
Charlton, Michael
2017-04-01
For more than a decade antihydrogen atoms have been formed by mixing antiprotons and positrons held in arrangements of charged particle (Penning) traps. More recently, magnetic minimum neutral atom traps have been superimposed upon the anti-atom production region, promoting the trapping of a small quantity of the antihydrogen yield. We will review these advances, and describe some of the first physics experiments performed on anrtihydrogen including the observation of the two-photon 1S-2S transition, invesigation of the charge neutrailty of the anti-atom and studies of the ground state hyperfine splitting. We will discuss the physics motivations for undertaking these experiments and describe some near-future initiatives.
Optimal Selective Harmonic Control for Power Harmonics Mitigation
DEFF Research Database (Denmark)
Zhou, Keliang; Yang, Yongheng; Blaabjerg, Frede
2015-01-01
of power harmonics. The proposed optimal SHC is of hybrid structure: all recursive SHC modules with weighted gains are connected in parallel. It bridges the real “nk+-m order RC” and the complex “parallel structure RC”. Compared to other IMP based control solutions, it offers an optimal trade-off among...
Excitation of high numbers harmonics by flows of oscillators in a periodic potential
International Nuclear Information System (INIS)
Buts, V.A.; Marekha, V.I.; Tolstoluzhsky, A.P.
2005-01-01
It is shown that the maximum of radiation spectrum of nonrelativistic oscillators, which move into a periodically inhomogeneous potential, can be in the region of high numbers harmonics. Spectrum of such oscillators radiation becomes similar to the radiation spectrum of relativistic oscillators. The equations, describing the non-linear self-consistent theory of excitations, of high numbers harmonics by ensemble of oscillators are formulated and its numerical analysis is conducted. The numerical analysis has confirmed the capability of radiation of high numbers of harmonics. Such peculiarity of radiation allows t expect of creation of nonrelativistic FEL
Propagation effects in the generation process of high-order vortex harmonics.
Zhang, Chaojin; Wu, Erheng; Gu, Mingliang; Liu, Chengpu
2017-09-04
We numerically study the propagation of a Laguerre-Gaussian beam through polar molecular media via the exact solution of full-wave Maxwell-Bloch equations where the rotating-wave and slowly-varying-envelope approximations are not included. It is found that beyond the coexistence of odd-order and even-order vortex harmonics due to inversion asymmetry of the system, the light propagation effect results in the intensity enhancement of a high-order vortex harmonics. Moreover, the orbital momentum successfully transfers from the fundamental laser driver to the vortex harmonics which topological charger number is directly proportional to its order.
Probabilistic Harmonic Modeling of Wind Power Plants
DEFF Research Database (Denmark)
Guest, Emerson; Jensen, Kim H.; Rasmussen, Tonny Wederberg
2017-01-01
A probabilistic sequence domain (SD) harmonic model of a grid-connected voltage-source converter is used to estimate harmonic emissions in a wind power plant (WPP) comprised of Type-IV wind turbines. The SD representation naturally partitioned converter generated voltage harmonics into those...... with deterministic phase and those with probabilistic phase. A case study performed on a string of ten 3MW, Type-IV wind turbines implemented in PSCAD was used to verify the probabilistic SD harmonic model. The probabilistic SD harmonic model can be employed in the planning phase of WPP projects to assess harmonic...
Ibrahim, Yehia M.; Smith, Richard D.
2016-01-26
An ion trap device is disclosed. The device includes a series of electrodes that define an ion flow path. A radio frequency (RF) field is applied to the series of electrodes such that each electrode is phase shifted approximately 180 degrees from an adjacent electrode. A DC voltage is superimposed with the RF field to create a DC gradient to drive ions in the direction of the gradient. A second RF field or DC voltage is applied to selectively trap and release the ions from the device. Further, the device may be gridless and utilized at high pressure.
Classical region of a trapped Bose gas
Energy Technology Data Exchange (ETDEWEB)
Blakie, P Blair [Jack Dodd Centre for Photonics and Ultra-Cold Atoms, University of Otago, Dunedin (New Zealand); Davis, Matthew J [ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, QLD 4072 (Australia)
2007-06-14
The classical region of a Bose gas consists of all single particle modes that have a high average occupation and are well described by a classical field. Highly occupied modes only occur in massive Bose gases at ultra-cold temperatures, in contrast to the photon case where there are highly occupied modes at all temperatures. For the Bose gas the number of these modes is dependent on the temperature, the total number of particles and their interaction strength. In this paper, we characterize the classical region of a harmonically trapped Bose gas over a wide parameter regime. We use a Hartree-Fock approach to account for the effects of interactions, which we observe to significantly change the classical region as compared to the idealized case. We compare our results to full classical field calculations and show that the Hartree-Fock approach provides a qualitatively accurate description of a classical region for the interacting gas.
FDTD for Hydrodynamic Electron Fluid Maxwell Equations
Directory of Open Access Journals (Sweden)
Yingxue Zhao
2015-05-01
Full Text Available In this work, we develop a numerical method for solving the three dimensional hydrodynamic electron fluid Maxwell equations that describe the electron gas dynamics driven by an external electromagnetic wave excitation. Our numerical approach is based on the Finite-Difference Time-Domain (FDTD method for solving the Maxwell’s equations and an explicit central finite difference method for solving the hydrodynamic electron fluid equations containing both electron density and current equations. Numerical results show good agreement with the experiment of studying the second-harmonic generation (SHG from metallic split-ring resonator (SRR.
International Nuclear Information System (INIS)
Faghihi-Nik, M.; Ghorbanalilu, M.; Shokri, B.
2010-01-01
Complete text of publication follows. Generation of harmonic radiation is an important subject of laser plasma interaction and attracts great attention due to a wide range of applications. It has been seen that intense electromagnetic and quasi-static transverse magnetic fields are generated in laser plasma interaction. An extremely intense magnetic field (up to hundreds of MG) has been observed by experimental measurements in interaction of short laser pulses with plasma. These self-generated or applied magnetic fields affect the propagation of the laser pulses. In most laser interactions with homogeneous plasma, odd harmonics of laser frequency are generated. In this paper, we point out the possibility of even harmonics generation when a linearly polarized laser beam propagates in homogeneous plasma in the presence of a transverse magnetic field. It is shown that applying external field induces a transverse current density oscillating twice of the laser field which leds to generation of second harmonic radiation. This current density is derived using the perturbation method, and the steady state amplitude of the second harmonic obtained by solution of the wave equation. By the same procedure the current density and then the steady state amplitude of higher order harmonics are calculated. The efficiency of harmonic generation (the ratio of harmonic power to incident power) is a drastically function of the strength of external magnetic field. It is found that the efficiency of even harmonics is zero in the absence of magnetic field and increases as the magnetic field is increased. For odd harmonics, applying the external magnetic field enhances the generated harmonics as well. The conversion efficiency also increases with increase in plasma density and intensity of the laser beam.
Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling
DEFF Research Database (Denmark)
Marchukov, O. V.; Fedorov, D. V.; Jensen, A. S.
2015-01-01
We investigate a two-dimensional system of fermions with two internal (spin) degrees of freedom. It is confined by a deformed harmonic trap and subject to a Zeeman field, Rashba or Dresselhaus one-body spin-orbit couplings and two-body short range repulsion. We obtain self-consistent mean-field $N...
Real-Time Dynamics of an Impurity in an Ideal Bose Gas in a Trap
DEFF Research Database (Denmark)
Volosniev, A. G.; Hammer, H. -W.; Zinner, N. T.
2015-01-01
We investigate the behavior of a harmonically trapped system consisting of an impurity in a dilute ideal Bose gas after the boson-impurity interaction is suddenly switched on. As theoretical framework, we use a field theory approach in the space-time domain within the T-matrix approximation. We...
Design of the LC+trap filter for a current source rectifier
DEFF Research Database (Denmark)
Min, Huang; Wang, Xiongfei; Loh, Poh Chiang
2015-01-01
This paper investigates an LC + trap filter for current source converters to improve the switching harmonic attenuation. The resonant frequency characteristics of the filter of current source rectifier are analyzed. A filter design procedure is proposed based on the input power factor, filter...
López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.
2012-08-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.
International Nuclear Information System (INIS)
López-Ruiz, F F; Guerrero, J; Aldaya, V; Cossío, F
2012-01-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.
Harmonic structures and intrinsic torsion
DEFF Research Database (Denmark)
Conti, Diego; Madsen, Thomas Bruun
We discuss the construction of 8-manifolds with harmonic Sp(2)Sp(1)-structures. In particular, we find 10 new examples of nilmanifolds that admit a closed 4-form Omega whose stabiliser is Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough...
Harmonic oscillator in Snyder space
Indian Academy of Sciences (India)
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual ...
Conformal invariance in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1985-01-01
N=2 conformal supersymmetry is realized in harmonic superspace, its peculiarities are analyzed. The coordinate group and analytical prepotentials for N=2 conformal supergravity are found. A new version of the N=2 Einstein supergravity with infinite number of auxiliary fields is suggested. A hypermultiplet without central charges and constraints is used as a compensator
Sums of Generalized Harmonic Series
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 9. Sums of Generalized Harmonic Series: For Kids from Five to Fifteen. Zurab Silagadze. General Article Volume 20 Issue 9 September 2015 pp 822-843. Fulltext. Click here to view fulltext PDF. Permanent link:
Coupled harmonic oscillators and their quantum entanglement
Makarov, Dmitry N.
2018-04-01
A system of two coupled quantum harmonic oscillators with the Hamiltonian H ̂=1/2 (1/m1p̂1 2+1/m2p̂2 2+A x12+B x22+C x1x2) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H ̂Ψ =i ℏ ∂/Ψ ∂ t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.
International Nuclear Information System (INIS)
Menou, Kristen
2013-01-01
Although tidally locked habitable planets orbiting nearby M-dwarf stars are among the best astronomical targets to search for extrasolar life, they may also be deficient in volatiles and water. Climate models for this class of planets show atmospheric transport of water from the dayside to the nightside, where it is precipitated as snow and trapped as ice. Since ice only slowly flows back to the dayside upon accumulation, the resulting hydrological cycle can trap a large amount of water in the form of nightside ice. Using ice sheet dynamical and thermodynamical constraints, I illustrate how planets with less than about a quarter the Earth's oceans could trap most of their surface water on the nightside. This would leave their dayside, where habitable conditions are met, potentially dry. The amount and distribution of residual liquid water on the dayside depend on a variety of geophysical factors, including the efficiency of rock weathering at regulating atmospheric CO 2 as dayside ocean basins dry up. Water-trapped worlds with dry daysides may offer similar advantages as land planets for habitability, by contrast with worlds where more abundant water freely flows around the globe
Directory of Open Access Journals (Sweden)
Eduarda Gomes
2014-06-01
In order to minimise the identified problems in the actual traps, the present work proposes a new design with the aim of reducing the volume and weight during transport, and also during onshore storage. Alternative materials to avoid corrosion and formation of encrustations were also proposed.
Energy Technology Data Exchange (ETDEWEB)
Menou, Kristen [Department of Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027 (United States)
2013-09-01
Although tidally locked habitable planets orbiting nearby M-dwarf stars are among the best astronomical targets to search for extrasolar life, they may also be deficient in volatiles and water. Climate models for this class of planets show atmospheric transport of water from the dayside to the nightside, where it is precipitated as snow and trapped as ice. Since ice only slowly flows back to the dayside upon accumulation, the resulting hydrological cycle can trap a large amount of water in the form of nightside ice. Using ice sheet dynamical and thermodynamical constraints, I illustrate how planets with less than about a quarter the Earth's oceans could trap most of their surface water on the nightside. This would leave their dayside, where habitable conditions are met, potentially dry. The amount and distribution of residual liquid water on the dayside depend on a variety of geophysical factors, including the efficiency of rock weathering at regulating atmospheric CO{sub 2} as dayside ocean basins dry up. Water-trapped worlds with dry daysides may offer similar advantages as land planets for habitability, by contrast with worlds where more abundant water freely flows around the globe.
Lenore White Harmon: One Woman's Career Development.
Fouad, Nadya A.
1997-01-01
Presents biographical information on Lenore White Harmon, noted professor, counselor, and researcher. In a question-and-answer section, Harmon describes her early career decisions, work history, research efforts, professional contributions, important influences and reflections on her career development. (KW)
Tides and tidal harmonics at Umbharat, Gujarat
Digital Repository Service at National Institute of Oceanography (India)
Suryanarayana, A.; Swamy, G.N.
A part of the data on tides recorded at Machiwada near Umbharat, Gulf of Cambay during April 1978 was subjected to harmonic analysis following the Admiralty procedure. The general tidal characteristics and the value of four major harmonic...
Difference equations in massive higher order calculations
International Nuclear Information System (INIS)
Bierenbaum, I.; Bluemlein, J.; Klein, S.; Schneider, C.
2007-07-01
The calculation of massive 2-loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter N. We report on the solution of these sums through higher order difference equations using the summation package Sigma. (orig.)
On fictitious domain formulations for Maxwell's equations
DEFF Research Database (Denmark)
Dahmen, W.; Jensen, Torben Klint; Urban, K.
2003-01-01
We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Omega) derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic formu...
Transmit beamforming for optimal second-harmonic generation.
Hoilund-Kaupang, Halvard; Masoy, Svein-Erik
2011-08-01
A simulation study of transmit ultrasound beams from several transducer configurations is conducted to compare second-harmonic imaging at 3.5 MHz and 11 MHz. Second- harmonic generation and the ability to suppress near field echoes are compared. Each transducer configuration is defined by a chosen f-number and focal depth, and the transmit pressure is estimated to not exceed a mechanical index of 1.2. The medium resembles homogeneous muscle tissue with nonlinear elasticity and power-law attenuation. To improve computational efficiency, the KZK equation is utilized, and all transducers are circular-symmetric. Previous literature shows that second-harmonic generation is proportional to the square of the transmit pressure, and that transducer configurations with different transmit frequencies, but equal aperture and focal depth in terms of wavelengths, generate identical second-harmonic fields in terms of shape. Results verify this for a medium with attenuation f1. For attenuation f1.1, deviations are found, and the high frequency subsequently performs worse than the low frequency. The results suggest that high frequencies are less able to suppress near-field echoes in the presence of a heterogeneous body wall than low frequencies.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Synchrotron radiation and absorption at electron cyclotron harmonics in inhomogeneous plasmas
International Nuclear Information System (INIS)
Hu, Jian-Long.
1993-01-01
In order to understand fully the absorption, emission and conversion phenomena for any electron cyclotron harmonic, one must include all relevant mode conversion processes and a finite parallel wave number k parallel . Relativistic plasma mode conversion and tunneling equations at the second and third electron cyclotron harmonics have been derived analytically. A finite k parallel has been introduced which keeps the coupling between the O-mode, the X-mode and the Bernstein wave in the mode conversion problems without absorption have been obtained, and the connection formulas between different wave branches have been established. The corresponding transmission, reflection and conversion coefficients have also been given. Mode conversion problem at any harmonic has been generalized to either a three branch or a five branch problem. A comparison between the coupled equation and the uncoupled equation has been made. The effort has been directed at the third harmonic since the adsorption at ω = 2ω ce is known to be very strong in virtually every fusion case. Both the low density limit and the high density limit cases have been studied separately. The relativistic effects on the mode conversion and absorption problem has been analyzed. The mode conversion equation with absorption has been solved by using the Green function method. The electron cyclotron emission experiments have already begun at 3ω ce , and the third harmonic is the first nontrivial case of importance
Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation
Cardoso, Wesley B.; Salasnich, Luca; Malomed, Boris A.
2017-05-01
We study effects of tight harmonic-oscillator confinement on the electromagnetic field in a laser cavity by solving the two-dimensional Lugiato-Lefever (2D LL) equation, taking into account self-focusing or defocusing nonlinearity, losses, pump, and the trapping potential. Tightly confined (quasi-zero-dimensional) optical modes (pixels), produced by this model, are analyzed by means of the variational approximation, which provides a qualitative picture of the ensuing phenomena. This is followed by systematic simulations of the time-dependent 2D LL equation, which reveal the shape, stability, and dynamical behavior of the resulting localized patterns. In this way, we produce stability diagrams for the expected pixels. Then, we consider the LL model with the vortical pump, showing that it can produce stable pixels with embedded vorticity (vortex solitons) in remarkably broad stability areas. Alongside confined vortices with the simple single-ring structure, in the latter case the LL model gives rise to stable multi-ring states, with a spiral phase field. In addition to the numerical results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Analysis of the main dosimetric peak of Al2O3:C compounds with a model of interacting traps
International Nuclear Information System (INIS)
Ortega, F.; Marcazzó, J.; Molina, P.; Santiago, M.; Lester, M.; Henniger, J.; Caselli, E.
2013-01-01
The glow curve of Al 2 O 3 :C compounds has been analyzed by employing a model consisting of two active traps, thermally disconnected traps and one recombination centre. The analysis takes into account interaction among traps and the thermal quenching of the thermoluminescent emission. - Highlights: • Glow curves of Al 2 O 3 :C for two doses have been analysed taking into account interactions among traps. • The system of differential equations describing the kinetics has been uncoupled. • The new system of equations takes into account equations without derivatives. • The algorithm used will not become stiff. • The kinetics parameters obtained do not depend on the dose
Evidence of the 2s2p(1P) doubly excited state in the harmonic generation spectrum of helium
International Nuclear Information System (INIS)
Ngoko Djiokap, J. M.; Starace, Anthony F.
2011-01-01
By solving the two-active-electron time-dependent Schroedinger equation in an intense, ultrashort laser field, we investigate evidence of electron correlations in the high-order harmonic generation spectrum of helium. As the frequency of the driving laser pulse varies from 4.6 to 6.6 eV, the 13th, 11th, and 9th harmonics sequentially become resonant with the transition between the ground state and the isolated 2s2p( 1 P) autoionizing state of helium, which dramatically enhances these harmonics and changes their profiles. When each of the 9th and 13th harmonics are in resonance with this autoionizing state, there is also a low-order multiphoton resonance with a Rydberg state, resulting in a particularly large enhancement of these harmonics relative to neighboring harmonics. When the 11th harmonic is in resonance with the 2s2p( 1 P) autoionizing state, the 13th harmonic is simultaneously in resonance with numerous higher-energy autoionizing states, resulting in a competition between these two harmonics for intensity. These results demonstrate that even electron correlations occurring over a narrow energy interval can have a significant effect on strong-field processes such as harmonic generation.
A Penning trap for advanced studies with particles in extreme laser fields
International Nuclear Information System (INIS)
Vogel, M.; Quint, W.; Paulus, G.G.; Stöhlker, Th.
2012-01-01
We present a Penning trap as a tool for advanced studies of particles in extreme laser fields. Particularly, trap-specific manipulation techniques allow control over the confined particles’ localization and spatial density by use of trap electrodes as ‘electrostatic tweezers’ and by application of a ‘rotating wall’, respectively. It is thereby possible to select and prepare well-defined ion ensembles and to optimize the laser–particle interaction. Non-destructive detection of reaction educts and products with up to single-ion sensitivity supports advanced studies by maintaining the products for further studies at extended confinement times of minutes and above. The trap features endcaps with conical openings for applications with strongly focused lasers. We show that such a modification of a cylindrical trap is possible while harmonicity and tunability are maintained.
A Penning trap for advanced studies with particles in extreme laser fields
Vogel, M.; Quint, W.; Paulus, G. G.; Stöhlker, Th.
2012-08-01
We present a Penning trap as a tool for advanced studies of particles in extreme laser fields. Particularly, trap-specific manipulation techniques allow control over the confined particles' localization and spatial density by use of trap electrodes as 'electrostatic tweezers' and by application of a 'rotating wall', respectively. It is thereby possible to select and prepare well-defined ion ensembles and to optimize the laser-particle interaction. Non-destructive detection of reaction educts and products with up to single-ion sensitivity supports advanced studies by maintaining the products for further studies at extended confinement times of minutes and above. The trap features endcaps with conical openings for applications with strongly focused lasers. We show that such a modification of a cylindrical trap is possible while harmonicity and tunability are maintained.
Harmonic disturbance location by applying Bayesian inference
Ye, G.; Xiang, Y.; Cuk, V.; Cobben, J.F.G.
2016-01-01
Harmonic pollution is one of the most important power quality issues in electric power systems. Correct location of the main harmonic disturbance source is a key step to solve the problem. This paper presents a method to detect the location of harmonic disturbance source in low voltage network
Detection of Harmonic Occurring using Kalman Filtering
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar; Shoro, Ghulam Mustafa; Imran, Raja Muhammed
2014-01-01
/current characteristic. These harmonics are not to be allowed to grow beyond a certain limit to avoid any grave consequence to the customer’s main supply. Filters can be implemented at the power source or utility location to eliminate these harmonics. In this paper we detect the instance at which these harmonics occur...
Third Harmonic Imaging using a Pulse Inversion
DEFF Research Database (Denmark)
Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt
2011-01-01
The pulse inversion (PI) technique can be utilized to separate and enhance harmonic components of a waveform for tissue harmonic imaging. While most ultrasound systems can perform pulse inversion, only few image the 3rd harmonic component. PI pulse subtraction can isolate and enhance the 3rd...
[Trapping techniques for Solenopsis invicta].
Liang, Xiao-song; Zhang, Qiang; Zhuang, Yiong-lin; Li, Gui-wen; Ji, Lin-peng; Wang, Jian-guo; Dai, Hua-guo
2007-06-01
A field study was made to investigate the trapping effects of different attractants, traps, and wind directions on Solenopsis invicta. The results showed that among the test attractants, TB1 (50 g fishmeal, 40 g peptone, 10 ml 10% sucrose water solution and 20 ml soybean oil) had the best effect, followed by TB2 (ham), TB6 (100 g cornmeal and 20 ml soybean oil) and TB4 (10 ml 10% sucrose water solution, 100 g sugarcane powder and 20 ml soybean oil), with a mean capture efficiency being 77.6, 58.7, 29 and 7.7 individuals per trap, respectively. No S. invicta was trapped with TB3 (10 ml 10% sucrose water solution, 100 g cornmeal and 20 ml soybean oil) and TB5 (honey). Tube trap was superior to dish trap, with a trapping efficiency of 75.2 and 35 individuals per trap, respectively. The attractants had better effects in leeward than in windward.
Optical trapping of gold aerosols
DEFF Research Database (Denmark)
Schmitt, Regina K.; Pedersen, Liselotte Jauffred; Taheri, S. M.
2015-01-01
Aerosol trapping has proven challenging and was only recently demonstrated.1 This was accomplished by utilizing an air chamber designed to have a minimum of turbulence and a laser beam with a minimum of aberration. Individual gold nano-particles with diameters between 80 nm and 200 nm were trapped...... in air using a 1064 nm laser. The positions visited by the trapped gold nano-particle were quantified using a quadrant photo diode placed in the back focal plane. The time traces were analyzed and the trapping stiffness characterizing gold aerosol trapping determined and compared to aerosol trapping...... of nanometer sized silica and polystyrene particles. Based on our analysis, we concluded that gold nano-particles trap more strongly in air than similarly sized polystyrene and silica particles. We found that, in a certain power range, the trapping strength of polystyrene particles is linearly decreasing...
Accurate calculation of high harmonics generated by relativistic Thomson scattering
International Nuclear Information System (INIS)
Popa, Alexandru
2008-01-01
The recent emergence of the field of ultraintense laser pulses, corresponding to beam intensities higher than 10 18 W cm -2 , brings about the problem of the high harmonic generation (HHG) by the relativistic Thomson scattering of the electromagnetic radiation by free electrons. Starting from the equations of the relativistic motion of the electron in the electromagnetic field, we give an exact solution of this problem. Taking into account the Lienard-Wiechert equations, we obtain a periodic scattered electromagnetic field. Without loss of generality, the solution is strongly simplified by observing that the electromagnetic field is always normal to the direction electron-detector. The Fourier series expansion of this field leads to accurate expressions of the high harmonics generated by the Thomson scattering. Our calculations lead to a discrete HHG spectrum, whose shape and angular distribution are in agreement with the experimental data from the literature. Since no approximations were made, our approach is also valid in the ultrarelativistic regime, corresponding to intensities higher than 10 23 W cm -2 , where it predicts a strong increase of the HHG intensities and of the order of harmonics. In this domain, the nonlinear Thomson scattering could be an efficient source of hard x-rays
3-D spherical harmonics code FFT3 by the finite Fourier transformation method
International Nuclear Information System (INIS)
Kobayashi, K.
1997-01-01
In the odd order spherical harmonics method, the rigorous boundary condition at the material interfaces is that the even moments of the angular flux and the normal components of the even order moments of current vectors must be continuous. However, it is difficult to derive spatial discretized equations by the finite difference or finite element methods, which satisfy this material interface condition. It is shown that using the finite Fourier transformation method, space discretized equations which satisfy this interface condition can be easily derived. The discrepancies of the flux distribution near void region between spherical harmonics method codes may be due to the difference of application of the material interface condition. (author)
A Method for Harmonic Sources Detection based on Harmonic Distortion Power Rate
Lin, Ruixing; Xu, Lin; Zheng, Xian
2018-03-01
Harmonic sources detection at the point of common coupling is an essential step for harmonic contribution determination and harmonic mitigation. The harmonic distortion power rate index is proposed for harmonic source location based on IEEE Std 1459-2010 in the paper. The method only based on harmonic distortion power is not suitable when the background harmonic is large. To solve this problem, a threshold is determined by the prior information, when the harmonic distortion power is larger than the threshold, the customer side is considered as the main harmonic source, otherwise, the utility side is. A simple model of public power system was built in MATLAB/Simulink and field test results of typical harmonic loads verified the effectiveness of proposed method.
Particle Trapping and Dropouts in Magnetic Turbulence in a Spherical Geometry
Tooprakai, P.; Ruffolo, D.; Matthaeus, W. H.; Chuychai, P.
2006-12-01
The observed dropouts of solar energetic particles from impulsive solar events (i.e., the inhomogeneity and sharp gradients in particle density) indicate the partial filamentation of magnetic connection from small regions of the corona to Earth orbit. This can be understood in terms of persistent trapping of field lines due to small- scale topological structures in the solar wind. We further explore how this turbulence structure should be manifest in particle observations, by evaluating particle trajectories obtained from the Newton-Lorentz equations. By adapting a two-component model of turbulence to spherical geometry, we include the adiabatic focusing of particles. The 2D magnetic field is generated by either 1) a 2D fast Fourier transform, a valid approximation over a small angular region, or 2) a spherical harmonic series with ℓ up to 2000. Dropout features at 1 AU are clearly indicated for low-energy particles, but these features are washed out for E >~ 100 MeV. Different time-intensity profiles are found at locations at 1 AU that are distinct with regard to the small-scale topology. Partially supported by the Thailand Research Fund, the Rachadapisek Sompoj Fund of Chulalongkorn University, and NASA Grant NNG05GG83G.
International Nuclear Information System (INIS)
Capuzzi, P.; Minguzzi, A.; Tosi, M.P.
2004-01-01
We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies s-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface (n=0) modes which are essentially unaffected by the interactions
International Nuclear Information System (INIS)
Hammoudeh, S.; Madan, V.
1994-01-01
In order to examine the implications of the weakening of OPEC's responsiveness in adjusting its production levels, this paper explicitly incorporates rigidity in the quantity adjustment mechanism, thereby extending previous research which assumed smooth quantity adjustments. The rigidity is manifested in a tolerance range for the discrepancy between the declared target price and that of the market. This environment gives rise to a 'tolerance trap' which impedes the convergence process and inevitably brings the market to a standstill before its reaches the targeted price and revenue objectives. OPEC's reaction to the standstill has important implications for the achievement of the target-based equilibrium and for the potential collapse of the market price. This paper examines OPEC's policy options in the tolerance trap and reveals that the optional policy in order to break this impasse and move closer to the equilibrium point is gradually to reduce output and not to flood the market. (Author)
Energy Technology Data Exchange (ETDEWEB)
Maunz, Peter Lukas Wilhelm
2017-04-01
Qubits can be encoded in clock states of trapped ions. These states are well isolated from the environment resulting in long coherence times [1] while enabling efficient high-fidelity qubit interactions mediated by the Coulomb coupled motion of the ions in the trap. Quantum states can be prepared with high fidelity and measured efficiently using fluorescence detection. State preparation and detection with 99.93% fidelity have been realized in multiple systems [1,2]. Single qubit gates have been demonstrated below rigorous fault-tolerance thresholds [1,3]. Two qubit gates have been realized with more than 99.9% fidelity [4,5]. Quantum algorithms have been demonstrated on systems of 5 to 15 qubits [6–8].
Harmonic Detection at Initialization With Kalman Filter
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar; Imran, Raja Muhammad; Shoro, Ghulam Mustafa
2014-01-01
Most power electronic equipment these days generate harmonic disturbances, these devices hold nonlinear voltage/current characteristic. The harmonics generated can potentially be harmful to the consumer supply. Typically, filters are integrated at the power source or utility location to filter out...... the affect of harmonics on the supply. For the detection of these harmonics various techniques are available and one of that technique is the Kalman filter. In this paper we investigate that what are the consequences when harmonic detection system based on Kalman Filtering is initialized...
Waveguide harmonic damper for klystron amplifier
International Nuclear Information System (INIS)
Kang, Y.
1998-01-01
A waveguide harmonic damper was designed for removing the harmonic frequency power from the klystron amplifiers of the APS linac. Straight coaxial probe antennas are used in a rectangular waveguide to form a damper. A linear array of the probe antennas is used on a narrow wall of the rectangular waveguide for damping klystron harmonics while decoupling the fundamental frequency in dominent TE 01 mode. The klystron harmonics can exist in the waveguide as waveguide higher-order modes above cutoff. Computer simulations are made to investigate the waveguide harmonic damping characteristics of the damper
Harmonic space and quaternionic manifolds
International Nuclear Information System (INIS)
Galperin, A.; Ogievetsky, O.; Ivanov, E.
1992-10-01
A principle of harmonic analyticity underlying the quaternionic (quaternion-Kaehler) geometry is found, and the differential constraints which define this geometry are solved. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. An one-to-one correspondence is established between the quaternionic spaces and off-shell N=2 supersymmetric sigma-models coupled to N=2 supergravity. Coordinates of the analytic subspace are identified with superfields describing N=2 matter hypermultiplets and a compensating hypermultiplet of N=2 supergravity. As an illustration the potentials for the symmetric quaternionic spaces are presented. (K.A.) 22 refs
Data harmonization and model performance
The Joint Committee on Urban Storm Drainage of the International Association for Hydraulic Research (IAHR) and International Association on Water Pollution Research and Control (IAWPRC) was formed in 1982. The current committee members are (no more than two from a country): B. C. Yen, Chairman (USA); P. Harremoes, Vice Chairman (Denmark); R. K. Price, Secretary (UK); P. J. Colyer (UK), M. Desbordes (France), W. C. Huber (USA), K. Krauth (FRG), A. Sjoberg (Sweden), and T. Sueishi (Japan).The IAHR/IAWPRC Joint Committee is forming a Task Group on Data Harmonization and Model Performance. One objective is to promote international urban drainage data harmonization for easy data and information exchange. Another objective is to publicize available models and data internationally. Comments and suggestions concerning the formation and charge of the Task Group are welcome and should be sent to: B. C. Yen, Dept. of Civil Engineering, Univ. of Illinois, 208 N. Romine St., Urbana, IL 61801.
Ion Motion Stability in Asymmetric Surface Electrode Ion Traps
Shaikh, Fayaz; Ozakin, Arkadas
2010-03-01
Many recently developed designs of the surface electrode ion traps for quantum information processing have asymmetry built into their geometries. The asymmetry helps rotate the trap axes to angles with respect to electrode surface that facilitate laser cooling of ions but introduces a relative angle between the RF and DC fields and invalidates the classical stability analysis of the symmetric case for which the equations of motion are decoupled. For asymmetric case the classical motion of a single ion is given by a coupled, multi-dimensional version of Mathieu's equation. In this poster we discuss the stability diagram of asymmetric surface traps by performing an approximate multiple scale perturbation analysis of the coupled Mathieu equations, and validate the results with numerical simulations. After obtaining the stability diagram for the linear fields, we simulate the motion of an ion in a given asymmetric surface trap, utilizing a method-of-moments calculation of the electrode fields. We obtain the stability diagram and compare it with the ideal case to find the region of validity. Finally, we compare the results of our stability analysis to experiments conducted on a microfabricated asymmetric surface trap.
Time-dependent coupled harmonic oscillators: classical and quantum solutions
International Nuclear Information System (INIS)
Macedo, D.X.; Guedes, I.
2014-01-01
In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m 1 = m 2 = m 0 e γt , ω 1 = ω 01 e -γt/2 , ω 2 = ω 02 e -γt/2 and k = k 0 . (author)
Variational and perturbative schemes for a spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Estevez, G.A.; Guardiola, R.
1989-01-01
A variational analysis of the spiked harmonic-oscillator Hamiltonian operator -d 2 /dx 2 + x 2 + l(l+1)/x 2 + λ |x| -α , where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schroedinger equation for the linear harmonic-oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provides accurate approximations for the ground-state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large-coupling pertubative-expansion is carried out and the contributions up to fourth order to the ground-state energy are explicitly evaluated. Numerical results are compared for the special case α=5/2. (author) [pt
Soliton ratchetlike dynamics by ac forces with harmonic mixing
DEFF Research Database (Denmark)
Salerno, Mario; Zolotaryuk, Yaroslav
2002-01-01
The possibility of unidirectional motion of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least biharmonic) and of zero mean, is presented. The dependence of the kink mean velocity on system parameters is investigated...... numerically and the results are compared with a perturbation analysis based on a point-particle representation of the soliton. We find that first order perturbative calculations lead to incomplete descriptions, due to the important role played by the soliton-phonon interaction in establishing the phenomenon...... in the system. Effective soliton transport is achieved when the internal mode and the external force get phase locked. We find that for kinks driven by biharmonic drivers consisting of the superposition of a fundamental driver with its first odd harmonic, the transport arises only due to this internal mode...
Harmonic oscillator on a lattice
International Nuclear Information System (INIS)
Ader, J.P.; Bonnier, B.; Hontebeyrie, M.; Meyers, C.
1983-01-01
The continuum limit of the ground state energy for the harmonic oscillator with discrete time is derived for all possible choices of the lattice derivative. The occurrence of unphysical values is shown to arise whenever the lattice laplacian is not strictly positive on its Brillouin zone. These undesirable limits can either be finite and arbitrary (multiple spectrum) or infinite (overlapping sublattices with multiple spectrum). (orig.)
Harmonic ratcheting for fast acceleration
Cook, N.; Brennan, J. M.; Peggs, S.
2014-04-01
A major challenge in the design of rf cavities for the acceleration of medium-energy charged ions is the need to rapidly sweep the radio frequency over a large range. From low-power medical synchrotrons to high-power accelerator driven subcritical reactor systems, and from fixed focus alternating gradient accelerators to rapid cycling synchrotrons, there is a strong need for more efficient, and faster, acceleration of protons and light ions in the semirelativistic range of hundreds of MeV/u. A conventional way to achieve a large, rapid frequency sweep (perhaps over a range of a factor of 6) is to use custom-designed ferrite-loaded cavities. Ferrite rings enable the precise tuning of the resonant frequency of a cavity, through the control of the incremental permeability that is possible by introducing a pseudoconstant azimuthal magnetic field. However, rapid changes over large permeability ranges incur anomalous behavior such as the "Q-loss" and "f-dot" loss phenomena that limit performance while requiring high bias currents. Notwithstanding the incomplete understanding of these phenomena, they can be ameliorated by introducing a "harmonic ratcheting" acceleration scheme in which two or more rf cavities take turns accelerating the beam—one turns on when the other turns off, at different harmonics—so that the radio frequency can be constrained to remain in a smaller range. Harmonic ratcheting also has straightforward performance advantages, depending on the particular parameter set at hand. In some typical cases it is possible to halve the length of the cavities, or to double the effective gap voltage, or to double the repetition rate. This paper discusses and quantifies the advantages of harmonic ratcheting in general. Simulation results for the particular case of a rapid cycling medical synchrotron ratcheting from harmonic number 9 to 2 show that stability and performance criteria are met even when realistic engineering details are taken into consideration.
Harmonic Lattice Dynamics of Germanium
Energy Technology Data Exchange (ETDEWEB)
Nelin, G
1974-07-01
The phonon dispersion relations of the DELTA-, LAMBDA-, and SIGMA-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field.
Harmonic Lattice Dynamics of Germanium
International Nuclear Information System (INIS)
Nelin, G.
1974-01-01
The phonon dispersion relations of the Δ-, Λ-, and Σ-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field
Representation Discovery using Harmonic Analysis
Mahadevan, Sridhar
2008-01-01
Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu
Symplectic tomography of nonclassical states of trapped ion
International Nuclear Information System (INIS)
Man'ko, O.
1996-03-01
The marginal distribution for two types of nonclassical states of trapped ion - for squeezed and correlated states and for squeezed even and odd coherent states (squeezed Schroedinger cat states) is studied. The obtained marginal distribution for the two types of states is shown to satisfy classical dynamical equation equivalent to standard quantum evolution equation for density matrix (wave function) derived in symplectic tomography scheme. (author). 20 refs
Sediment Trapping in Estuaries
Burchard, Hans; Schuttelaars, Henk M.; Ralston, David K.
2018-01-01
Estuarine turbidity maxima (ETMs) are generated by a large suite of hydrodynamic and sediment dynamic processes, leading to longitudinal convergence of cross-sectionally integrated and tidally averaged transport of cohesive and noncohesive suspended particulate matter (SPM). The relative importance of these processes for SPM trapping varies substantially among estuaries depending on topography, fluvial and tidal forcing, and SPM composition. The high-frequency dynamics of ETMs are constrained by interactions with the low-frequency dynamics of the bottom pool of easily erodible sediments. Here, we use a transport decomposition to present processes that lead to convergent SPM transport, and review trapping mechanisms that lead to ETMs at the landward limit of the salt intrusion, in the freshwater zone, at topographic transitions, and by lateral processes within the cross section. We use model simulations of example estuaries to demonstrate the complex concurrence of ETM formation mechanisms. We also discuss how changes in SPM trapping mechanisms, often caused by direct human interference, can lead to the generation of hyperturbid estuaries.
Trapping time statistics and efficiency of transport of optical excitations in dendrimers
Heijs, D.J.; Malyshev, V.A.; Knoester, J.
2004-01-01
We theoretically study the trapping time distribution and the efficiency of the excitation energy transport in dendritic systems. Trapping of excitations, created at the periphery of the dendrimer, on a trap located at its core, is used as a probe of the efficiency of the energy transport across the dendrimer. The transport process is treated as incoherent hopping of excitations between nearest-neighbor dendrimer units and is described using a rate equation. We account for radiative and non-r...
Expansion into lattice harmonics in cubic symmetries
Kontrym-Sznajd, G.
2018-05-01
On the example of a few sets of sampling directions in the Brillouin zone, this work shows how important the choice of the cubic harmonics is on the quality of approximation of some quantities by a series of such harmonics. These studies led to the following questions: (1) In the case that for a given l there are several independent harmonics, can one use in the expansion only one harmonic with a given l?; (2) How should harmonics be ordered: according to l or, after writing them in terms of (x4 + y4 + z4)n (x2y2z2)m, according to their degree q = n + m? To enable practical applications of such harmonics, they are constructed in terms of the associated Legendre polynomials up to l = 26. It is shown that electron momentum densities, reconstructed from experimental data for ErGa3 and InGa3, are described much better by harmonics ordered with q.
Complex harmonic modal analysis of rotor systems
International Nuclear Information System (INIS)
Han, Dong Ju
2015-01-01
Complex harmonic analysis for rotor systems has been proposed from the strict complex modal analysis based upon Floquet theory. In this process the harmonic balance method is adopted, effectively associated with conventional eigenvalue analysis. Also, the harmonic coefficients equivalent to dFRFs in harmonic mode has been derived in practice. The modes are classified from identifying the modal characteristics, and the adaptation of harmonic balance method has been proven by comparing the results of the stability analyses from Floque theory and the eigen analysis. The modal features of each critical speed are depicted in quantitatively and qualitatively by showing that the strengths of each component of the harmonic coefficients are estimated from the order of magnitude analysis according to their harmonic patterns. This effectiveness has been verified by comparing with the numerical solutions
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Electromagnetic radiation trapped in the magnetosphere above the plasma frequency
Gurnett, D. A.; Shaw, R. R.
1973-01-01
An electromagnetic noise band is frequently observed in the outer magnetosphere by the Imp 6 spacecraft at frequencies from about 5 to 20 kHz. This noise band generally extends throughout the region from near the plasmapause boundary to near the magnetopause boundary. The noise typically has a broadband field strength of about 5 microvolts/meter. The noise band often has a sharp lower cutoff frequency at about 5 to 10 kHz, and this cutoff has been identified as the local electron plasma frequency. Since the plasma frequency in the plasmasphere and solar wind is usually above 20 kHz, it is concluded that this noise must be trapped in the low-density region between the plasmapause and magnetopause boundaries. The noise bands often contain a harmonic frequency structure which suggests that the radiation is associated with harmonics of the electron cyclotron frequency.
Diffusion and trapping of positive muons in niobium
International Nuclear Information System (INIS)
Boekema, C.; Heffner, R.H.; Hutson, R.L.; Leon, M.; Schillaci, M.E.; Kossler, W.J.; Numan, M.; Dodds, S.A.
1982-01-01
Using zero- and longitudinal-field muon spin relaxation, the conventional interpretation of the ''double-humped'' behavior of the μ + -depolarization rate in Nb has been established unambiguously. Thus the μ + mobility is shown to increase monotonically with temperature. The widths of the magnetic field distributions (due to the Nb nuclear moments) and the rates for finding or escaping from traps have been measured at several temperatures. In addition, equations are presented which govern the time evolution of the μ + polarization, when the muons are finding traps, escaping from traps, or both, for zero, longitudinal, and transverse external magnetic fields. A method for including the effect of more than one kind of trap acting at a particular temperature is given
Diffusion and trapping of positive muons in niobium
International Nuclear Information System (INIS)
Boekema, C.; Heffner, R.H.; Hutson, R.L.; Leon, M.; Schillaci, M.E.; Kossler, W.J.; Numan, M.; Dodds, S.A.
1982-01-01
Using zero- and longitudinal-field μSR, the conventional interpretation of the double-humped behavior of the μ + -depolarization rate in Nb has been established unambiguously. Thus the μ + mobility is shown to increase monotonically with temperature. The widths of the magnetic field distributions (due to the Nb nuclear moments) and the rates for finding or escaping from traps have been measured at several temperatures. In addition, equations are presented which govern the time-evolution of the μ + polarization, when the muons are finding traps, escaping from traps, or both, for zero, longitudinal, and transverse external magnetic fields. A method for including the effect of more than one kind of trap acting at a particular temperature is given
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Evaluation of chromatic cues for trapping Bactrocera tau.
Li, Lei; Ma, Huabo; Niu, Liming; Han, Dongyin; Zhang, Fangping; Chen, Junyu; Fu, Yueguan
2017-01-01
Trapping technology based on chromatic cues is an important strategy in controlling Tephritidae (fruit flies). The objectives of this present study were to evaluate the preference of Bactrocera tau for different chromatic cues, and to explore an easy method to print and reproduce coloured paper. Chromatic cues significantly affected the preference of adult B. tau. Wavelengths in the 515-604 nm range were the suitable wavelengths for trapping B. tau. Different-day-old B. tau had different colour preferences. Virtual wavelengths of 595 nm (yellow) and 568 nm (yellowish green) were the optimum wavelengths for trapping 5-7-day-old B. tau and 30-32-day-old B. tau respectively. The trap type and height significantly influenced B. tau attraction efficiency. The number of B. tau on coloured traps hung perpendicular to plant rows was not significantly higher than the number on traps hung parallel to plant rows. The quantisation of colour on the basis of Bruton's wavelength to RGB function can serve as an alternative method for printing and reproducing coloured paper, but a corrected equation should be established between the theoretical wavelength and actual wavelength of coloured paper. Results show that a compound paper coloured yellow (595 nm) and yellowish green (568 nm) installed at 60 and 90 cm above the ground shows the maximum effect for trapping B. tau. © 2016 Society of Chemical Industry. © 2016 Society of Chemical Industry.
Homoclinic chaos in the discrete self-trapping trimer
DEFF Research Database (Denmark)
Hennig, D.; Gabriel, H.; Jørgensen, Michael Finn
1995-01-01
We study the discrete self-trapping (DST) equation with three degrees of freedom. By taking the DST dimer as the underlying unperturbed system we treat the coupling to the additional oscillator as a small perturbation. Using the generalized Melnikov method we prove the existence of homoclinic chaos...
An extension of the multiple-trapping model
International Nuclear Information System (INIS)
Shkilev, V. P.
2012-01-01
The hopping charge transport in disordered semiconductors is considered. Using the concept of the transport energy level, macroscopic equations are derived that extend a multiple-trapping model to the case of semiconductors with both energy and spatial disorders. It is shown that, although both types of disorder can cause dispersive transport, the frequency dependence of conductivity is determined exclusively by the spatial disorder.
Nonlinear trapped electron mode and anomalous heat transport in tokamaks
International Nuclear Information System (INIS)
Kaw, P.K.
1982-01-01
We take the phenomenological point of view that the anomalous electron thermal conductivity produced by the non-linear trapped electron mode should also influence the stability properties of the mode itself. Using a model equation, we show that this effect makes the mode self-stabilizing. A simple expression for the anomalous thermal conductivity is derived, and its scaling properties are discussed. (orig.)
Trapping time statistics and efficiency of transport of optical excitations in dendrimers
Heijs, Dirk-Jan; Malyshev, Victor A.; Knoester, Jasper
2004-09-01
We theoretically study the trapping time distribution and the efficiency of the excitation energy transport in dendritic systems. Trapping of excitations, created at the periphery of the dendrimer, on a trap located at its core, is used as a probe of the efficiency of the energy transport across the dendrimer. The transport process is treated as incoherent hopping of excitations between nearest-neighbor dendrimer units and is described using a rate equation. We account for radiative and nonradiative decay of the excitations while diffusing across the dendrimer. We derive exact expressions for the Laplace transform of the trapping time distribution and the efficiency of trapping, and analyze those for various realizations of the energy bias, number of dendrimer generations, and relative rates for decay and hopping. We show that the essential parameter that governs the trapping efficiency is the product of the on-site excitation decay rate and the trapping time (mean first passage time) in the absence of decay.
Third order harmonic imaging for biological tissues using three phase-coded pulses.
Ma, Qingyu; Gong, Xiufen; Zhang, Dong
2006-12-22
Compared to the fundamental and the second harmonic imaging, the third harmonic imaging shows significant improvements in image quality due to the better resolution, but it is degraded by the lower sound pressure and signal-to-noise ratio (SNR). In this study, a phase-coded pulse technique is proposed to selectively enhance the sound pressure of the third harmonic by 9.5 dB whereas the fundamental and the second harmonic components are efficiently suppressed and SNR is also increased by 4.7 dB. Based on the solution of the KZK nonlinear equation, the axial and lateral beam profiles of harmonics radiated from a planar piston transducer were theoretically simulated and experimentally examined. Finally, the third harmonic images using this technique were performed for several biological tissues and compared with the images obtained by the fundamental and the second harmonic imaging. Results demonstrate that the phase-coded pulse technique yields a dramatically cleaner and sharper contrast image.
On bunch lengthening using the fourth harmonic cavity in the NSLS VUV ring
International Nuclear Information System (INIS)
Wachtel, J.M.
1988-02-01
It has been suggested that the phase of the beam excited voltage in the harmonic cavity can be controlled by detuning its resonant frequency from the beam current harmonic. Unfortunately the detuning needed to flatten the acceleration waveform also corresponds to the region of Robinson instability for the harmonic cavity. Therefore, lengthening the bunch may be followed by large amplitude synchrotron oscillation of the bunch center of mass. Bunch lengthening is discussed in this note from several points of view. There follows a simple review of single electron oscillations in a quartic potential. Then equations are developed for the coupled oscillations of a cavity and a rigid bunch as a fully nonlinear, time dependent initial value problem. Next, a computer program that solves these equations for one, two or more cavities, with and without externally driven fields, is described and some simulations of the harmonic cavity interaction are shown. Finally, the fully nonlinear equations are linearized to derive a dispersion relation for the case of beam excitation in the harmonic cavity. 6 refs., 5 figs
Covariant quantization of the d=4 Brink-Schwarz superparticle using Lorentz harmonics
International Nuclear Information System (INIS)
Zima, V.G.; Fedoryuk, S.A.
1995-01-01
Covariant first and second quantizations of the free d=4 massless superparticle are implemented with the introduction of purely gauge auxiliary spinor Lorentz harmonics. It is shown that the general solution of the condition of masslessness is a sum of two independent chiral superfields with each of them corresponding to finite superspin. A translationally covariant, in general bijective correspondence between harmonic and massless superfields is constructed. By calculation of the commutation function it is shown that in the considered approach only harmonic fields with the correct connection between spin and statistics and with integer negative homogeneity index satisfy the microcausality condition. It is emphasized that the harmonic fields that arise are reducible at integer points. The index spinor technique is used to describe infinite-component fields of finite spin; the equations of motion of such fields are obtained, and for them Weinberg's theorem on the connection between massless helicity particles and the type of nongauge field that describes them is generalized
On stochastic differential equations with random delay
International Nuclear Information System (INIS)
Krapivsky, P L; Luck, J M; Mallick, K
2011-01-01
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an nth-order equation with random delay, the corresponding deterministic equation has order n + 1. We analyze various examples of dynamical systems of this kind, and find a number of unusual behaviors. For instance, for the harmonic oscillator with random delay, the energy grows as exp((3/2) t 2/3 ) in reduced units. We then investigate the effect of introducing a discrete time step ε. At variance with the continuous situation, the discrete random recursion relations thus obtained have intrinsic fluctuations. The crossover between the fluctuating discrete problem and the deterministic continuous one as ε goes to zero is studied in detail on the example of a first-order linear differential equation
Pseudodifferential equations over non-Archimedean spaces
Zúñiga-Galindo, W A
2016-01-01
Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applica...
Lekala, M. L.; Chakrabarti, B.; Das, T. K.; Rampho, G. J.; Sofianos, S. A.; Adam, R. M.; Haldar, S. K.
2017-05-01
We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (˜ 3) to very large (˜ 10^7) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter C6. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.
Second harmonic generation in a bounded magnetoplasma
International Nuclear Information System (INIS)
Thomas, D.G.
1975-01-01
An experimental study of second harmonic generation in a magnetized plasma contained in a cylindrical cavity resonator shows how the harmonic power varies with fundamental power, background gas pressure, and magnetization. Two cavities were designed. For each the TM010 resonance was in the S-band and the TM011 resonance in the C-band. Both frequencies were harmonically related when the d.c. discharge sustaining the plasma was adjusted to give plasma frequencies of approximately 0.7 GHz and 1.53 GHz. The experimental results show the harmonic power approximately proportional to the square of the fundamental power from 5 to 100 mw, and a decreasing function of pressure from 10 to 150 millitorr. Experiments at constant plasma frequency and varying magnetic field from 0 to 3000 Gauss show a sharp drop in harmonic power to undetectable levels when the electron cyclotron frequency approximates either the fundamental or second harmonic frequencies. These effects are attributed, respectively, to the coupling of fundamental power to other modes and to cavity detuning away from the harmonic. With the plasma frequency adjusted to maintain simultaneous resonance of fundamental and harmonic, a harmonic signal maximum occurred when the upper hybrid frequency approximated the harmonic frequency. Several anomalies, apparently related to the magnetization, background gas, and electron density distribution were observed. Otherwise, the results are qualitatively consistent with the first order theory for a cold, collisional plasma
Stable Trapping of Multielectron Helium Bubbles in a Paul Trap
Joseph, E. M.; Vadakkumbatt, V.; Pal, A.; Ghosh, A.
2017-06-01
In a recent experiment, we have used a linear Paul trap to store and study multielectron bubbles (MEBs) in liquid helium. MEBs have a charge-to-mass ratio (between 10^{-4} and 10^{-2} C/kg) which is several orders of magnitude smaller than ions (between 10^6 and 10^8 C/kg) studied in traditional ion traps. In addition, MEBs experience significant drag force while moving through the liquid. As a result, the experimental parameters for stable trapping of MEBs, such as magnitude and frequency of the applied electric fields, are very different from those used in typical ion trap experiments. The purpose of this paper is to model the motion of MEBs inside a linear Paul trap in liquid helium, determine the range of working parameters of the trap, and compare the results with experiments.
Trapped Fermions with Density Imbalance in the Bose-Einstein Condensate Limit
International Nuclear Information System (INIS)
Pieri, P.; Strinati, G.C.
2006-01-01
We analyze the effects of imbalancing the populations of two-component trapped fermions, in the Bose-Einstein condensate limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we derive a set of coupled equations that describe composite bosons and excess fermions. We include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths. The coupled equations are then solved in the Thomas-Fermi approximation to obtain the density profiles for composite bosons and excess fermions, which are relevant to the recent experiments with trapped fermionic atoms
Energy Technology Data Exchange (ETDEWEB)
Lu, Z.-T.; Bailey, K.; Chen, C.-Y.; Du, X.; Li, Y.-M.; O' Connor, T. P.; Young, L.
2000-05-25
A new method of ultrasensitive trace-isotope analysis has been developed based upon the technique of laser manipulation of neutral atoms. It has been used to count individual {sup 85}Kr and {sup 81}Kr atoms present in a natural krypton sample with isotopic abundances in the range of 10{sup {minus}11} and 10{sup {minus}13}, respectively. The atom counts are free of contamination from other isotopes, elements,or molecules. The method is applicable to other trace-isotopes that can be efficiently captured with a magneto-optical trap, and has a broad range of potential applications.
International Nuclear Information System (INIS)
Lu, Z.-T.; Bailey, K.; Chen, C.-Y.; Du, X.; Li, Y.-M.; O'Connor, T. P.; Young, L.
2000-01-01
A new method of ultrasensitive trace-isotope analysis has been developed based upon the technique of laser manipulation of neutral atoms. It has been used to count individual 85 Kr and 81 Kr atoms present in a natural krypton sample with isotopic abundances in the range of 10 -11 and 10 -13 , respectively. The atom counts are free of contamination from other isotopes, elements,or molecules. The method is applicable to other trace-isotopes that can be efficiently captured with a magneto-optical trap, and has a broad range of potential applications
High-order harmonic propagation in gases within the discrete dipole approximation
International Nuclear Information System (INIS)
Hernandez-Garcia, C.; Perez-Hernandez, J. A.; Ramos, J.; Jarque, E. Conejero; Plaja, L.; Roso, L.
2010-01-01
We present an efficient approach for computing high-order harmonic propagation based on the discrete dipole approximation. In contrast with other approaches, our strategy is based on computing the total field as the superposition of the driving field with the field radiated by the elemental emitters of the sample. In this way we avoid the numerical integration of the wave equation, as Maxwell's equations have an analytical solution for an elementary (pointlike) emitter. The present strategy is valid for low-pressure gases interacting with strong fields near the saturation threshold (i.e., partially ionized), which is a common situation in the experiments of high-order harmonic generation. We use this tool to study the dependence of phase matching of high-order harmonics with the relative position between the beam focus and the gas jet.
Symmetries of the quantum damped harmonic oscillator
International Nuclear Information System (INIS)
Guerrero, J; López-Ruiz, F F; Aldaya, V; Cossío, F
2012-01-01
For the non-conservative Caldirola–Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg–Weyl algebra can be found. The inclusion of the standard time evolution generator (which is not a symmetry) as a symmetry in this algebra, in a unitary manner, requires a non-trivial extension of this basic algebra and hence of the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman dual system, which now includes a new particle acting as an energy reservoir. In addition, the Caldirola–Kanai dissipative system can be retrieved by imposing constraints. The algebra of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schrödinger equation. As opposed to other approaches, where it is claimed that the spectrum of the Bateman Hamiltonian is complex and discrete, we obtain that it is real and continuous, with infinite degeneracy in all regimes. (paper)
Magnetic traps with a sperical separatrix: Tornado traps
International Nuclear Information System (INIS)
Peregood, B.P.; Lehnert, B.
1979-11-01
A review is given on the features of magnetic traps with a spherical separatrix, with special emphesis on Tornado spiral coil configurations. The confinement and heating of static plasmas in Tornado traps is treated, including the topology of the magnetic field structure, the magneto-mechanical properties of the magnetic coil system, as well as the particle orbits and plasma behaviour in these traps. In additio, the mode of rotating plasma operation by crossed electric and magnetic fields is being described. The results of experiments on static and rotating plasmas are summarized, and conclusions are drawn about future possibilities of Tornado traps for the creation and containment of hot plasmas. (author)
Magnetic traps with a spherical separatrix: Tornado traps
International Nuclear Information System (INIS)
Peregood, B.P.; Lehnert, B.
1981-01-01
A review is given on the features of magnetic traps with a spherical separatrix, with special emphasis on Tornado spiral coil configurations. The confinement and heating of static plasms in Tornado traps is treated, including the topology of the magnetic field structure, the magneto-mechanical properties of the magnetic coil system, as well as the particle orbits and plasma behaviour in these traps. In addition, the mode of rotating plasma operation by crossed electric and magnetic fields is described. The results of experiments on static and rotating plasmas are summarized, and conclusions are drawn about future possibilities of Tornado traps in the creation and containment of hot plasmas. (orig.)
Characteristics of trapped electrons and electron traps in single crystals
International Nuclear Information System (INIS)
Budzinski, E.E.; Potter, W.R.; Potienko, G.; Box, H.C.
1979-01-01
Two additional carbohydrates are reported whose crystal structures trap electrons intermolecularly in single crystals x irradiated at low temperature, namely sucrose and rhamnose. Five carbohydrate and polyhydroxy compounds are now known which exhibit this phenomenon. The following characteristics of the phenomenon were investigated: (1) the hyperfine couplings of the electron with protons of the polarized hydroxy groups forming the trap; (2) the distances between these protons and the trapped electron; (3) the spin density of the electron at the protons and (4) the relative stabilities of the electron trapped in various crystal structures
Nuclear pharmacy education: international harmonization
International Nuclear Information System (INIS)
Shaw, S.M.; Cox, P.H.
1998-01-01
Education of nuclear pharmacists exists in many countries around the world. The approach and level of education varies between countries depending upon the expectations of the nuclear pharmacist, the work site and the economic environment. In Australia, training is provided through distance learning. In Europe and Canada, nuclear pharmacists and radiochemists receive postgraduate education in order to engage in the small-scale preparation and quality control of radiopharmaceuticals as well as research and development. In the U.S.A., nuclear pharmacy practitioners obtain basic knowledge primarily through undergraduate programs taken when pursuit the first professional degree in pharmacy. Licensed practitioners in pharmacy enter the practice of nuclear pharmacy through distance learning programs or short courses. While different approaches to education exist, there is a basic core of knowledge and a level of competence required of all nuclear pharmacists and radiochemists providing radiopharmaceutical products and services. It was with this realization that efforts were initiated to develop harmonization concepts and documents pertaining to education in nuclear pharmacy. The benefits of international harmonization in nuclear pharmacy education are numerous. Assurance of the availability of quality professionals to provide optimal products and care to the patient is a principle benefit. Spanning national barriers through the demonstration of self governance and unification in education will enhance the goal of increased freedom of employment between countries. Harmonization endeavors will improve existing education programs through sharing of innovative concepts and knowledge between educators. Documents generated will benefit new educational programs especially in developing nations. A committee on harmonization in nuclear pharmacy education was formed consisting of educators and practitioners from the international community. A working document on education was
The Harmonics of Kansei Images
DEFF Research Database (Denmark)
Su, Jianning; Restrepo-Giraldo, John Dairo
2008-01-01
sensibility it elicits on a person (kansei), is a key factor in the design of tools to support designers in delivering the right product’s appearance. This paper presents an approach to mathematically represent a product’s kansei based on the frequency signature (harmonics) of a shape. This mathematical...... representation should allow the automatic indexing and retrieval of images from a repository of design precedents. This is done through a series of experiments aiming at determining the relation between images, kansei words and the frequency signatures of those images. Tests suggest the method is promising...... and can be used for indexing images in Content Based Image Retrieval Systems....
An improved filtered spherical harmonic method for transport calculations
International Nuclear Information System (INIS)
Ahrens, C.; Merton, S.
2013-01-01
Motivated by the work of R. G. McClarren, C. D. Hauck, and R. B. Lowrie on a filtered spherical harmonic method, we present a new filter for such numerical approximations to the multi-dimensional transport equation. In several test problems, we demonstrate that the new filter produces results with significantly less Gibbs phenomena than the filter used by McClarren, Hauck and Lowrie. This reduction in Gibbs phenomena translates into propagation speeds that more closely match the correct propagation speed and solutions that have fewer regions where the scalar flux is negative. (authors)
Classical dynamics of triatomic system: energized harmonic molecules
International Nuclear Information System (INIS)
Parr, C.A.; Kuppermann, A.; Porter, R.N.
1976-01-01
The dynamical assumptions underlying the Slater and RRK classical-mechanical theories of unimolecular reaction rates are investigated. The predictions of these theories for several nonlinear, triatomic, harmonically-bonded molecular models are compared with the results obtained from the integration of the classical equations of motion. The accuracy of the small-vibration and weak-coupling assumptions are found to break down at energies above about one quarter of a bond dissociation energy. Nonetheless, the small-vibration approximation predicts reaction frequencies in good agreement with the exact results for the models. The effects of rotation on intramolecular energy exchange are examined and found to be significant
Spectra of electron pair under harmonic and Debye potential
Energy Technology Data Exchange (ETDEWEB)
Munjal, D. [Department of Physics and Astrophysics, University of Delhi (India); Department of Physics, Swami Shraddhanand College, University of Delhi (India); Prasad, V. [Department of Physics, Swami Shraddhanand College, University of Delhi (India)
2017-02-15
Two electron systems confined by harmonic potential is known as harmonium. Such a system has been studied for many reasons in the literature. In this work we study harmonium under Debye potential. We use higher order finite difference method for the solution of Schrodinger equation. Complete energy spectrum of harmonium and harmonium under Debye potential is studied. Debye screening length shows considerable effect on the energy levels and the radial matrix elements. The results are analysed in the light of existing results and the comparison with available results shows remarkable agreement. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Multiphoton excitation and high-harmonics generation in topological insulator.
Avetissian, H K; Avetissian, A K; Avchyan, B R; Mkrtchian, G F
2018-05-10
Multiphoton interaction of coherent electromagnetic radiation with 2D metallic carriers confined on the surface of the 3D topological insulator is considered. A microscopic theory describing the nonlinear interaction of a strong wave and metallic carriers with many-body Coulomb interaction is developed. The set of integrodifferential equations for the interband polarization and carrier occupation distribution is solved numerically. Multiphoton excitation of Fermi-Dirac sea of 2D massless carriers is considered for a THz pump wave. It is shown that in the moderately strong pump wave field along with multiphoton interband/intraband transitions the intense radiation of high harmonics takes place.
Elementary derivation of the quantum propagator for the harmonic oscillator
Shao, Jiushu
2016-10-01
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.
Multiphoton excitation and high-harmonics generation in topological insulator
Avetissian, H. K.; Avetissian, A. K.; Avchyan, B. R.; Mkrtchian, G. F.
2018-05-01
Multiphoton interaction of coherent electromagnetic radiation with 2D metallic carriers confined on the surface of the 3D topological insulator is considered. A microscopic theory describing the nonlinear interaction of a strong wave and metallic carriers with many-body Coulomb interaction is developed. The set of integrodifferential equations for the interband polarization and carrier occupation distribution is solved numerically. Multiphoton excitation of Fermi–Dirac sea of 2D massless carriers is considered for a THz pump wave. It is shown that in the moderately strong pump wave field along with multiphoton interband/intraband transitions the intense radiation of high harmonics takes place.
The pseudo-harmonics method applied to depletion calculation
International Nuclear Information System (INIS)
Silva, F.C. da; Amaral, J.A.C.; Thome, Z.D.
1989-01-01
In this paper, a new method for performing depletion calculations, based on the use of the Pseudo-Harmonics perturbation method, was developed. The fuel burnup was considered as a global perturbation and the multigroup difusion equations were rewriten in such a way as to treat the soluble boron concentration as the eigenvalue. By doing this, the critical boron concentration can be obtained by a perturbation method. A test of the new method was performed for a H 2 O-colled, D 2 O-moderated reactor. Comparison with direct calculation showed that this method is very accurate and efficient. (author) [pt
Integrability of N=3 super Yang-Mills equations
International Nuclear Information System (INIS)
Devchand, C.; Ogievetsky, V.
1993-10-01
We describe the harmonic superspace formulation of the Witten-Manin supertwistor correspondence for N=3 extended super Yang-Mills theories. The essence in that on being sufficiently supersymmetrised (up to the N=3 extension), the Yang-Mills equations of motion can be recast in the form of Cauchy-Riemann-like holomorphicity conditions for a pair of prepotentials in the appropriate harmonic superspace. This formulation makes the explicit construction of solutions a rather more tractable proposition than previous attempts. (orig.)
The spherical harmonics method, 1 (general development of the theory)
International Nuclear Information System (INIS)
Mark, C.
1957-02-01
A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle Ψ(→/r, →/Ω) in spherical harmonic tensors formed from →/Ω the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density Ψ (o) (r). This equation has the form where the numbers ν i depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of Ψ(→/r, →/Ω) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of Ψ(→/r, →/Ω) which we retain be continuous; and this determines the constants in the solution for Ψ (o) (→/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)
The spherical harmonics method, 1 (general development of the theory)
Energy Technology Data Exchange (ETDEWEB)
Mark, C
1957-02-15
A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle {Psi}({yields}/r, {yields}/{Omega}) in spherical harmonic tensors formed from {yields}/{Omega} the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density {Psi}{sup (o)}(r). This equation has the form where the numbers {nu}{sub i} depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of {Psi}({yields}/r, {yields}/{Omega}) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of {Psi}({yields}/r, {yields}/{Omega}) which we retain be continuous; and this determines the constants in the solution for {Psi}{sup (o)}({yields}/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)
ATRAP - Progress Towards Trapped Antihydrogen
International Nuclear Information System (INIS)
Grzonka, D.; Goldenbaum, F.; Oelert, W.; Sefzick, T.; Zhang, Z.; Comeau, D.; Hessels, E.A.; Storry, C.H.; Gabrielse, G.; Larochelle, P.; Lesage, D.; Levitt, B.; Speck, A.; Haensch, T.W.; Pittner, H.; Walz, J.
2005-01-01
The ATRAP experiment at the CERN antiproton decelerator AD aims for a test of the CPT invariance by a high precision comparison of the 1s-2s transition in the hydrogen and the antihydrogen atom.Antihydrogen production is routinely operated at ATRAP and detailed studies have been performed in order to optimize the production efficiency of useful antihydrogen.For high precision measurements of atomic transitions cold antihydrogen in the ground state is required which must be trapped due to the low number of available antihydrogen atoms compared to the cold hydrogen beam used for hydrogen spectroscopy. To ensure a reasonable antihydrogen trapping efficiency a magnetic trap has to be superposed the nested Penning trap. First trapping tests of charged particles within a combined magnetic/Penning trap have started at ATRAP
ATRAP Progress Towards Trapped Antihydrogen
Grzonka, D; Gabrielse, G; Goldenbaum, F; Hänsch, T W; Hessels, E A; Larochelle, P; Le Sage, D; Levitt, B; Oelert, W; Pittner, H; Sefzick, T; Speck, A; Storry, C H; Walz, J; Zhang, Z
2005-01-01
The ATRAP experiment at the CERN antiproton decelerator AD aims for a test of the CPT invariance by a high precision comparison of the 1s‐2s transition in the hydrogen and the antihydrogen atom. Antihydrogen production is routinely operated at ATRAP and detailed studies have been performed in order to optimize the production efficiency of useful antihydrogen. For high precision measurements of atomic transitions cold antihydrogen in the ground state is required which must be trapped due to the low number of available antihydrogen atoms compared to the cold hydrogen beam used for hydrogen spectroscopy. To ensure a reasonable antihydrogen trapping efficiency a magnetic trap has to be superposed the nested Penning trap. First trapping tests of charged particles within a combined magnetic/Penning trap have started at ATRAP.
Coherent states for the time dependent harmonic oscillator: the step function
International Nuclear Information System (INIS)
Moya-Cessa, Hector; Fernandez Guasti, Manuel
2003-01-01
We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for a continuous treatment that differs from former studies that involve the matching of two time independent solutions at the time when the step occurs
Quantum properties of transverse pattern formation in second-harmonic generation
DEFF Research Database (Denmark)
Bache, Morten; Scotto, P.; Zambrini, R.
2002-01-01
these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold...
Hermitian harmonic maps into convex balls
International Nuclear Information System (INIS)
Li Zhenyang; Xi Zhang
2004-07-01
In this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is compact Hermitian manifold with non-empty boundary. The case where the domain manifold is complete(noncompact) is also studied. (author)
Calibration of optically trapped nanotools
Energy Technology Data Exchange (ETDEWEB)
Carberry, D M; Simpson, S H; Grieve, J A; Hanna, S; Miles, M J [H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Wang, Y; Schaefer, H; Steinhart, M [Institute for Chemistry, University of Osnabrueck, Osnabrueck (Germany); Bowman, R; Gibson, G M; Padgett, M J, E-mail: m.j.miles@bristol.ac.uk [SUPA, Department of Physics and Astronomy, University of Glasgow, Science Road, Glasgow G12 8QQ (United Kingdom)
2010-04-30
Holographically trapped nanotools can be used in a novel form of force microscopy. By measuring the displacement of the tool in the optical traps, the contact force experienced by the probe can be inferred. In the following paper we experimentally demonstrate the calibration of such a device and show that its behaviour is independent of small changes in the relative position of the optical traps. Furthermore, we explore more general aspects of the thermal motion of the tool.
Introduction to classical and quantum harmonic oscillators
Bloch, Sylvan C
2013-01-01
From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con
Optical traps with geometric aberrations
International Nuclear Information System (INIS)
Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G.
2006-01-01
We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems
Experimental and numerical investigation of tissue harmonic imaging (THI)
Jing, Yuan; Yang, Xinmai; Cleveland, Robin O.
2003-04-01
In THI the probing ultrasonic pulse has enough amplitude that it undergoes nonlinear distortion and energy shifts from the fundamental frequency of the pulse into its higher harmonics. Images generated from the second harmonic (SH) have superior quality to the images formed from the fundamental frequency. Experiments with a single element focused ultrasound transducer were used to compare a line target embedded in a tissue phantom using either fundamental or SH imaging. SH imaging showed an improvement in both the axial resolution (0.70 mm vs 0.92 mm) and the lateral resolution (1.02 mm vs 2.70 mm) of the target. In addition, the contrast-to-tissue ratio of the target was 2 dB higher with SH imaging. A three-dimensional model of the forward propagation has been developed to simulate the experimental system. The model is based on a time-domain code for solving the KZK equation and accounts for arbitrary spatial variations in all tissue properties. The code was used to determine the impact of a nearfield layer of fat on the fundamental and second harmonic signals. For a 15 mm thick layer the SH side-lobes remained the same but the fundamental side-lobes increased by 2 dB. [Work supported by the NSF through the Center for Subsurface Sensing and Imaging Systems.
Foam flow in a model porous medium: II. The effect of trapped gas.
Jones, S A; Getrouw, N; Vincent-Bonnieu, S
2018-05-09
Gas trapping is an important mechanism in both Water or Surfactant Alternating Gas (WAG/SAG) and foam injection processes in porous media. Foams for enhanced oil recovery (EOR) can increase sweep efficiency as they decrease the gas relative permeability, and this is mainly due to gas trapping. However, gas trapping mechanisms are poorly understood. Some studies have been performed during corefloods, but little work has been carried out to describe the bubble trapping behaviour at the pore scale. We have carried out foam flow tests in a micromodel etched with an irregular hexagonal pattern. Image analysis of the foam flow allowed the bubble centres to be tracked and local velocities to be obtained. It was found that the flow in the micromodel is dominated by intermittency and localized zones of trapped gas. The quantity of trapped gas was measured both by considering the fraction of bubbles that were trapped (via velocity thresholding) and by measuring the area fraction containing immobile gas (via image analysis). A decrease in the quantity of trapped gas was observed for both increasing total velocity and increasing foam quality. Calculations of the gas relative permeability were made with the Brooks Corey equation, using the measured trapped gas saturations. The results showed a decrease in gas relative permeabilities, and gas mobility, for increasing fractions of trapped gas. It is suggested that the shear thinning behaviour of foam could be coupled to the saturation of trapped gas.
Gap solitons in elongated geometries: The one-dimensional Gross-Pitaevskii equation and beyond
International Nuclear Information System (INIS)
Mateo, A. Munoz; Delgado, V.; Malomed, Boris A.
2011-01-01
We report results of a systematic analysis of matter-wave gap solitons (GSs) in three-dimensional self-repulsive Bose-Einstein condensates (BECs) loaded into a combination of a cigar-shaped trap and axial optical-lattice (OL) potential. Basic cases of the strong, intermediate, and weak radial (transverse) confinement are considered, as well as settings with shallow and deep OL potentials. Only in the case of the shallow lattice combined with tight radial confinement, which actually has little relevance to realistic experimental conditions, does the usual one-dimensional (1D) cubic Gross-Pitaevskii equation (GPE) furnish a sufficiently accurate description of GSs. However, the effective 1D equation with the nonpolynomial nonlinearity, derived in Ref. [Phys. Rev. A 77, 013617 (2008)], provides for quite an accurate approximation for the GSs in all cases, including the situation with weak transverse confinement, when the soliton's shape includes a considerable contribution from higher-order transverse modes, in addition to the usual ground-state wave function of the respective harmonic oscillator. Both fundamental GSs and their multipeak bound states are considered. The stability is analyzed by means of systematic simulations. It is concluded that almost all the fundamental GSs are stable, while their bound states may be stable if the underlying OL potential is deep enough.
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
A live-trap and trapping technique for fossorial mammals
African Journals Online (AJOL)
mammals. G.C. Hickman. An effective live-trap was designed for Cryptomys hottentotus .... that there is an animal in the burrow system, and to lessen the likelihood of the .... the further testing and modification of existing trap types. Not only is it ...