Exact solution of the classical mechanical quadratic Zeeman effect
Indian Academy of Sciences (India)
Sambhu N Datta; Anshu Pandey
2007-06-01
We address the curious problem of quadratic Zeeman effect at the classical mechanical level. The problem has been very well understood for decades, but an analytical solution of the equations of motion is still to be found. This state of affairs persists because the simultaneous presence of the Coulombic and quadratic terms lowers the dynamical symmetry. Energy and orbital angular momentum are still constants of motion. We find the exact solutions by introducing the concept of an image ellipse. The quadratic effect leads to a dilation of space–time, and a one-to-one correspondence is observed for pairs of physical quantities like energy and angular momentum, and the maximum and minimum distances from the Coulomb center for the Zeeman orbit and the corresponding pairs for the image ellipse. Thus, instead of finding additional conserved quantities, we find constants of motion for an additional dynamics, namely, the image problem. The trajectory is open, in agreement with Bertrand's theorem, but necessarily bound. A stable unbound trajectory does not exist for real values of energy and angular momentum. The radial distance, the angle covered in the plane of the orbit, and the time are uniquely determined by introducing further the concept of an image circle. While the radial distance is defined in a closed form as a transcendental function of the image-circular angle, the corresponding orbit angle and time variables are found in the form of two convergent series expansions. The latter two variables are especially contracted, thereby leading to a precession of the open cycles around the Coulomb center. It is expected that the space–time dilation effect observed here would somehow influence the solution of the quantum mechanical problem at the non-relativistic level.
High resolution spectra of novae and the quadratic zeeman effect
Directory of Open Access Journals (Sweden)
Robert Williams
2006-01-01
Full Text Available Los espectros de alta resoluci on de novas despu es de las erupciones revelan caracter sticas distintivas en los per les e intensidades de las l neas. Las l neas de Balmer m as altas son frecuentemente m as anchas que los miembros m as bajos de la serie, y los per les e intensidades relativos del doblete [O I] 6300, 6364 di eren de los valores normales. Nosotros sugerimos que estos aspectos pueden ser producidos por el efecto cuadr atico Zeeman desde campos magn eticos que exceden B=106 gauss. Tomadas juntas, las l neas de emisi on y absorci on indican m ultiples or genes para los materiales expulsados, tanto en las enanas blancas eruptivas como en las estrellas secundarias fr as.
McGuyer, B H; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T
2013-01-01
Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold $^{88}$Sr$_2$ molecules near the intercombination line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to fourth-order contributions and to nearby opposite $f$-parity states, and provide a stringent test of a state-of-the-art ab initio model.
Quadratic Zeeman effect and spin-lattice relaxation of Tm$^{3+}$:YAG at high magnetic fields
Veissier, Lucile; Lutz, Thomas; Barclay, Paul E; Tittel, Wolfgang; Cone, Rufus L
2016-01-01
Anisotropy of the quadratic Zeeman effect for the $^3{\\rm H}_6 \\rightarrow \\, ^3{\\rm H}_4$ transition at 793 nm wavelength in $^{169}$Tm$^{3+}$-doped Y$_3$Al$_5$O$_{12}$ is studied, revealing shifts ranging from near zero up to + 4.69 GHz/T$^2$ for ions in magnetically inequivalent sites. This large range of shifts is used to spectrally resolve different subsets of ions and study nuclear spin relaxation as a function of temperature, magnetic field strength, and orientation in a site-selective manner. A rapid decrease in spin lifetime is found at large magnetic fields, revealing the weak contribution of direct-phonon absorption and emission to the nuclear spin-lattice relaxation rate. We furthermore confirm theoretical predictions for the phonon coupling strength, finding much smaller values than those estimated in the limited number of past studies of thulium in similar crystals. Finally, we observe a significant -- and unexpected -- magnetic field dependence of the two-phonon Orbach spin relaxation process a...
Mott-insulator phases of spin-3/2 fermions in the presence of quadratic Zeeman coupling
Rodriguez, K.; Argueelles, A.; Colome-Tatche, M.; Vekua, T.; Santos, L.
2010-01-01
We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2) circle times SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotro
The Zeeman effect in stellar spectra
Romanyuk, I. I.
A short biography of Pieter Zeeman is presented. The main formulae for the normal, anomalous, quadratic Zeeman effects and Paschen-Back effect are given. Instrumentation for Zeeman effect measurements in stellar spectra is described, the most important scientific achievements in magnetic stars investigations with the world's largest telescopes for 50 years are demonstrated. The devices for magnetic measurements made at SAO and the main results of stellar magnetic observations obtained with the 6 m telescope are described in detail.
Zeeman Effect in Ruby at High Pressures
Dan, Ioana
2012-02-01
We have developed a versatile fiber-coupled system for magneto-optical spectroscopy measurements at high pressure. The system is based on a miniature Cu-alloy Diamond Anvil Cell (from D'Anvils, Ltd) fitted with a custom-designed He gas-actuated membrane for in-situ pressure control, and coupled with a He transfer cryostat incorporating a superconducting magnet (from Quantum Designs). This system allows optical measurements (Raman, photoluminescence, reflectivity) within wide ranges of pressures (up to 100GPa), temperatures (4.2-300K) and magnetic fields (0-9T). We employ this system to examine the effect of pressure and non-hydrostatic stress on the Zeeman split d-d transitions of Cr^3+ in ruby (Al2O3: Cr^3+). We determine the effect of pressure and non-hydrostaticity on the trigonal crystal field in this material, and discuss the use of the Zeman-split ruby fluorescence as a possible probe for deviatoric stresses in diamond anvil cell experiments.
Observations of the Zeeman effect in Class I methanol masers
Pratim Sarma, Anuj; Momjian, Emmanuel
2017-01-01
We present observations of the Zeeman effect in Class I methanol maser sources toward high mass star forming regions. Toward DR21(OH), we have detected the Zeeman effect at 44 GHz in a 219 Jy/beam maser centered at an LSR velocity of 0.83 km/s, and we find $zB_\\text{los} = 53.5 \\pm 2.7$ Hz. If 44 GHz methanol masers are excited at $10^{7-8}$ cm$^{-3}$, then magnetic fields in DR21(OH) should be ~10 mG. Our detected $zB_\\text{los}$ would then imply that the Zeeman splitting factor for the 44 GHz methanol maser line should be ~5 Hz/mG. Such small values for z would not be surprising, since the methanol molecule is non-paramagnetic, like H2O. Since there are no direct measurements or calculations of the 44 GHz methanol maser Zeeman splitting factor to date, such empirical attempts could prove valuable in building a repository of measurements from which to gain an understanding of the magnitude of z.
Theory and Modeling of the Zeeman and Paschen-Back effects in Molecular Lines
Ramos, A. Asensio; Bueno, J. Trujillo
2005-01-01
This paper describes a very general approach to the calculation of the Zeeman splitting effect produced by an external magnetic field on the rotational levels of diatomic molecules. The method is valid for arbitrary values of the total electronic spin and of the magnetic field strength -that is, it holds for molecular electronic states of any multiplicity and for both the Zeeman and incomplete Paschen-Back regimes. It is based on an efficient numerical diagonalization of the effective Zeeman ...
The Zeeman effect for helium atom
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The g-factors of the 23P, 21P, and 33P states of the helium atom are calculated by using the vatiational wave functions constructed from the linear combinations of Slater-type basis sets. The relativistic corrections to order α2(a.u.) and the effect of the motion of the center of mass are treated by using first-order perturbation theory. Most of our predicted results are in good agreement with recent results of Yan and Drake, which were obtained by using the wave functions with doubled Hylleraas coordinates. Based on the analysis of the convergence pattern in our calculation, we believe that our predicted value of the δgL-factor for 33P state in 4He, 2.914 15×10-7, ought to be reasonable and accurate, although there are no corresponding experimental data available in the liteature yet to be compared with.
Berdyugina, S. V.; Solanki, S. K.
2002-04-01
An overview of the theory of the Zeeman effect in diatomic molecules for the limiting Hund's cases (a) and (b) is given and a numerical approach for the intermediate coupling case (a-b) is developed. In contrast to earlier derivations, which were limited to doublets, this approach is valid for terms of any multiplicity. General properties of the Zeeman effect for the various cases are deduced. Finally, calculated Landé factors for prominent molecular bands in sunspot and cool-star spectra are employed to predict the general behaviour of these bands in the presence of a magnetic field below the Paschen-Back limit. The limiting field strength is calculated and listed.
A Classical Theory of the Anomalous Zeeman Effect
Espinosa, James; Woodyard, James
2010-10-01
Over a hundred years ago, it was discovered that spectral lines were shifted by magnetic fields. Lorentz was able to explain a small set of phenomena that was ironically called the normal Zeeman effect. It took more than twenty years for Lande to arrive at a vector model of the atom to explain the majority of shiftings called the anomalous Zeeman effect. Within a couple of years, Uhlenbeck and Goudsmit introduced the idea of a spinning electron that would give an underlying explanation of the vector model rules. It is generally taught that without the concept of spin there can be no explanation of all the spectral splittings caused by a magnetic field. We will present a purely classical model developed by Woldemar Voigt to describe the most famous anomalous splitting, the sodium D line. In addition, his theory correctly describes the transition from the weak field state to the strong one, called the Paschen-Back effect. We will show how his theory matches well with our classical picture of the atom.
Wubs KL; Groot G de
1989-01-01
Er wordt een onderzoek beschreven naar de toepasbaarheid van Zeeman- effect achtergrondcorrectie bij de kwantitatieve bepaling van cadmium in urine met atomaire absorptiespectrofotometrie en elektrothermische atomisatie. De meerwaarde van Zeeman-effect achtergrondcorrectie is onderzocht ten opzi
An Essay on Interactive Investigations of the Zeeman Effect in the Interstellar Medium
Woolsey, Lauren
2015-01-01
The paper presents an interactive module created through the Wolfram Demonstrations Project that visualizes the Zeeman effect for the small magnetic field strengths present in the interstellar medium. The paper provides an overview of spectral lines and a few examples of strong and weak Zeeman splitting before discussing the module in depth.…
Polarization Gradient Cooling by Zeeman-Effect-Assisted Saturated Absorption
Institute of Scientific and Technical Information of China (English)
HAN Shun-Li; CHENG Bing; ZHANG Jiag-Fang; XU Yun-Fei; WANG Zhao-Ying; LIN Qiang
2009-01-01
A novel and simple method to realize polarization gradient cooling(PGC)is reported.The stabilizing,shifting and rapid tuning of the frequency of the external cavity diode laser is realized by using the Zeeman-effect-assisted Doppler-free saturated absorption technique.Based on this convenient technique,~(87)Rb cold atoms are captured from room-temperature background vapor in the magneto-optical trap(MOT).Meanwhile,the steady-state number,the density and the lifetime of atoms in the MOT are measured.Subsequently,a frequency-fast-varying circuit is designed to realize PGC,which is demonstrated effectively and reliably in experiments.The temperature of the cold atom cloud is measured by two different methods,which coincide with each other.
Institute of Scientific and Technical Information of China (English)
ZHANG Jun-Hai; WANG Feng-Zhi; YANG Dong-Hai
2004-01-01
An experimental test of ac Zeeman effect in an optically pumped caesium beam frequency standard is reported and analysed. An interference pattern of the atomic energy level shift as a function of the applied microwave field near the atomic transition frequency was observed. It was superimposed on the dispersion lineshape of a normal ac Zeeman effect. This effect was analysed with the atomic wavefunction phase analysing method.
Theory and Modeling of the Zeeman and Paschen-Back Effects in Molecular Lines
Asensio Ramos, A.; Trujillo Bueno, J.
2006-01-01
This paper describes a very general approach to the calculation of the Zeeman splitting effect produced by an external magnetic field on the rotational levels of diatomic molecules. The method is valid for arbitrary values of the total electronic spin and of the magnetic field strength-that is, it holds for molecular electronic states of any multiplicity and for both the Zeeman and incomplete Paschen-Back regimes. It is based on an efficient numerical diagonalization of the effective Zeeman Hamiltonian, which can incorporate easily all the contributions one may eventually be interested in, such as the hyperfine interaction of the external magnetic field with the spin motions of the nuclei. The reliability of the method is demonstrated by comparing our results with previous ones obtained via formulae valid only for doublet states. We also present results for molecular transitions arising between nondoublet electronic states, illustrating that their Zeeman patterns show signatures produced by the Paschen-Back effect.
Mapping Magnetic Fields in Molecular Clouds with the CN Zeeman Effect
Crutcher, Richard
2017-06-01
The role of magnetic fields in star formation remains controversial. Observations of the Zeeman effect provide the only available technique for directly measuring the strengths of magnetic fields in molecular clouds. We have mapped the Zeeman effect toward the massive star forming complex W3OH in the CN N=2-1 transition at 226 GHz with both the IRAM 30-m telescope and the CARMA array and have combined these data to produce a fully spatially sampled map of the magnetic field along the line of sight, with approximately 4 arcsec resolution. These are both the first CN Zeeman maps and the first detections of the Zeeman effect in the CN N=2-1 transition. We will present this map and discuss the astrophysical implications. This work may be considered to be a pathfinder for future similar ALMA observations, which have the potential to advance considerably our understanding of the role of magnetic fields in the star formation process.
Institute of Scientific and Technical Information of China (English)
DONG Zhengchao
2006-01-01
We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman energy difference between the two splitting peaks in the conductance spectrum is equal to2h0 (h0 is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks,however, neither of them can influence the Zeeman effect.
Theory and Modeling of the Zeeman and Paschen-Back effects in Molecular Lines
Bueno, A A R J T
2005-01-01
This paper describes a very general approach to the calculation of the Zeeman splitting effect produced by an external magnetic field on the rotational levels of diatomic molecules. The method is valid for arbitrary values of the total electronic spin and of the magnetic field strength -that is, it holds for molecular electronic states of any multiplicity and for both the Zeeman and incomplete Paschen-Back regimes. It is based on an efficient numerical diagonalization of the effective Zeeman Hamiltonian, which can incorporate easily all the contributions one may eventually be interested in, such as the hyperfine interaction of the external magnetic field with the spin motions of the nuclei. The reliability of the method is demonstrated by comparing our results with previous ones obtained via formulae valid only for doublet states. We also present results for molecular transitions arising between non-doublet electronic states, illustrating that their Zeeman patterns show signatures produced by the Paschen-Back...
Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla
Stier, Andreas V.; McCreary, Kathleen M.; Jonker, Berend T.; Kono, Junichiro; Crooker, Scott A.
2016-02-01
In bulk and quantum-confined semiconductors, magneto-optical studies have historically played an essential role in determining the fundamental parameters of excitons (size, binding energy, spin, dimensionality and so on). Here we report low-temperature polarized reflection spectroscopy of atomically thin WS2 and MoS2 in high magnetic fields to 65 T. Both the A and B excitons exhibit similar Zeeman splittings of approximately -230 μeV T-1 (g-factor ~=-4), thereby quantifying the valley Zeeman effect in monolayer transition-metal disulphides. Crucially, these large fields also allow observation of the small quadratic diamagnetic shifts of both A and B excitons in monolayer WS2, from which radii of ~1.53 and ~1.16 nm are calculated. Further, when analysed within a model of non-local dielectric screening, these diamagnetic shifts also constrain estimates of the A and B exciton binding energies (410 and 470 meV, respectively, using a reduced A exciton mass of 0.16 times the free electron mass). These results highlight the utility of high magnetic fields for understanding new two-dimensional materials.
Alternating Current Zeeman and Stark Interference Effect in Ramsey Separated Oscillating Fields
Institute of Scientific and Technical Information of China (English)
CHEN Jing-Biao; WANG Feng-Zhi; YANG Dong-Hai; WANG Yi-Qiu
2001-01-01
Analytic expressions have been derived of the alternating current (ac) Zeeman and ac Stark effect in an atomic beam magnetic resonance method using Ramsey separated oscillating fields. An interesting feature which will affect the normal Ramsey pattern is that an interference fringe is superimposed on the dispersion lineshapes of the normal ac Zeeman or ac Stark effect. We point out that this new character of ac Zeeman (ac Stark) effect generally exists in all kinds of Ramsey method, for example, in the optical Ramsey atomic interferometer and atomic beam frequency standard. An important implication is that, particularly in an atomic beam frequency standard using Ramsey method, this effect has an influence on the evaluation of the second-order Doppler frequency shift.PACS: 32. 60. ＋i, 06. 20. Fn, 32. 30. Dx
Bianchi I solutions of effective quadratic gravity
Müller, Daniel
2012-01-01
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model $E^3$ for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for non diagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi $I$ spaces.
Theory, Observation, and Modeling of the Zeeman and Paschen-Back Effects in Molecular Lines
Asensio Ramos, A.
2006-12-01
We present a historical review of the theory of the Zeeman effect in molecular lines, from its discovery at the end of the 19th century till today. The fast development of the quantum theory owes much to the impulse given by the experimental investigation of the molecular Zeeman effect. Laboratory experiments produced fruitful results after the predictions made by the quantum theory. The introduction by Racah of the powerful angular momentum algebra gave a second impulse to the theory and allowed to fully understand the fine structure and polarization properties of molecular transitions. At present, the theory of the Zeeman and Paschen-Back effects in molecular lines is being applied to spectro-(polarimetric) observations to infer the physical and magnetic properties of cold plasmas in the atmospheres of the Sun and of other stars.
An Essay On Interactive Investigations Of The Zeeman Effect In The Interstellar Medium
Woolsey, Lauren N
2015-01-01
The paper presents an interactive module created through the Wolfram Demonstrations Project that visualizes the Zeeman effect for the small magnetic field strengths present in the interstellar medium. The paper provides an overview of spectral lines and a few examples of strong and weak Zeeman splitting before discussing the module in depth. Student discovery is aided with example situations to investigate using the interactive module, which is targeted at the upper undergraduate or early graduate level. This module (http://demonstrations.wolfram.com/TheZeemanEffectInTheInterstellarMedium), which uses free software, can be used in classroom activities or as a means of introducing students to the Wolfram Demonstrations Project as a learning resource.
Zeeman effect in sulfur monoxide. A tool to probe magnetic fields in star forming regions
Cazzoli, Gabriele; Lattanzi, Valerio; Coriani, Sonia; Gauss, Jürgen; Codella, Claudio; Ramos, Andrés Asensio; Cernicharo, José; Puzzarini, Cristina
2017-09-01
Context. Magnetic fields play a fundamental role in star formation processes and the best method to evaluate their intensity is to measure the Zeeman effect of atomic and molecular lines. However, a direct measurement of the Zeeman spectral pattern from interstellar molecular species is challenging due to the high sensitivity and high spectral resolution required. So far, the Zeeman effect has been detected unambiguously in star forming regions for very few non-masing species, such as OH and CN. Aims: We decided to investigate the suitability of sulfur monoxide (SO), which is one of the most abundant species in star forming regions, for probing the intensity of magnetic fields via the Zeeman effect. Methods: We investigated the Zeeman effect for several rotational transitions of SO in the (sub-)mm spectral regions by using a frequency-modulated, computer-controlled spectrometer, and by applying a magnetic field parallel to the radiation propagation (i.e., perpendicular to the oscillating magnetic field of the radiation). To support the experimental determination of the g factors of SO, a systematic quantum-chemical investigation of these parameters for both SO and O2 has been carried out. Results: An effective experimental-computational strategy for providing accurate g factors as well as for identifying the rotational transitions showing the strongest Zeeman effect has been presented. Revised g factors have been obtained from a large number of SO rotational transitions between 86 and 389 GHz. In particular, the rotational transitions showing the largest Zeeman shifts are: N,J = 2, 2 ← 1, 1 (86.1 GHz), N,J = 4, 3 ← 3, 2 (159.0 GHz), N,J = 1, 1 ← 0, 1 (286.3 GHz), N,J = 2, 2 ← 1, 2 (309.5 GHz), and N,J = 2, 1 ← 1, 0 (329.4 GHz). Our investigation supports SO as a good candidate for probing magnetic fields in high-density star forming regions. The complete list of measured Zeeman components is only available at the CDS via anonymous ftp to http
Impurity effects in the magnetic oscillations on doped graphene with Zeeman splitting
Escudero, F.; Ardenghi, J. S.; Jasen, Paula; Juan, A.
2017-08-01
The aim of this work is to describe the electronic and magnetic properties of graphene in a constant magnetic field, in the long wavelength approximation with random disorder. Taking into account the Zeeman effect, the electronic density of states for each spin is found and the de Haas van Alphen oscillations (dHvA) are found. The magnetic field is found to modulate the de Haas-van Alphen magnetization through the ratio of the Zeeman coupling and pseudospin-Landau coupling. In turn, the Pauli magnetization is studied showing that the Zeeman splitting and disorder introduces a dHvA oscillation period that depends on the magnetic field strength and generalizes the Onsager relation. In turn, a beat frequency appears that does not depend on B but increase linearly with the chemical potential. These results, which are different from those obtained in the standard nonrelativistic 2D electron gas, are attributed to its anomalous Landau level spectrum in graphene.
Zeeman- and Paschen-Back-effect of the hyperfine structure of the sodium D 2-line
Windholz, L.; Musso, M.
1988-09-01
Using high resolution laser-atomic-beam spectroscopy, Zeeman- and Paschen-Back-effects of the hyperfine structure of the sodium resonance lines were studied in magnetic fields up to 280 Gauss without perturbation by cross-over resonances. The observed behaviour of the components of the D 2-line is compared with results of theoretical calculations for the splitting and the relative intensity of each Zeeman-component of the line. Full agreement between theory and experiment can be stated. Additionally, the relative intensities of the components of the D 1-line are given.
Relativistic Corrections to the Zeeman Effect of Helium Atom
Institute of Scientific and Technical Information of China (English)
关晓旭; 李白文; 王治文
2002-01-01
The high-order relativistic corrections to the Zeeman g-factors of the helium atom are calculated. AII the relativistic correction terms and the term describing the motion of the mass centre are treated as perturbations. Most of our results are in good agreement with those of Yah and Drake [Phys. Rev. A 50 (1994)R1980/, who used the wavefunctions constructed by Hylleraas coordinates. For the correction δg of the g-factor of the 3 3P state in 4He, our result, 2.91415 × 10-7 a.u., should be more reasonable and accurate, although there are no experimental data available in the literature to compare.
Zeeman Effect In The Framework of Moyal Noncommutativity and String Theory
Boukili, A E; Sedra, M B
2006-01-01
Stimulated by the importance of noncommutative geometry in recent developments in string theory, the discovery of D-branes and integrable systems, one intends in this work to present a new insight towards adapting the famous idea of Zeeman effect to noncommutativity \\`a la Moyal and develop an analysis leading to connect our results to the Bigatti-Suskind (BS) formulation.
Zeeman- and Paschen-Back-effect of the hyperfine structure of the sodium D 1-line
Windholz, L.
1985-06-01
Using high-resolution laser-atomic-beam spectroscopy, Zeeman- and Paschen-Back-effects of the hyperfine structure of the sodium resonance lines were studied in fields up to app. 280 G. The results derived for the D 1-line are given in graphical form and show clearly the change in the coupling of J and I of the upper level.
AC Zeeman Effect of Atom%原子的交流塞曼效应
Institute of Scientific and Technical Information of China (English)
邢爱堂
1999-01-01
The formula of level shifts in AC Zeeman effect is derived on the base of a simple semiclassical method. The theoretical predictions of this formula are qualitatively in good agreement with the phenomena observed in AC Zeeman experiment. Furthermore,two important properties of AC Zeeman effect are predicted in theory:the level shifts in AC Zeeman effect of atom are the transient courses concurring with transition;the level shifts have saturation property.%用一种简单的半经典方法推导出了交流塞曼效应中的能级移动公式.从这一公式得到的结果与实验中观察到的现象是一致的,而且从理论上预言了交流塞曼效应的2个重要性质:原子交流塞曼效应中的能级移动是与跃迁同时发生的瞬态过程;能级移动具有饱和性.
Effect of external and internal magnetic fields on the bias stability in a Zeeman laser gyroscope
Energy Technology Data Exchange (ETDEWEB)
Kolbas, Yu Yu; Saveliev, I I; Khokhlov, N I [Open Joint-Stock Company M.F. Stel' makh Polyus Research Institute, Moscow (Russian Federation)
2015-06-30
With the specific features of electronic systems of a Zeeman laser gyroscope taken into account, the basic physical mechanisms of the magnetic field effect on the bias stability and the factors giving rise to the internal magnetic fields are revealed. The hardware-based methods of reducing the effect of external and internal magnetic fields are considered, as well as the algorithmic methods for increasing the stability of the bias magnetic component by taking into account its reproducible temperature and time dependences. Typical experimental temperature and time dependences of the magnetic component of the Zeeman laser gyro bias are presented, and by their example the efficiency of the proposed methods for reducing the effect of magnetic fields is shown. (laser gyroscopes)
Tiemann, Eberhard; Pachomow, Evgenij; Riehle, Fritz; Sterr, Uwe
2015-01-01
We present calculations of the Zeeman effect of narrow photoassociation lines of $^{40}$Ca near the $^3$P$_1$ + $^1$S$_0$ asymptote. Using a coupled-channel model we find a nonlinear Zeeman effect that even at low fields of a few mT amounts to several kHz. With this model we analyze previous measurements and give corrected long range dispersion coefficients of the $^3\\Pi_{u}$ and $^3\\Sigma^+ _{u}$ states.
Zeeman Effect observations toward 36 GHz methanol masers in the Galactic Center
Potvin, Justin A.; Momjian, Emmanuel; Pratim Sarma, Anuj
2017-01-01
We present observations of 36 GHz Class I methanol masers taken with the Karl G. Jansky Very Large Array (VLA) in the B configuration with the aim of detecting the Zeeman Effect. We targeted several 36 GHz Class I methanol masers associated with supernova remnants (SNRs) toward the Galactic Center. Each source was observed in dual circular polarizations for three hours. The observed spectral profiles of the masers are complex, with several components blended in velocity. In only one case was the Stokes V maser profile prominent enough to reveal a 2-sigma hint of a magnetic field of zBlos = 14.56 +/- 5.60 Hz; we have chosen to express our results in terms of zBlos since the Zeeman splitting factor (z) for 36 GHz methanol masers has not been measured. There are several hints that these spectra would reveal significant magnetic fields if they could be spatially and spectrally resolved.
High-field Zeeman and Paschen-Back effects at high pressure in oriented ruby
Millot, Marius; Broto, Jean-Marc; Gonzalez, Jesus
2008-10-01
High-field Zeeman and Paschen-Back effects have been observed in single crystals of ruby submitted to hydrostatic pressure up to 10 GPa. A specific setup with a miniature diamond-anvil cell has been developed to combine high pressure and pulsed magnetic fields and to perform magnetophotoluminescence measurements. Careful analysis of low-temperature (4.2 and 77 K) photoluminescence spectra with a 56 T magnetic field applied along the c axis allows for the rectification of the assignment of observed emission lines to corresponding Zeeman-split levels. Besides, the intrinsic Zeeman-splitting factors of excited states reveal a linear pressure-induced increase. This enhancement is a signature of an increase in trigonal distortion induced by hydrostatic pressure. Moreover, spectra with magnetic field perpendicular to crystallographic c axis exhibit a Paschen-Back effect reflecting the progressive alignment of Cr3+ ions spin along the applied field. However, no pressure modification is observed in this compound, contrarily to the Heisenberg-to-Ising spin character pressure-induced transition observed in alexandrite.
The Zeeman Effect in the 44 GHz Class I Methanol Maser Line toward DR21(OH)
Momjian, E.; Sarma, A. P.
2017-01-01
We report detection of the Zeeman effect in the 44 GHz Class I methanol maser line, toward the star-forming region DR21(OH). In a 219 Jy beam‑1 maser centered at an LSR velocity of 0.83 km s‑1, we find a 20-σ detection of zBlos = 53.5 ± 2.7 Hz. If 44 GHz methanol masers are excited at n ∼ 107–8 cm‑3, then the B versus n1/2 relation would imply, from comparison with Zeeman effect detections in the CN(1 ‑ 0) line toward DR21(OH), that magnetic fields traced by 44 GHz methanol masers in DR21(OH) should be ∼10 mG. Combined with our detected zBlos = 53.5 Hz, this would imply that the value of the 44 GHz methanol Zeeman splitting factor z is ∼5 Hz mG‑1. Such small values of z would not be a surprise, as the methanol molecule is non-paramagnetic, like H2O. Empirical attempts to determine z, as demonstrated, are important because there currently are no laboratory measurements or theoretically calculated values of z for the 44 GHz CH3OH transition. Data from observations of a larger number of sources are needed to make such empirical determinations robust.
The Zeeman Effect in the 44 GHz Class I Methanol Maser Line toward DR21(OH)
Momjian, E
2016-01-01
We report the detection of the Zeeman effect in the 44 GHz Class I methanol maser line toward the star forming region DR21(OH). In a 219 Jy/beam maser centered at an LSR velocity of 0.83 km s$^{-1}$, we find a 20-$\\sigma$ detection of $zB_{\\text{los}} = 53.5 \\pm 2.7$ Hz. If 44 GHz methanol masers are excited at $n \\sim 10^{7-8}$ cm$^{-3}$, then the $B~vs.~n^{1/2}$ relation would imply from comparison with Zeeman effect detections in the CN($1-0$) line toward DR21(OH) that magnetic fields traced by 44 GHz methanol masers in DR21(OH) should be $\\sim$10 mG. Together with our detected $zB_{\\text{los}} = 53.5$ Hz, this would imply that the value of the 44 GHz methanol Zeeman splitting factor $z$ is $\\sim$5 Hz mG$^{-1}$. Such small values of $z$ would not be a surprise, as the methanol molecule is non paramagnetic, like H$_2$O. Empirical attempts to determine $z$, as demonstrated, are important because currently there are no laboratory measurements or theoretically calculated values of $z$ for the 44 GHz methanol t...
Detection of the Zeeman effect in atmospheric O2 using a ground-based microwave radiometer
Navas-Guzmán, Francisco; Kämpfer, Niklaus; Murk, Axel; Larsson, Richard; Buehler, Stefan A.; Eriksson, Patrick
2015-04-01
In this work we study the Zeeman effect on stratospheric O2 using ground-based microwave radiometer measurements. The Zeeman effect is a phenomenon which occurs when an external magnetic field interacts with a molecule or an atom of total electron spin different from zero. Such an interaction will split an original energy level into several sub-levels [1]. In the atmosphere, oxygen is an abundant molecule which in its ground electronic state has a permanent magnetic dipole moment coming from two parallel electron spins. The interaction of the magnetic dipole moment with the Earth magnetic field leads to a Zeeman splitting of the O2 rotational transitions which polarizes the emission spectra. A special campaign was carried out in order to measure this effect in the oxygen emission line centered at 53.07 GHz in Bern (Switzerland). The measurements were possible using a Fast Fourier Transform (FFT) spectrometer with 1 GHz of band width to measure the whole oxygen emission line centered at 53.07 GHz and a narrow spectrometer (4 MHz) to measure the center of the line with a very high resolution (1 kHz). Both a fixed and a rotating mirror were incorporated to the TEMPERA (TEMPERature RAdiometer) radiometer in order to be able to measure under different observational angles. This new configuration allowed us to change the angle between the observational path and the Earth magnetic field direction. The measured spectra showed a clear polarized signature when the observational angles were changed evidencing the Zeeman effect in the oxygen molecule. In addition, simulations carried out with the Atmospheric Radiative Transfer Simulator (ARTS) [2] allowed us to verify the microwave measurements showing a very good agreement between model and measurements. The incorporation of this effect to the forward model will allow to extend the temperature retrievals beyond 50 km. This improvement in the forward model will be very useful for the assimilation of brightness temperatures in
Hemmes, K.; WIND, M.M.; Lepoole, R.; Habing, P.E.
1994-01-01
Abstract of WO 9416310 (A1) Ellipsometer comprising at least a Zeeman laser (Z) to generate two beams (g1, g2) which are slightly shifted in frequency and (after transmission through a birefringent crystal (quarter-wave plate)) are both polarized linearly but perpendicular to one another, a non-
Observation of Magnetic Fields in Laser-Produced Plasma Using the Zeeman Effect.
1983-09-30
Back 9 effect ), Irons, McWhirter and Peacock ° did extensive spectroscopic investigations of the C+4 ions pro- duced by the laser irradiation of...8. N.J. Peacock and B.A. Norton, Phys. Rev. A 11, 2142 (1975). 9. F. Paschen and E. Back , Ann. Physik 39, 897 (1912); 40, 960 (1913). 10. F.E. Irons...ZEEMAN EFFECT 6. PERFORMING ORG. REPORT NUMBER 7. AUTI4OR(e) 11. CONTRACT OR GRANT NUMER(a) E. A. McLean, J. A. Stamper, C. K. Manka,* H. R. Griem,** D. W
Frequency-Shift of a Frequency Stabilized Laser Based on Zeeman Effect
Institute of Scientific and Technical Information of China (English)
魏荣; 邓见辽; 钱勇; 张宇; 王育竹
2003-01-01
We introduce a new method of frequency-shifting for a diode laser in laser cooling experiments, the method is based on the Zeeman effect of 87Rb atoms. The laser frequency is stabilized by absorption spectrum line of atoms in magnetic field. We show that a magnetic field can be added up to 10-2T. The corresponding frequency shift is 102MHz and the response time is about 1 ms. The large range of the frequency shift is sufficient for laser-cooling experiments.
Zeeman effects on Josephson current in d-wave superconductor/d-wave superconductor junctions
Institute of Scientific and Technical Information of China (English)
Liao Yan-Hua; Dong Zheng-Chao; Yin Zai-Feng; Fu Hao
2008-01-01
This paper solves a self-consistent equation for the d-wave superconducting gap and the effective exchange field in the mean-field approximation,and studies the Zeeman effects on the d-wave superconducting gap and thermodynamic potential.The Josephson currents in the d-wave superconductor(S)/insulating layer(I)/d-wave S junctions are calculated as a function of the temperature,exchange field,and insulating barrier strength under a Zeeman magnetic field on the two d-wave Ss.It is found that the Josephson critical currents in d-wave S/d-wave S junction to a great extent depend on the relative orientation of the effective exchange field of the two S electrodes,and the crystal orientation of the d-wave S.The exchange field under certain conditions can enhance the Josephson critical current in a d-wave S/I/d-wave S junction.
Discovery of the Zeeman Effect in the 44 GHz Class I methanol maser line
Sarma, A P
2011-01-01
We report the discovery of the Zeeman effect in the 44 GHz Class I methanol maser line. The observations were carried out with 22 antennas of the EVLA toward a star forming region in OMC-2. Based on our adopted Zeeman splitting factor of z = 1.0 Hz/mG, we detect a line of sight magnetic field of 18.4 +/- 1.1 mG toward this source. Since such 44 GHz methanol masers arise from shocks in the outflows of star forming regions, we can relate our measurement of the post-shock magnetic field to field strengths indicated by species tracing pre-shock regions, and thus characterize the large scale magnetic field. Moreover, since Class I masers trace regions more remote from the star forming core than Class II masers, and possibly earlier phases, magnetic fields detected in 6.7 GHz Class II and 36 GHz and 44 GHz Class I methanol maser lines together offer the potential of providing a more complete picture of the magnetic field. This motivates further observations at high angular resolution to find the positional relation...
Time Ordering Effects on Hydrogen Zeeman-Stark Line Profiles in Low-Density Magnetized Plasmas
Directory of Open Access Journals (Sweden)
J. Rosato
2010-01-01
Full Text Available Stark broadening of hydrogen lines is investigated in low-density magnetized plasmas, at typical conditions of magnetic fusion experiments. The role of time ordering is assessed numerically, by using a simulation code accounting for the evolution of the microscopic electric field generated by the charged particles moving at the vicinity of the atom. The Zeeman effect due to the magnetic field is also retained. Lyman lines with a low principal quantum number n are first investigated, for an application to opacity calculations; next Balmer lines with successively low and high principal quantum numbers are considered for diagnostic purposes. It is shown that neglecting time ordering results in a dramatic underestimation of the Stark effect on the low-n lines. Another conclusion is that time ordering becomes negligible only when ion dynamics effects vanish, as shown in the case of high-n lines.
The Hanle and Zeeman Effects in Solar Spicules: A Novel Diagnostic Window on Chromospheric Magnetism
Bueno, J T; Centeno, R; Collados, M; Landi degl'Innocenti, E
2005-01-01
An attractive diagnostic tool for investigating the magnetism of the solar chromosphere is the observation and theoretical modeling of the Hanle and Zeeman effects in spicules, as shown in this letter for the first time. Here we report on spectropolarimetric observations of solar chromospheric spicules in the He I 10830 \\AA multiplet and on their theoretical modeling accounting for radiative transfer effects. We find that the magnetic field in the observed (quiet Sun) spicular material at a height of about 2000 km above the visible solar surface has a strength of the order of 10 G and is inclined by approximately $35^{\\circ}$ with respect to the local vertical direction. Our empirical finding based on full Stokes-vector spectropolarimetry should be taken into account in future magnetohydrodynamical simulations of spicules.
Zeeman effect of weak La I lines investigated by the use of optogalvanic spectroscopy
Sobolewski, Ł. M.; Windholz, L.; Kwela, J.
2017-03-01
New Landé- gJ factors of 35 energy levels of La I, found from investigations of 40 spectral lines in the wavelength range 562.959÷609.537 nm, were determined. As a source of free La atoms a hollow cathode discharge lamp was used. We monitored the signal of the optogalvanic effect appearing when a laser beam is passing through the hollow cathode. Spectra were recorded in the presence of a magnetic field of about 800 G produced by a permanent magnet, for two linear polarizations of the exciting laser light. Optogalvanic spectroscopy is a very sensitive method, so we were able to observe the Zeeman effect of very weak atomic lines. In this way we have determined for the first time the Landé-gJ factors for 35 recently found levels of neutral La. The Landé gJ- factors for several other levels were reinvestigated.
Tahir, M.
2013-12-10
Since the discovery of graphene, a lot of interest has been attracted by the zeroth Landau level, which has no analog in the conventional two dimensional electron gas. Recently, lifting of the spin and valley degeneracies has been confirmed experimentally by capacitance measurements, while in transport experiments, this is difficult due to the scattering in the device. In this context, we model interaction effects on the quantum capacitance of graphene in the presence of a perpendicular magnetic field, finding good agreement with experiments. We demonstrate that the valley degeneracy is lifted by the substrate and by Kekule distortion, whereas the spin degeneracy is lifted by Zeeman interaction. The two cases can be distinguished by capacitance measurements.
Zeeman and spin-orbit effects in the Andreev spectra of nanowire junctions
van Heck, B.; Väyrynen, J. I.; Glazman, L. I.
2017-08-01
We study the energy spectrum and the electromagnetic response of Andreev bound states in short Josephson junctions made of semiconducting nanowires. We focus on the joint effect of Zeeman and spin-orbit coupling on the Andreev level spectra. Our model incorporates the penetration of the magnetic field in the proximitized wires, which substantially modifies the spectra. We pay special attention to the occurrence of fermion-parity switches at increasing values of the field and to the magnetic field dependence of the absorption strength of microwave-induced transitions. Our calculations can be used to extract quantitative information from microwave and tunneling spectroscopy experiments, such as the recently reported measurements in Van Woerkom et al. [Nat. Phys. (2017), doi:, 10.1038/nphys4150].
Robust effective Zeeman energy in monolayer MoS2 quantum dots
Dias, A. C.; Fu, Jiyong; Villegas-Lelovsky, L.; Qu, Fanyao
2016-09-01
We report a theoretical investigation on the energy spectrum and the effective Zeeman energy (EZE) in monolayer MoS2 circular quantum dots, subjected to an out-of-plane magnetic field. Interestingly, we observe the emergence of energy-locked modes, depending on the competition between the dot confinement and the applied magnetic field, for either the highest K-valley valence band or the lowest {{K}\\prime} -valley conduction band. Moreover, an unusual dot-size-independent EZE behavior of the highest valence and the lowest conduction bands is found. Although the EZEs are insensitive to the variation of quantum confinement, both of them grow linearly with the magnetic field, similar to that in the monolayer MoS2 material. The EZEs along with their ‘robustness’ against dot confinements open opportunities of a universal magnetic control over the valley degree of freedom, for quantum dots of all sizes.
Fermi surface distortion induced by interaction between Rashba and Zeeman effects
Energy Technology Data Exchange (ETDEWEB)
Choi, Won Young; Koo, Hyun Cheol, E-mail: hckoo@kist.re.kr [Spin Convergence Research Center, Korea Institute of Science and Technology, Seoul 136-791 (Korea, Republic of); KU-KIST Graduate School of Converging Science and Technology, Korea University, Seoul 136-701 (Korea, Republic of); Chang, Joonyeon; Kim, Hyung-jun [Spin Convergence Research Center, Korea Institute of Science and Technology, Seoul 136-791 (Korea, Republic of); Lee, Kyung-Jin, E-mail: kj-lee@korea.ac.kr [KU-KIST Graduate School of Converging Science and Technology, Korea University, Seoul 136-701 (Korea, Republic of); Department of Materials Science and Engineering, Korea University, Seoul 136-701 (Korea, Republic of)
2015-05-07
To evaluate Fermi surface distortion induced by interaction between Rashba and Zeeman effects, the channel resistance in an InAs quantum well layer is investigated with an in-plane magnetic field transverse to the current direction. In the magnetoresistance curve, the critical point occurs at ∼3.5 T, which is approximately half of the independently measured Rashba field. To get an insight into the correlation between the critical point in magnetoresistance curve and the Rashba strength, the channel conductivity is calculated using a two-dimensional free-electron model with relaxation time approximation. The critical point obtained from the model calculation is in agreement with the experiment, suggesting that the observation of critical point can be an alternative method to experimentally determine the Rashba parameter.
Energy Technology Data Exchange (ETDEWEB)
Tahir, M. [PSE Division, KAUST, Thuwal 23955-6900 (Saudi Arabia); Department of Physics, University of Sargodha, Sargodha 40100 (Pakistan); Sabeeh, K. [Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Shaukat, A. [Department of Physics, University of Sargodha, Sargodha 40100 (Pakistan); Schwingenschlögl, U., E-mail: Udo.Schwingenschlogl@kaust.edu.sa [PSE Division, KAUST, Thuwal 23955-6900 (Saudi Arabia)
2013-12-14
Since the discovery of graphene, a lot of interest has been attracted by the zeroth Landau level, which has no analog in the conventional two dimensional electron gas. Recently, lifting of the spin and valley degeneracies has been confirmed experimentally by capacitance measurements, while in transport experiments, this is difficult due to the scattering in the device. In this context, we model interaction effects on the quantum capacitance of graphene in the presence of a perpendicular magnetic field, finding good agreement with experiments. We demonstrate that the valley degeneracy is lifted by the substrate and by Kekule distortion, whereas the spin degeneracy is lifted by Zeeman interaction. The two cases can be distinguished by capacitance measurements.
Magnetic catalysis effect in the (2+1-dimensional Gross–Neveu model with Zeeman interaction
Directory of Open Access Journals (Sweden)
Klimenko K.G.
2015-01-01
Full Text Available Magnetic catalysis of the chiral symmetry breaking and other magnetic properties of the (2+1-dimensional Gross–Neveu model are studied taking into account the Zeeman interaction of spin-1/2 quasi-particles (electrons with tilted (with respect to a system plane external magnetic field B→ = B→⊥ + B→∥$\\vec B\\, = \\,{\\vec B_ \\bot }\\, + \\,{\\vec B_\\parallel }$. The Zeeman interaction is proportional to magnetic moment μB of electrons. For simplicity, temperature and chemical potential are equal to zero throughout the paper. We compare in the framework of the model the above mentioned phenomena both at μB = 0 and μB ≠ 0. It is shown that at μB ≠ 0 the magnetic catalysis effect is drastically changed in comparison with the μB = 0 case. Namely, at μB ≠ 0 the chiral symmetry, being spontaneously broken by B→$\\vec B$ at subcritical coupling constants, is always restored at |B→$\\vec B$| → ∞ (even at B→∥$\\vec B_\\parallel$ = 0. Moreover, it is proved in this case that chiral symmetry can be restored simply by tilting B→$\\vec B$ to a system plane, and in the region B⊥ → 0 the de Haas – van Alphen oscillations of the magnetization are observed. At supercritical values of coupling constant we have found two chirally non-invariant phases which respond differently on the action of B→$\\vec B$. The first (at rather small values of |B→$\\vec B$| is a diamagnetic phase, in which there is an enhancement of chiral condensate, whereas the second is a paramagnetic chirally broken phase. Numerical estimates show that phase transitions described in the paper can be achieved at low enough laboratory magnetic fields.
Gravitomagnetic effects in quadratic gravity with a scalar field
Finch, Andrew
2016-01-01
The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.
Measurement of quadratic electrogyration effect in castor oil
Izdebski, Marek; Ledzion, Rafał; Górski, Piotr
2015-07-01
This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.
Analysis of Zeeman effect experiment%塞曼效应实验探析
Institute of Scientific and Technical Information of China (English)
杜雪莲
2011-01-01
Investigating splitting of spectrum of Zeeman-effect by the JWG-based computer experimental apparatus,and the high-contrast and clear split spectrum could be obtained after optimally adjusting optical system.Using of data processing system of computer to analyze the captured and high-resolution π spectral lines,and measure electron charge-mass ratio of 1.759×1011 C/kg.Compared with well-accepted value of 1.76×1011 C/kg,the relative error is 0.029%;and Compared and precision measurement value of 1.75881962×1011 C/kg,relative error is 0.38‰.The results show that a high-contrast and clear split spectrum not only can directly and accurately demonstrate Zeeman-effect but also greatly improve the accuracy of experimental results.%用JWG型微机塞曼效应实验仪研究分析谱线分裂,调节出最佳的光学系统,得到高对比度、清晰可辨的干涉条纹的分裂谱图.利用计算机图像数据处理系统分析所拍摄的高对比度、清晰的π线谱图,测得电子的荷质比为1.759×1011 C/kg,与公认值1.76×1011 C/kg的相对误差为0.029%,与精确测量值1.75881962×1011 C/kg的相对误差为0.38‰.结果表明,高对比度、清晰可辨的分裂谱图不仅直观、准确演示塞曼效应,也极大提高实验结果的精确度.
Isotope dependence of the Zeeman effect in lithium-like calcium
Köhler, Florian; Blaum, Klaus; Block, Michael; Chenmarev, Stanislav; Eliseev, Sergey; Glazov, Dmitry A.; Goncharov, Mikhail; Hou, Jiamin; Kracke, Anke; Nesterenko, Dmitri A.; Novikov, Yuri N.; Quint, Wolfgang; Minaya Ramirez, Enrique; Shabaev, Vladimir M.; Sturm, Sven; Volotka, Andrey V.; Werth, Günter
2016-01-01
The magnetic moment μ of a bound electron, generally expressed by the g-factor μ=-g μB s ħ-1 with μB the Bohr magneton and s the electron's spin, can be calculated by bound-state quantum electrodynamics (BS-QED) to very high precision. The recent ultra-precise experiment on hydrogen-like silicon determined this value to eleven significant digits, and thus allowed to rigorously probe the validity of BS-QED. Yet, the investigation of one of the most interesting contribution to the g-factor, the relativistic interaction between electron and nucleus, is limited by our knowledge of BS-QED effects. By comparing the g-factors of two isotopes, it is possible to cancel most of these contributions and sensitively probe nuclear effects. Here, we present calculations and experiments on the isotope dependence of the Zeeman effect in lithium-like calcium ions. The good agreement between the theoretical predicted recoil contribution and the high-precision g-factor measurements paves the way for a new generation of BS-QED tests.
Ramos, A Asensio; Degl'Innocenti, E Landi
2008-01-01
A big challenge in solar and stellar physics in the coming years will be to decipher the magnetism of the solar outer atmosphere (chromosphere and corona) along with its dynamic coupling with the magnetic fields of the underlying photosphere. To this end, it is important to develop rigorous diagnostic tools for the physical interpretation of spectropolarimetric observations in suitably chosen spectral lines. Here we present a computer program for the synthesis and inversion of Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects in some spectral lines of diagnostic interest, such as those of the He I 10830 A and D_3 multiplets. It is based on the quantum theory of spectral line polarization, which takes into account all the relevant physical mechanisms and ingredients (optical pumping, atomic level polarization, Zeeman, Paschen-Back and Hanle effects). The influence of radiative transfer on the emergent spectral line radiation is taken into account through a...
Broad-band polarization in molecular spectra. [Zeeman effect in magnetic stars
Illing, R. M. E.
1981-01-01
The rotational lines of the CN(0,0) red system have been observed to show a strongly asymmetric Zeeman profile. Certain molecules are very susceptible to magnetic perturbation because of the weakness of their spin-rotation coupling; a fairly weak magnetic field can cause a complete Paschen-Back effect. The calculation of transition probabilities incorporating this effect into the Hamiltonian is discussed, and the detailed calculation is then given. The resulting transition probabilities are transformed into synthetic line profiles by using the Unno (1956) model of polarized radiation transfer. The dependence of the net polarized flux on magnetic field and equivalent width is investigated. It is shown that entire band systems may be significantly polarized. Broad-band circular polarization of sunspots may be due, in part, to molecular bands. Analysis of the CH G band indicates a magnetic field of 0.25-0.50 x 10 to the 6th gauss in the white dwarf G99-37, an order of magnitude lower than previous estimates.
Rotational Rydberg states of polar molecules: Hund's classification and Zeeman effect
Danilyan, A. V.; Chernov, V. E.
2008-01-01
The rotational Rydberg states of polar molecules, which arise as a result of the interaction of a Rydberg electron with core rotations, are considered. A large number of angular momenta in the core-electron system lead to a considerably greater number of possible coupling schemes of these momenta compared to the number of schemes determined by the classical five Hund's cases for lower excited electron states of molecules. As a result of such detailed Hund's classification, more than 30 different coupling schemes (Hund's subcases) are constructed for rotational Rydberg states of molecules. The conditions of their realization are indicated in terms of the relative quantities of intramolecular interactions, for which analytical estimates are presented. For a large number of subcases, analytical expressions for the molecular matrix elements are found. These expressions can be useful in classification of the experimental spectra of highly excited molecules. As an application, for each of the subcases considered, analytical expressions are given, which describe the linear Zeeman effect and the Paschen-Back effect.
Zeeman effect and optical pumping in atomic rubidium: a teaching experiment in quantum physics
Energy Technology Data Exchange (ETDEWEB)
Butcher, R.J.; Adams, S.; Seddon, G.; Golby, J.A.; Massey, D.R.
1987-01-01
The authors describe an experiment developed recently in an undergraduate laboratory to measure the Zeeman splitting of the ground state of atomic rubidium. An optical pumping technique is employed and the magnetic field is calibrated by using free-electron spin resonance. Multiphoton absorption and power broadening of transitions are also investigated and a number of quantum principles introduced experimentally.
Stark and Zeeman effects on the lower electronic states of s-triazine
Aartsma, Thijs J.; Wiersma, Douwe A.
1973-01-01
A detailed optical study of the lower electronic states of s-triazine in a pure crystal at 1.8 degrees K is presented. Stark and Zeeman experiments on these States give no Support to previous assignments. The experiments indicate that the lowest triplet state observed In s-triazine corresponds to ei
Single crystal zeeman effect studies on 35Cl NQR lines of 2,6-dichlorophenol
Prasad, N. V. L. N.; Venkatacharyulu, P.; Premaswarup, D.
1987-10-01
Zeeman effect studies on the two 35Cl NQR lines in cylindrical single crystals of 2,6-dichlorophenol were carried out using a self-quenched super-regenerative NQR spectrometer to obtain information on the nature of the crystalline unit cell and the effect of hydrogen bonding on the electric field gradient tensor. Analysis of the experimental data reveals: (1) the results are in good agreement with those reported from X-ray studies; (2) the crystal is unequivocally identified as belonging to the orthorhombic system; (3) there are two crystallographically equivalent and four physically nonequivalent directions for the principal field gradients for both the low and high frequency resonance lines; (4) the directions of the crystalline a, b, c axes are uniquely identified as (90°, 0°), (0°, -), and (90°, 90°); (5) the b-axis is identified as the growth axis; (6) there are a minimum of four molecules per unit cell, the four molecules lie in different planes, which are, however, connected by symmetry operations; (7)_there exists a weak intramolecular hydrogen bonding in the crystal; (8) the asymmetry parameters for the loci corresponding to the low frequency resonance line, which is affected by hydrogen bonding, are less than the asymmetry parameters of the loci corresponding to the high frequency resonance line, which is not affected by hydrogen bonding; (9) the single bond and ionic bond characters for the hish frequency line are less than that of the low frequency line, while the double bond character for the low frequency line is less than that of the high frequency line and (10) the small deviation between the single bond and double bond characters of the two resonance lines is attributed to the existence of weak hydrogen bonding in the crystal.
Measuring Magnetic Fields Near and Far with the SKA via the Zeeman Effect
Robishaw, Timothy; Surcis, Gabriele; Vlemmings, Wouter; Richards, A M S; Etoka, Sandra; Bourke, Tyler; Fish, Vincent; Gray, Malcolm; Imai, Hiroshi; Kramer, Busaba; McBride, James; Momjian, Emmanuel; Sarma, Anuj; Zijlstra, Albert
2015-01-01
The measurement of Zeeman splitting in spectral lines---both in emission and absorption---can provide direct estimates of the magnetic field strength and direction in atomic and molecular clouds, both in our own Milky Way and in external galaxies. This method will probe the magnetic field in the warm and cold neutral components of the interstellar medium, providing a complement to the extensive SKA Faraday studies planning to probe the field in the ionized components.
Abramochkin, A. I.; Tatur, V. V.; Tikhomirov, A. A.
2017-01-01
The intensities of the π and of the sum of the σ+ and σ- components of radiation emitted by low-pressure mercury capillary lamps filled with mercury of the natural isotopic composition are investigated in the transverse Zeeman effect experiment. The effect of the magnetic induction, inner diameter of the capillary, high-frequency excitation voltage of the lamp, and environmental temperature on the relationship between these intensities is estimated. It is established that the intensity of the σ component is always less than the sum of the intensities of σ+ and σ- components.
Asensio Ramos, A.; Trujillo Bueno, J.; Landi Degl'Innocenti, E.
2008-08-01
A big challenge in solar and stellar physics in the coming years will be to decipher the magnetism of the solar outer atmosphere (chromosphere and corona) along with its dynamic coupling with the magnetic fields of the underlying photosphere. To this end, it is important to develop rigorous diagnostic tools for the physical interpretation of spectropolarimetric observations in suitably chosen spectral lines. Here we present a computer program for the synthesis and inversion of Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects in some spectral lines of diagnostic interest, such as those of the He I 10830 Å and 5876 Å (or D3) multiplets. It is based on the quantum theory of spectral line polarization, which takes into account in a rigorous way all the relevant physical mechanisms and ingredients (optical pumping, atomic level polarization, level crossings and repulsions, Zeeman, Paschen-Back, and Hanle effects). The influence of radiative transfer on the emergent spectral line radiation is taken into account through a suitable slab model. The user can either calculate the emergent intensity and polarization for any given magnetic field vector or infer the dynamical and magnetic properties from the observed Stokes profiles via an efficient inversion algorithm based on global optimization methods. The reliability of the forward modeling and inversion code presented here is demonstrated through several applications, which range from the inference of the magnetic field vector in solar active regions to determining whether or not it is canopy-like in quiet chromospheric regions. This user-friendly diagnostic tool called "HAZEL" (from HAnle and ZEeman Light) is offered to the astrophysical community, with the hope that it will facilitate new advances in solar and stellar physics.
Radial velocity signatures of Zeeman broadening
Reiners, Ansgar; Anglada-Escude, Guillem; Jeffers, Sandra V; Morin, Julien; Zechmeister, Mathias; Kochukhov, Oleg; Piskunov, Nikolai
2013-01-01
Stellar activity signatures such as spots and plage can significantly limit the search for extrasolar planets. Current models of activity-induced radial velocity (RV) signals focused on the impact of temperature contrast in spots predicting the signal to diminish toward longer wavelengths. On the other hand, the relative importance of the Zeeman effect on RV measurements should grow with wavelength, because the Zeeman displacement itself grows with \\lambda, and because a magnetic and cool spot contributes more to the total flux at longer wavelengths. We model the impact of active regions on stellar RV measurements including both temperature contrast in spots and Zeeman line broadening. We calculate stellar line profiles using polarized radiative transfer models including atomic and molecular Zeeman splitting from 0.5 to 2.3\\mum. Our results show that the amplitude of the RV signal caused by the Zeeman effect alone can be comparable to that caused by temperature contrast. Furthermore, the RV signal caused by c...
Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
Neumeyer, S.; Sorokin, V. S.; Thomsen, J. J.
2017-01-01
We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing-Mathieu equation with appended quadratic nonlinearity is considered as the model system, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic nonlinearities may generate additional amplitude-frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi-stability in the amplitude-phase characteristics are predicted, supporting previously reported experimental observations.
Zeeman Effect of Sm Atoms by High-Resolution Diode-Laser Spectroscopy
Directory of Open Access Journals (Sweden)
Wei-Guo Jin
2013-01-01
Full Text Available High-resolution atomic-beam diode-laser spectroscopy in Sm I has been performed. Zeeman spectra have been measured for the three optical transitions at different external magnetic fields and well resolved at the magnetic fields of stronger than 6.0 mT. Using the known precise Landé -factors of the ground multiplet, the Landé -factors of the upper 4f66s6p and levels have been determined, and their precision has been improved compared with the reference values.
Energy Technology Data Exchange (ETDEWEB)
Azarova, V V; Golyaev, Yu D; Saveliev, I I [Open Joint-Stock Company M.F. Stel' makh Polyus Research Institute, Moscow (Russian Federation)
2015-02-28
The history of invention and development of Zeeman laser gyroscopes, specific features of their optical scheme and operation principle are described. The construction and element base of modern laser angular velocity sensors with Zeeman-based frequency biasing are considered. The problems and prospects of their development are discussed. (laser gyroscopes)
Observations of the Joint Action of the Hanle and Zeeman Effects in the D2 Line of BaII
Ramelli, R; Bueno, J Trujillo; Belluzzi, L; Degl'Innocenti, E Landi
2009-01-01
We show a selection of high-sensitivity spectropolarimetric observations obtained over the last few years in the Ba II D2-line with the Zurich Imaging Polarimeter (ZIMPOL) attached to the Gregory Coude Telescope of IRSOL. The measurements were collected close to the solar limb, in several regions with varying degree of magnetic activity. The Stokes profiles we have observed show clear signatures of the joint action of the Hanle and Zeeman effects, in very good qualitative agreement with the theoretical expectations. Polarimetric measurements of this line show to be very well suited for magnetic field diagnostics of the lower solar chromosphere, from regions with field intensities as low as 1 gauss to strongly magnetized ones having kG field strengths.
Zeeman atomic absorption spectrometry
Energy Technology Data Exchange (ETDEWEB)
Hadeishi, T.; McLaughlin, R.
1978-08-01
The design and development of a Zeeman atomic absorption spectrometer for trace element analysis are described. An instruction manual is included which details the operation, adjustment, and maintenance. Specifications and circuit diagrams are given. (WHK)
Modelling the molecular Zeeman effect in M-dwarfs: methods and first results
Shulyak, D; Wende, S; Kochukhov, O; Piskunov, N; Seifahrt, A
2010-01-01
We present first quantitative results of the surface magnetic field measurements in selected M-dwarfs based on detailed spectra synthesis conducted simultaneously in atomic and molecular lines of the FeH Wing-Ford $F^4\\,\\Delta-X^4\\,\\Delta$ transitions. A modified version of the Molecular Zeeman Library (MZL) was used to compute Land\\'e g-factors for FeH lines in different Hund's cases. Magnetic spectra synthesis was performed with the Synmast code. We show that the implementation of different Hund's case for FeH states depending on their quantum numbers allows us to achieve a good fit to the majority of lines in a sunspot spectrum in an automatic regime. Strong magnetic fields are confirmed via the modelling of atomic and FeH lines for three M-dwarfs YZ~CMi, EV~Lac, and AD~Leo, but their mean intensities are found to be systematically lower than previously reported. A much weaker field ($1.7-2$~kG against $2.7$~kG) is required to fit FeH lines in the spectra of GJ~1224. Our method allows us to measure average...
The Maraner effect as a particular case of the quadratic Sagnac effect
Malykin, G. B.; Pozdnyakova, V. I.
2016-12-01
The quadratic Sagnac effect consists in a Michelson interferometer (MI) being located on a rotating base with a phase difference in its arms arising, the value of which depends on the orientation of the MI arms relative to the rotating base and on the angle of its rotation. This phase difference is caused by different values of the Newtonian (nonrelativistic) scalar gravitational potential of Coriolis forces acting on different MI arms, which leads to time dilation and varies with change in the angle of MI rotation. Distributions of the scalar gravitational potential of Coriolis forces over different parts of MI arms are considered. Allowance for this distribution makes it possible to calculate a value of the certain effect that is a higher approximation of the quadratic Sagnac effect. This effect is shown to be the Maraner effect known earlier, which also leads to a change in the phase difference of MI arms, but differs in value from the quadratic Sagnac effect. Consequently, the Maraner effect is a particular case of the quadratic Sagnac effect. Numerical estimations are performed.
Institute of Scientific and Technical Information of China (English)
Dong Zheng-Chao
2005-01-01
The coherent quantum transport is investigated in normal-metal/superconductor/normal-metal (N/S/N) double tunnel junctions under a Zeeman magnetic field on the S. Taking simultaneously into account the electron-injected current from one N electrode and the hole-injected current from the other N electrode, we derive a general formula for the differential conductance in the N/S/N system. It is shown that the conductance spectrum exhibits oscillatory behaviour with the bias voltage, and the oscillation amplitude is reduced with increasing temperature and Zeeman magnetic field, the Zeeman energy can lead to the Zeeman splitting of conductance peaks. In the tunnel limit, a series of bound states of quasiparticles will form in the S.
Stark and Zeeman effect in the [18.6]3.5 – X(1)4.5 transition of uranium monofluoride, UF
Energy Technology Data Exchange (ETDEWEB)
Linton, C., E-mail: colinton@unb.ca [Centre for Laser, Atomic, and Molecular Sciences, Physics Department, University of New Brunswick, 8 Bailey Drive, Fredericton, New Brunswick E3B 5A3 (Canada); Adam, A. G. [Centre for Laser, Atomic, and Molecular Sciences, Chemistry Department, University of New Brunswick, 30 Dineen Drive, Fredericton, New Brunswick E3B 5A3 (Canada); Steimle, T. C. [Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604 (United States)
2014-06-07
High resolution spectra of the 0-0 band of the [18.6]3.5 – X(1)4.5 transition of uranium monofluoride, UF, obtained using a laser ablation spectrometer, showed a perturbation in the upper state. Examination of the Stark and Zeeman effects yielded permanent electric dipole moments of 2.01 and 1.88 D and magnetic g-factors of 3.28 and 3.26 for the ground and excited states, respectively. Both the dipole moment and g-factor of the ground state are in good agreement with ab initio calculations [I. O. Antonov and M. C. Heaven, J. Phys. Chem. A 117, 9684 (2013)]. The Zeeman effect results confirm that the ground state arises primarily from the U{sup +}(5f {sup 3}7s{sup 24}I{sub 4.5})F{sup −} configuration and suggest several possible configurations for the upper state.
Institute of Scientific and Technical Information of China (English)
Xue Hui-Jie; Lü Tian-Quan; Zhang Hong-Chen; Yin Hai-Tao; Cui Lian; He Ze-Long
2012-01-01
The thermoelectric and the thermospin transport properties,including electrical conductivity,Seebeck coefficient,thermal conductivity,and thermoelectric figure of merit,of a parallel coupled double-quantum-dot Aharonov-Bohm interferometer are investigated by means of the Green function technique.The periodic Anderson model is used to describe the quantum dot system,the Rashba spin-orbit interaction and the Zeeman splitting under a magnetic field are considered.The theoretical results show the constructive contribution of the Rashba effect and the influence of the magnetic field on the thermospin effects.We also show theoretically that material with a high figure of merit can be obtained by tuning the Zeeman splitting energy only.
Energy Technology Data Exchange (ETDEWEB)
Terent' ev, Ya. V. [Physics Department, University of Regensburg, 93040 Regensburg (Germany); Ioffe Physical-Technical Institute, 194021 St. Petersburg (Russian Federation); Danilov, S. N.; Plank, H.; Loher, J.; Schuh, D.; Bougeard, D.; Weiss, D.; Ganichev, S. D. [Physics Department, University of Regensburg, 93040 Regensburg (Germany); Durnev, M. V.; Ivanov, S. V. [Ioffe Physical-Technical Institute, 194021 St. Petersburg (Russian Federation); Tarasenko, S. A.; Rozhansky, I. V. [Ioffe Physical-Technical Institute, 194021 St. Petersburg (Russian Federation); St. Petersburg State Polytechnic University, 195251 St. Petersburg (Russian Federation); Yakovlev, D. R. [Ioffe Physical-Technical Institute, 194021 St. Petersburg (Russian Federation); Experimentelle Physik 2, Technische Universität Dortmund, 44227 Dortmund (Germany)
2015-09-21
We report on a magneto-photoluminescence (PL) study of Zeeman effect in Mn modulation-doped InAs/InGaAs/InAlAs quantum wells (QW). Two PL lines corresponding to the radiative recombination of photoelectrons with free and bound-on-Mn holes have been observed. In the presence of a magnetic field applied in the Faraday geometry, both lines split into two circularly polarized components. While temperature and magnetic field dependence of the splitting are well described by the Brillouin function, providing an evidence for exchange interaction with spin polarized manganese ions, the value of the splitting exceeds by two orders of magnitude the value of the giant Zeeman splitting estimated for the average Mn density in QW obtained by the secondary ion mass spectroscopy.
Zeeman Spectroscopy of Tokamak Edge Plasmas
Hey, J. D.; Chu, C. C.; Mertens, Ph.
2002-12-01
Zeeman spectroscopy is a valuable tool both for diagnostic purposes, and for more fundamental studies of atomic and molecular processes in the boundary region of magnetically confined fusion plasmas (B ≃ 1 to 10 T). The method works well when the Zeeman (Paschen-Back) effect plays an important, or dominant, rôle in relation to other broadening mechanisms (Doppler, Stark, resonant excitation transfer) in determining the spectral line shape. For impurity species identification and temperature determination, Zeeman spectroscopy has advantages over charge-exchange recombination spectroscopy from highly excited radiator states, since spectral features practically unique to the species under investigation are analysed. It also provides useful information on probable mechanisms of line production (e.g. sputtering mechanisms, electron impact-induced dissociative excitation from molecules in the edge plasma), and on the temperature evolution of lower charge states in the process of convection inwards or diffusion outwards from the hotter plasma interior. Where different physical processes are responsible for different sections of the line profile — especially in the case of hydrogen isotopes — Zeeman spectroscopy can provide a set of characteristic temperatures for each section. The method is introduced in both passive and active spectroscopy, and general principles of the Zeeman effect are discussed with special reference to régimes of interest for the tokamak. Relevant physical processes (sputtering mechanisms, electron impact-induced dissociative excitation from molecules in the edge plasma, and ion-atom collisional heating mechanisms) are illustrated by sample spectra.
Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Bang, Ole; Kivshar, Yu.S.
1997-01-01
We show that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic (or chi((2))) medium is strongly influenced by induced Kerr effects, such as self- and cross-phase modulation. We prove the existence of rapidly oscillating solitary waves (a spatial analog of the g......We show that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic (or chi((2))) medium is strongly influenced by induced Kerr effects, such as self- and cross-phase modulation. We prove the existence of rapidly oscillating solitary waves (a spatial analog...
AP stars with resolved Zeeman split lines
Mathys, G.
1990-06-01
High-resolution, high SNR observations of a sample of sharp-lined A stars and of Ap stars showing resolved Zeeman split lines are presented. The Fe II lines 6147.7 A and 6149.2 A unexpectedly appear to be asymmetric in all stars where they are resolved. The blue component of the 6149.2 line, which is a Zeeman doublet, is deeper and narrower than its red component. For line 6147.7, whose Zeeman pattern does not differ much from a quadruplet, the red components are deeper than the blue ones. It is shown that a partial Paschen-Back effect can account for these properties. The potential implications of this finding for studies of magnetic Ap stars are discussed.
Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.
2011-01-01
Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…
Asensio Ramos, Andrés; Trujillo Bueno, Javier; Landi Degl'Innocenti, E.
2011-09-01
A big challenge in solar and stellar physics in the coming years will be to decipher the magnetism of the solar outer atmosphere (chromosphere and corona) along with its dynamic coupling with the magnetic fields of the underlying photosphere. To this end, it is important to develop rigorous diagnostic tools for the physical interpretation of spectropolarimetric observations in suitably chosen spectral lines. HAZEL is a computer program for the synthesis and inversion of Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects in some spectral lines of diagnostic interest, such as those of the He I 1083.0 nm and 587.6 nm (or D3) multiplets. It is based on the quantum theory of spectral line polarization, which takes into account in a rigorous way all the relevant physical mechanisms and ingredients (optical pumping, atomic level polarization, level crossings and repulsions, Zeeman, Paschen-Back and Hanle effects). The influence of radiative transfer on the emergent spectral line radiation is taken into account through a suitable slab model. The user can either calculate the emergent intensity and polarization for any given magnetic field vector or infer the dynamical and magnetic properties from the observed Stokes profiles via an efficient inversion algorithm based on global optimization methods.
Directory of Open Access Journals (Sweden)
A.P. Samila
2016-12-01
Full Text Available Using pulsed nuclear quadrupole resonance method with a fast Fourier transform of the free induction decay signals, the influence of a weak magnetic field (0 ÷ 10 Gauss on NQR spectral lines 69Ga and 115In in layered semiconductors GaSe and InSe was investigated. It has been found that the splitting of resonance lines, caused by the Zeeman effect, can be used to determine the magnitude and direction of the applied magnetic field.
Ballester, Ernest Alsina; Bueno, Javier Trujillo
2016-01-01
We highlight the main results of a radiative transfer investigation on the magnetic sensitivity of the solar Mg ii k resonance line at 2795.5 angstrom, accounting for the joint action of the Hanle and Zeeman effects as well as partial frequency redistribution (PRD) phenomena. We confirm that at the line center, the linear polarization signals produced by scattering processes are measurable, and that they are sensitive, via the Hanle effect, to magnetic fields with strengths between 5 and 50 G, approximately. We also show that the Zeeman effect produces conspicuous circular polarization signals, especially for longitudinal fields stronger than 50 G, which can be used to estimate the magnetization of the solar chromosphere via the familiar magnetograph formula. The most novel result is that magneto-optical effects produce, in the wings of the line, a decrease of the Q/I scattering polarization pattern and the appearance of U/I signals (i.e., a rotation of the plane of linear polarization). This sensitivity of t...
Simple quadratic magneto-optic Kerr effect measurement system using permanent magnets.
Pradeep, A V; Ghosh, Sayak; Anil Kumar, P S
2017-01-01
In recent times, quadratic magneto-optic Kerr effect (QMOKE) is emerging as an important experimental tool to investigate higher-order spin-orbit interactions in magnetic thin films and heterostructures. We have designed and constructed a simple, cost-effective QMOKE measurement system using permanent magnets. The permanent magnets are mounted on the inner surface of a cylindrical ferromagnetic yoke which can be rotated about its axis. Our system is sensitive to both the quadratic and linear MOKE signals. We use rotating field method to extract the QMOKE components in saturation. This system is capable of extracting the QMOKE signal from single crystals and thin film samples. Here we present the construction and working of the QMOKE measurement system using permanent magnets and report, for the first time, the QMOKE signal from Fe3O4 single crystal.
DEFF Research Database (Denmark)
Larsen, Erik Huusfeldt; Ekelund, J.
1989-01-01
A method for the determination of total selenium in nutritional supplements and selenised yeast is described. The samples were ashed in nitric acid. Hydrochloric acid was used to prevent precipitation of, in particular, iron salts. After appropriate dilutions, the selenium was determined by Zeeman...... the content of selenium in a selenised yeast check sample. Accuracy was assured using this sample and by recovery experiments. Between-day random error showed a coefficient of variation of 4.2%. Results from the analysis of eight different commercial supplements were in good agreement with declared contents....
Canavos, G. C.
1974-01-01
A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.
Sakaguchi, Hidetsugu; Malomed, Boris A
2016-01-01
We present an analysis of two-dimensional (2D) matter-wave solitons, governed by the pseudo-spinor system of Gross-Pitaevskii equations with self- and cross-attraction, which includes the spin-orbit coupling (SOC) in the general Rashba-Dresselhaus form, and, separately, the Rashba coupling and the Zeeman splitting. Families of semi-vortex (SV) and mixed-mode (MM) solitons are constructed, which exist and are stable in free space, as the SOC terms prevent the onset of the critical collapse and create the otherwise missing ground states in the form of the solitons. The Dresselhaus SOC produces a destructive effect on the vortex solitons, while the Zeeman term tends to convert the MM states into the SV ones, which eventually suffer delocalization. Existence domains and stability boundaries are identified for the soliton families. For physically relevant parameters of the SOC system, the number of atoms in the 2D solitons is limited by $\\sim 1.5\\times 10^{4}$. The results are obtained by means of combined analyti...
Sakaguchi, Hidetsugu; Sherman, E. Ya.; Malomed, Boris A.
2016-09-01
We present an analysis of two-dimensional (2D) matter-wave solitons, governed by the pseudospinor system of Gross-Pitaevskii equations with self- and cross attraction, which includes the spin-orbit coupling (SOC) in the general Rashba-Dresselhaus form, and, separately, the Rashba coupling and the Zeeman splitting. Families of semivortex (SV) and mixed-mode (MM) solitons are constructed, which exist and are stable in free space, as the SOC terms prevent the onset of the critical collapse and create the otherwise missing ground states in the form of the solitons. The Dresselhaus SOC produces a destructive effect on the vortex solitons, while the Zeeman term tends to convert the MM states into the SV ones, which eventually suffer delocalization. Existence domains and stability boundaries are identified for the soliton families. For physically relevant parameters of the SOC system, the number of atoms in the 2D solitons is limited by ˜1.5 ×104 . The results are obtained by means of combined analytical and numerical methods.
Induced Kerr effects and self-guided beams in quasi-phase-matched quadratic media [CBC4
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Bang, Ole; Kivshar, Yuri S.
1997-01-01
We show that quasi-phase-matching of quadratic media induces Kerr effects, such as self- and cross-phase modulation, and leads to the existence of a novel class of solitary waves, QPM-solitons......We show that quasi-phase-matching of quadratic media induces Kerr effects, such as self- and cross-phase modulation, and leads to the existence of a novel class of solitary waves, QPM-solitons...
Zamani, Ali; Azargoshasb, Tahereh; Niknam, Elahe
2017-10-01
In current article, the Zeeman effect is considered in the presence of simultaneous Rashba and Dresselhaus spin-orbit interactions (SOI) and under such circumstances the second and third harmonic generations (SHG and THG) of a GaAs quantum ring are investigated at finite temperature. The effective Hamiltonian is derived in cylindrical coordinate while the angular part is eliminated because of axial symmetry and the energy eigenvalues and eigenvectors of two lowest levels are obtained numerically. Eventually, the optical properties of such system are studied hiring compact density matrix approach. The results show that, an increase in the magnetic field, leads to blue shift in resonant peaks of both SHG and THG. Furthermore, by reducing the temperature, all the resonant peaks of both SHG and THG experience a red shift. Finally, the effect of the structure dimension is studied and results illustrate that variation of size leads to both red and blue shifts in resonant peaks.
Zeeman spectrum and magnetic effect of trapped 199Hg+ ions%囚禁汞(199Hg+)离子Zeeman谱及磁场效应
Institute of Scientific and Technical Information of China (English)
黄雄; 杨玉娜; 柳浩; 高克林; 佘磊; 李交美
2011-01-01
The experiment of optical-microwave double-resonance in trapped mercury is the basis for the research of mercury ion microwave frequency standard.The second-order Zeeman effect is one of the important factor affecting frequency stability and the magnetic field effect.The Zeeman spectrum of ground state of trapped 199Hg+ ion was measured by the method of optical-microwave double-resonance.The clock transition frequency and linewidth of the clock transition line were obtained by scanning the microwave frequency in a narrow region.The magnetic field in trapping area was shielded by the materials of permalloy.The linewidth of the clock transition line is decreased to about 1.5 Hz.Comparing the clock transition frequency without magnetic shielding, the clock transition frequency of magnetic shielding decreases 13.5 Hz.According to the second-order Zeeman effect, it's calculated that the magnetic field of trapped region is about 0.1 Guass.%囚禁汞离子的光微波双共振实验是开展汞离子微波频标的实验基础.二级Zeeman效应是影响频率稳定度和磁场效应的重要因素之一.利用光学微波双共振方法测量了囚禁199Hg+离子基态Zeeman分裂.通过减小微波扫描的频率范围,得到钟跃迁频率和谱线线宽.采用磁屏蔽材料(坡莫合金)对离子阱囚禁区域的磁场进行屏蔽.使得囚禁汞离子的钟跃迁谱线的线宽减小到1.5 Hz.相对于无磁场屏蔽时,钟跃迁频率减小13.5 Hz,并利用二级Zeeman效应估算出磁屏蔽后离子囚禁区域磁场大小为0.1高斯.
CounterPoint: Zeeman-split absorption lines
Deen, Casey
2015-12-01
CounterPoint works in concert with MoogStokes (ascl:1308.018). It applies the Zeeman effect to the atomic lines in the region of study, splitting them into the correct number of Zeeman components and adjusting their relative intensities according to the predictions of Quantum Mechanics, and finally creates a Moog-readable line list for use with MoogStokes. CounterPoint has the ability to use VALD and HITRAN line databases for both atomic and molecular lines.
Directory of Open Access Journals (Sweden)
R. Larsson
2015-10-01
Full Text Available We present a comparison of a reference and a fast radiative transfer model using numerical weather prediction profiles for the Zeeman-affected high altitude Special Sensor Microwave Imager/Sounder channels 19–22. We find that the models agree well for channels 21 and 22 compared to the channels' system noise temperatures (1.9 and 1.3 K, respectively and the expected profile errors at the affected altitudes (estimated to be around 5 K. For channel 22 there is a 0.5 K average difference between the models, with a standard deviation of 0.24 K for the full set of atmospheric profiles. Same channel, there is 1.2 K in average between the fast model and the sensor measurement, with 1.4 K standard deviation. For channel 21 there is a 0.9 K average difference between the models, with a standard deviation of 0.56 K. Same channel, there is 1.3 K in average between the fast model and the sensor measurement, with 2.4 K standard deviation. We consider the relatively small model differences as a validation of the fast Zeeman effect scheme for these channels. Both channels 19 and 20 have smaller average differences between the models (at below 0.2 K and smaller standard deviations (at below 0.4 K when both models use a two-dimensional magnetic field profile. However, when the reference model is switched to using a full three-dimensional magnetic field profile, the standard deviation to the fast model is increased to almost 2 K due to viewing geometry dependencies causing up to ± 7 K differences near the equator. The average differences between the two models remain small despite changing magnetic field configurations. We are unable to compare channels 19 and 20 to sensor measurements due to limited altitude range of the numerical weather prediction profiles. We recommended that numerical weather prediction software using the fast model takes the available fast Zeeman scheme into account for data assimilation of the affected sensor channels to better
Momjian, E
2012-01-01
We present a second epoch of observations of the 44 GHz Class I methanol maser line toward the star forming region OMC-2. The observations were carried out with the Very Large Array, and constitute one of the first successful Zeeman effect detections with the new WIDAR correlator. Comparing to the result of our earlier epoch of data for this region, we find that the intensity of the maser increased by 50%, but the magnetic field value has stayed the same, within the errors. This suggests that the methanol maser may be tracing the large-scale magnetic field that is not affected by the bulk gas motions or turbulence on smaller scales that is causing the change in maser intensity.
Ryckelynck, Philippe
2011-01-01
This paper addresses the classical and discrete Euler-Lagrange equations for systems of $n$ particles interacting quadratically in $\\mathbb{R}^d$. By highlighting the role played by the center of mass of the particles, we solve the previous systems via the classical quadratic eigenvalue problem (QEP) and its discrete transcendental generalization. The roots of classical and discrete QEP being given, we state some conditional convergence results. Next, we focus especially on periodic and choreographic solutions and we provide some numerical experiments which confirm the convergence.
The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery.
Kirkpatrick, John P; Meyer, Jeffrey J; Marks, Lawrence B
2008-10-01
The linear-quadratic (LQ) model is widely used to model the effect of total dose and dose per fraction in conventionally fractionated radiotherapy. Much of the data used to generate the model are obtained in vitro at doses well below those used in radiosurgery. Clinically, the LQ model often underestimates tumor control observed at radiosurgical doses. The underlying mechanisms implied by the LQ model do not reflect the vascular and stromal damage produced at the high doses per fraction encountered in radiosurgery and ignore the impact of radioresistant subpopulations of cells. The appropriate modeling of both tumor control and normal tissue toxicity in radiosurgery requires the application of emerging understanding of molecular-, cellular-, and tissue-level effects of high-dose/fraction-ionizing radiation and the role of cancer stem cells.
Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
DEFF Research Database (Denmark)
Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel
2016-01-01
We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system, a...
Application of SP2000 Spectrograph in Experiment of Zeeman Effect%SP2000摄谱仪在塞曼效应实验中的应用
Institute of Scientific and Technical Information of China (English)
杨能勋; 王玉清
2011-01-01
Zeemen Effect measurement is executed using old Zeemen Effect instrument remodeled by SP2000 spectrograph, and the method of data measurement of circle figure is converted spectrum figure of Zeemen Effect fission. The spectrum figure of Zeemen Effect fission is used to detect peak using SP2000 spectrograph and the data acquisition and processing is processed by computer auxiliary equipment. The stability and precision of measurement are improved, and the measurement method of Zeeman Effect experiment is expanded.%利用SP2000摄谱仪改装旧塞曼效应仪进行塞曼效应测量。将塞曼效应分裂圆环图的数据测量方法转换为塞曼效应分裂光谱图的数据测量方法，利用SP2000摄谱仪系统软件对采集的光谱图进行检峰，计算机辅助设备采集和处理数据，从而提高了测量的稳定性和精确度，拓展了塞曼效应实验的测量方法。
Berdyugina, S. V.; Braun, P. A.; Fluri, D. M.; Solanki, S. K.
2005-12-01
Many diatomic molecules present in the atmospheres of the Sun and cool stars exhibit the Paschen-Back effect at field strengths typical of sunspots and active cool stars. Here we present a complete theoretical description of the molecular Paschen-Back efect in Hund's cases (a), (b) and all cases intermediate to them. This description allows us to compute the splitting of levels of any multiplicity and the transitions between them. We also introduce a generalized description of the effective magnetic Landé factor applicable not just in the Zeeman regime, but also in the Paschen-Back regime. We find that in the regime of the partial Paschen-Back effect strongly asymmetric Stokes profiles are produced, whose strengths and asymmetries depend sensitively on the magnetic field. In the regime of the complete Paschen-Back effect the profiles become symmetric again (although they may be strongly shifted). The strength of the forbidden and satellite transitions increases rapidly with field strength in the partial Paschen-Back regime, while the strength of the main branch transitions decreases. These signatures hold promise to form the basis of new diagnostics of solar and stellar magnetic fields.
AC Zeeman potentials for atom chip-based ultracold atoms
Fancher, Charles; Pyle, Andrew; Ziltz, Austin; Aubin, Seth
2015-05-01
We present experimental and theoretical progress on using the AC Zeeman force produced by microwave magnetic near-fields from an atom chip to manipulate and eventually trap ultracold atoms. These AC Zeeman potentials are inherently spin-dependent and can be used to apply qualitatively different potentials to different spin states simultaneously. Furthermore, AC Zeeman traps are compatible with the large DC magnetic fields necessary for accessing Feshbach resonances. Applications include spin-dependent trapped atom interferometry and experiments in 1D many-body physics. Initial experiments and results are geared towards observing the bipolar detuning-dependent nature of the AC Zeeman force at 6.8 GHz with ultracold 87Rb atoms trapped in the vicinity of an atom chip. Experimental work is also underway towards working with potassium isotopes at frequencies of 1 GHz and below. Theoretical work is focused on atom chip designs for AC Zeeman traps produced by magnetic near-fields, while also incorporating the effect of the related electric near-fields. Electromagnetic simulations of atom chip circuits are used for mapping microwave propagation in on-chip transmission line structures, accounting for the skin effect, and guiding impedance matching.
Radiobiological effect based treatment plan optimization with the linear quadratic model
Energy Technology Data Exchange (ETDEWEB)
Schell, Stefan; Wilkens, Jan J.; Oelfke, Uwe [German Cancer Research Center, Heidelberg (Germany). Dept. of Medical Physics in Radiation Oncology
2010-07-01
As an approach towards more biology-oriented treatment planning for external beam radiation therapy, we present the incorporation of local radiation damage models into three dimensional treatment planning. This allows effect based instead of dose based plan optimization which could potentially better match the biologically relevant tradeoff between target and normal tissues. In particular, our approach facilitates an effective comparison of different fractionation schemes. It is based on the linear quadratic model to describe the biological radiation effect. Effect based optimization was integrated into our inverse treatment planning software KonRad, and we demonstrate the resulting differences between conventional and biological treatment planning. Radiation damage can be analyzed both qualitatively and quantitatively in dependence of the fractionation scheme and tissue specific parameters in a three dimensional voxel based system. As an example the potential advantages as well as the associated risks of hypofractionation for prostate cancer are analyzed and visualized with the help of effective dose volume histograms. Our results suggest a very conservative view regarding alternative fractionation schemes since uncertainties in biological parameters are still too big to make reliable clinical predictions. (orig.)
Institute of Scientific and Technical Information of China (English)
罗洋城
2001-01-01
本文通过对文献 [1] 关于塞曼效应实验原理的分析，指出了其实验内容之测电子荷质比的不当之处.%By analysing the experimental principle of Zeeman effect in document[1],it is pointed out in this paper that the experiment content about the measurement of the charge-mass ratio of electron in document[1]is improper.
塞曼效应实验仪器快速调试原则%The Speedy Adjustment Principle of Zeeman Effect Experiment
Institute of Scientific and Technical Information of China (English)
张广平
2011-01-01
提出在塞曼效应实验仪器快速调试中，要掌握在一定的仪器顺序不变，光学元件紧靠在一起并且相对位置不变的条件下，将摄像头三个旋钮从有连线的一端观看逆时针旋到底的粗调原则，才能快速调试实验所需干涉圆环．%As is mentioned in the paper, it needs to master a certain order of instruments in the process of adjusting devices of Zeeman Effect at a high speed. Only when the components of optics are closely related to each other and keep in a constantly relative position, can the principle of rough adjustment test the needed intervening ring by watching through the camera with three line -linked buttons anticlockwise.
On the structure of quadratic Gauss sums in the Talbot effect.
Fernández-Pousa, Carlos R
2017-05-01
We report on the detailed derivation of the Gauss sums leading to the weighting phase factors in the fractional Talbot effect. In contrast to previous approaches, the derivation is directly based on the two coprime integers p and q that define the fractional Talbot effect so that, using standard techniques from the number theory, the computation is reduced, up to a global phase, to the trivial completion of the exponential of the square of a sum. In addition, it is shown that the Gauss sums can be reduced to only two cases, depending on the parity of integer q. Explicit and simpler expressions for the two forms of the Talbot weighting phases are also provided. The Gauss sums are presented as a discrete Fourier transform pair between quadratic phase sequences showing perfect periodic autocorrelation and a connection with the theory of biunimodular sequences is presented. In addition, the Talbot weighting factors of orders 1/q and 2/q are reduced to a closed form, and the equivalence to existing characterizations of Talbot weighting phases is also discussed. The relationship with one-dimensional multilevel phase structures is exemplified by the study of Talbot array illuminators. These results simplify and extend the description of the role played by Gauss sums in the fractional Talbot effect, providing a compact synthesis of previous results.
Detailed study of a transverse field Zeeman slower
Ben Ali, D.; Badr, T.; Brézillon, T.; Dubessy, R.; Perrin, H.; Perrin, A.
2017-03-01
We present a thorough analysis of a Zeeman slower for sodium atoms made of permanent magnets in a Halbach configuration. Due to the orientation of the magnetic field, the polarization of the slowing laser beam cannot be purely circular, leading to optical leakages into dark states. To circumvent this effect, we propose an atomic state preparation stage that is able to significantly increase the performance of the Zeeman slower. After a careful theoretical analysis of the problem, we experimentally implement an optical pumping stage leading to an increase in the magneto-optical trap loading rate by 3.5. Such a method is easy to set up and could be extended to other Zeeman slower architectures.
Detailed study of a transverse field Zeeman slower
Ali, Dany Ben; Brézillon, T; Dubessy, Romain; Perrin, Hélène; Perrin, A
2016-01-01
We present a thorough analysis of a Zeeman slower for sodium atoms made of permanent magnets in a Halbach configuration. Due to the orientation of the magnetic field, the polarisation of the slowing laser beam cannot be purely circular leading to optical leakages into dark states. To circumvent this effect, we propose an atomic state preparation stage able to significantly increase the performances of the Zeeman slower. After a careful theoretical analysis of the problem, we experimentally implement an optical pumping stage leading to an increase of the magneto-optical trap loading rate by 3.5. Such method is easy to set up and could be extended to other Zeeman slower architectures.
Lu, Peng
2015-10-01
Cooperation is vital in human societies and therefore is widely investigated in the evolutionary game theory. Varieties of mechanisms have been proposed to overcome temptation and promote cooperation. Existing studies usually believe that agents are rational, but irrationalism such as emotions and feelings matters as well. Winner and loser are defined by their payoffs. In addition to admiring and imitating winners, the mechanism of sympathizing and imitating losers is introduced into the model as an alternative action rule, and each one plays the prisoners' dilemma game with eight neighbors under the influence of both irrationalism and rationalism. Rationalism refers to imitating winner to get highest payoff, and irrationalism means that people sympathize and adopt the actions of losers. As it is widely recognized that temptation reduces cooperation, this study focuses on the effect of sympathy on cooperation within a certain group or society. If it overcomes temptation that leads to defection, sympathy will be a powerful mechanism to promote cooperative behavior. Simulation results indicate that sympathy and temptation shares similar quadratic relationships with cooperation. Both sympathy and temptation undermine cooperation below their thresholds, and they both promote cooperation above their thresholds. Temptation not only reduces cooperation but also promote it as temptation goes beyond the threshold. Although sympathy is a good merit or human nature that is beneficial to society, a crisis or collapse of cooperation is inevitable when the sympathy propensity is relatively smaller. After cooperation reaches a minimal bottom, it then rises increasingly and dramatically, which brings a much brighter future of the society.
Description of anomalous Zeeman patterns in stellar astrophysics
Pain, Jean-Christophe
2013-01-01
The influence of a magnetic field on the broadening of spectral lines and transition arrays in complex spectra is investigated. The anomalous absorption or emission Zeeman pattern is a superposition of many profiles with different relative strengths, shifts, widths, asymmetries and sharpnesses. The "sigma" and "pi" profiles can be described statistically, using the moments of the Zeeman components. We present two statistical modellings: the first one provides a diagnostic of the magnetic field and the second one can be used to include the effect of a magnetic field on simulated atomic spectra in an approximate way.
Quadratic solitons as nonlocal solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole
2003-01-01
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...
2012-02-09
several optimization models and algorithm design for problems from computer vision and learning , research on sparse solutions in quadratic optimization...following papers: [9] L. Mukherjee, V. Singh, J. Peng and C. Hinrichs. Learning kernels for variants of normalized cuts: Convex relaxations and...are very small gaps compared to state-of-the-art knowledge in comunications . Table 1. Bounds for adjacency matrix
Characterization of anomalous Zeeman patterns in complex atomic spectra
Pain, Jean-Christophe
2012-01-01
The modeling of complex atomic spectra is a difficult task, due to the huge number of levels and lines involved. In the presence of a magnetic field, the computation becomes even more difficult. The anomalous Zeeman pattern is a superposition of many absorption or emission profiles with different Zeeman relative strengths, shifts, widths, asymmetries and sharpnesses. We propose a statistical approach to study the effect of a magnetic field on the broadening of spectral lines and transition arrays in atomic spectra. In this model, the sigma and pi profiles are described using the moments of the Zeeman components, which depend on quantum numbers and Land\\'{e} factors. A graphical calculation of these moments, together with a statistical modeling of Zeeman profiles as expansions in terms of Hermite polynomials are presented. It is shown that the procedure is more efficient, in terms of convergence and validity range, than the Taylor-series expansion in powers of the magnetic field which was suggested in the past...
Solvable quadratic Lie algebras
Institute of Scientific and Technical Information of China (English)
ZHU; Linsheng
2006-01-01
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.
The recondite intricacies of Zeeman Doppler mapping
Stift, M J; Cowley, C R
2011-01-01
We present a detailed analysis of the reliability of abundance and magnetic maps of Ap stars obtained by Zeeman Doppler mapping (ZDM). It is shown how they can be adversely affected by the assumption of a mean stellar atmosphere instead of appropriate "local" atmospheres corresponding to the actual abundances in a given region. The essenceof the difficulties was already shown by Chandrasekhar's picket-fence model. The results obtained with a suite of Stokes codes written in the Ada programming language and based on modern line-blanketed atmospheres are described in detail. We demonstrate that the high metallicity values claimed to have been found in chemically inhomogeneous Ap star atmospheres would lead to local temperature structures, continuum and line intensities, and line shapes that differ significantly from those predicted by a mean stellar atmosphere. Unfortunately, past applications of ZDM have consistently overlooked the intricate aspects of metallicity with their all-pervading effects. The erroneou...
Tuning Characteristics of Frequency Difference for Zeeman-Birefringence He-Ne Dual Frequency Laser
Institute of Scientific and Technical Information of China (English)
肖岩; 张书练; 李岩; 朱钧
2003-01-01
Characteristics of frequency difference tuning of Zeeman-birefringence He-Ne dual frequency lasers (ZBDFLs) are explored. We design an automatic system of tuning cavity and power detection, which can tune the laser cavity and record the tuning curves of light power and frequency difference simultaneously. A synthetic phenomenon by Zeeman effect, mode pulling effect and birefringence effect is verified to exist in ZBDFLs. By analysing the tuning behaviour, this synthetic phenomenon is discovered and qualitatively explained for the first time.
Tang, Chun-Ming; Jian, Jin-Bao
2008-10-01
Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The "active set" strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered.
Institute of Scientific and Technical Information of China (English)
罗剑峰; 兰勇; 康冬丽; 尹红伟
2011-01-01
The charge-mass ratio of electron can be measured from Zeeman effect experiment.In the experiment performed by the students,the measured value is 30～50% less than the standard value,and through detailedly studying we finally find that the main reason accounting for this big error is that the distance between the two pieces of reflecting mirror installed within Fabry-Perot standard device,offered by the paraphrastic list,is not correct.Moreover,in order to improve the measuring accuracy of charge-mass ratio of electron,the Tesla meter,which is used to measure the intensity of magnetic field,should be equipped for Zeeman effect experiment.%塞曼效应实验可以测量电子荷质比,实验中发现测量值比公认值小30%～50%,通过查找原因最终发现说明书所提供的法布里-珀罗标准具两块镜片的间距不准确是导致误差的主要原因。为提高测量准确性,应当为塞曼效应实验配备测量磁场强度的特斯拉仪。
利用智能手机拍照功能研究塞曼效应实验%Research of Zeeman Effect Based on the Camera of Smart Phone
Institute of Scientific and Technical Information of China (English)
刘卫卫
2015-01-01
It using smart phone to shoot Zeeman effect map and using CorelDraw to handle the data of the im-age. And then,calculates the charge-mass ratio of electron. By this method,the charge-mass ratio of electron was calculated about 1. 749 × 1011 C/Kg. The percentage error is 0. 63% when compared with theoretical val-ue. This method provides a convenient way to study Zeeman effect and calculate the charge-mass ratio of elec-tron.%利用智能手机对塞曼效应图谱进行拍摄，并利用Coreldraw软件对图像进行处理，从而计算出电子的荷质比。通过本方法所测得的电子荷质比为1.75×1011 C/Kg，与理论值的相对误差仅为0.63%。智能手机的照相功能为研究塞曼效应以及测量电子荷质比提供了一种简便的方法。
Design and characterization of a Zeeman Slower
Guevara-Bertsch, Milena; Chavarría-Sibaja, Andrés; Avendaño, Esteban; Herrera-Sancho, Óscar Andrey
2016-01-01
We report on an investigation of a method that applies simultaneously two different mathematical models in order to optimize the design of a Zeeman Slower towards the implementation of ultra cold atoms in solid state physics. We introduce the implementation of a finite element simulation that allows us to predict with great accuracy the magnetic field intensity profile generated by the proposed design. Through the prediction of the behavior of the Zeeman Slower a greater control is acquired, which allows the optimization of the different experimental variables. We applied the method in the design of a multilayer solenoidal "Spin-Flip" Zeeman Slower for strontium atoms. The magnetic intensity profile generated by the Zeeman Slower is in agreement with the magnetic field strength profile necessary for the atom cooling and tends to zero in both end sides. The latter terms are essential in order to optimize the amount of trapped and cooled atoms.
Institute of Scientific and Technical Information of China (English)
章苗苗; 朱雷丽; 王强; 杨建宋
2014-01-01
在简要回顾了汞光谱塞曼效应原理后，本文详细研究了运用法布里-帕罗干涉仪所得的汞光谱π分量谱线和σ分量谱线特征，包括如何由π线图像确定汞光源所处的磁感应强度，在σ分量谱线图像中K级前三条谱线的丢失及原因的理论分析，汞光谱诸塞曼谱线相对强度的测量及分析。%After a brief review of the principles of mercury spectral Zeeman effect ,the characteristics of π component andσcomponent spectral lines of mercury spectrum are studied in detail by using Fabry-Perot interferometer ,including how to determine the magnetic induction intensity in the mercury light source by the π spectral line image , the loss of the beginning three spectral lines of K level in the σcomponent spectral line image and the corresponding theoretical analysis , and the measurement of the relative intensity of Zeeman spectral lines .
An Effective Branch-and-Bound Algorithm for Convex Quadratic Integer Programming
Buchheim, Christoph; Caprara, Alberto; Lodi, Andrea
We present a branch-and-bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the variables, a lower bound is given by the continuous minimum of the restricted objective function. We improve this bound by exploiting the integrality of the variables using suitably-defined lattice-free ellipsoids. Experiments show that our approach is very fast on both unconstrained problems and problems with box constraints. The main reason is that all expensive calculations can be done in a preprocessing phase, while a single node in the enumeration tree can be processed in linear time in the problem dimension.
Stellar longitudinal magnetic field determination through multi-Zeeman signatures
Vélez, J C Ramírez; Navarro, S G; Córdova, J P; Sabin, L; Ruelas-Mayorga, A
2016-01-01
Context. A lot of effort has been put into the detection and determination of stellar magnetic fields using the spectral signal obtained from the combination of hundreds or thousands of individual lines, an approach known as multi-line techniques. However, so far most of multi-line techniques developed that retrieve stellar mean longitudinal magnetic fields recourse to sometimes heavy simplifications concerning line shapes and Zeeman splittings. Aims. To determine stellar longitudinal magnetic fields by means of the Principal Components Analysis and Zeeman Doppler Imaging (PCA-ZDI) multi-line technique, based on accurate polarised spectral line synthesis. Methods. In this paper we present the methodology to perform inversions of profiles obtained with PCA-ZDI. Results. Inversions with various magnetic geometries, field strengths and rotational velocities show that we can correctly determine the effective longitudinal magnetic field in stars using the PCA-ZDI method.
Wang, Xuping; Liu, Bing; Yang, Yuguo; Zhang, Yuanyuan; Lv, Xianshun; Wei, Lei; Xu, Jianhua; Ma, Ling; Wang, Jiyang
2017-06-01
Copper doped KTN crystals with different doping concentrations were grown by the Czochralski method. The XRD patterns show that all of the crystals are in cubic phase at room temperature. The influences of the CuO doping concentrations on dielectric properties of the crystals were measured. Cu: KTN crystals exhibited color changes depending on the doping concentrations. It was found that the inhomogeneous composition property can be used to form gradient refractivity effect in the case of ion doping. The refractive index gradient reaches 33×10-3/mm for the grown Cu: KTNN crystals. Base on the interaction between the quadratic electro-optic effect and the gradient refractivity effect, the deflection and the intensity of a Cu: KTa0.62Nb0.38O3 sample were modulated in different orientations of the crystal. The deflection efficiency and the half-wave voltage of the modulation are 45 mrad/kV and 75 V, respectively.
Westgate, Philip M; Braun, Thomas M
2012-09-10
Generalized estimating equations (GEE) are commonly used for the analysis of correlated data. However, use of quadratic inference functions (QIFs) is becoming popular because it increases efficiency relative to GEE when the working covariance structure is misspecified. Although shown to be advantageous in the literature, the impacts of covariates and imbalanced cluster sizes on the estimation performance of the QIF method in finite samples have not been studied. This cluster size variation causes QIF's estimating equations and GEE to be in separate classes when an exchangeable correlation structure is implemented, causing QIF and GEE to be incomparable in terms of efficiency. When utilizing this structure and the number of clusters is not large, we discuss how covariates and cluster size imbalance can cause QIF, rather than GEE, to produce estimates with the larger variability. This occurrence is mainly due to the empirical nature of weighting QIF employs, rather than differences in estimating equations classes. We demonstrate QIF's lost estimation precision through simulation studies covering a variety of general cluster randomized trial scenarios and compare QIF and GEE in the analysis of data from a cluster randomized trial. Copyright © 2012 John Wiley & Sons, Ltd.
Bian, Lin
2004-12-01
Distortion product otoacoustic emissions (DPOAEs) are generated from the nonlinear transduction n cochlear outer hair cells. The transducer function demonstrating a compressive nonlinearity can be estimated from low-frequency modulation of DPOAEs. Experimental results from the gerbils showed that the magnitude of quadratic difference tone (QDT, f2-f1) was either enhanced or suppressed depending on the phase of the low-frequency bias tone. Within one period of the bias tone, QDT magnitudes exhibited two similar modulation patterns, each resembling the absolute value of the second derivative of the transducer function. In the time domain, the center notches of the modulation patterns occurred around the zero crossings of the bias pressure, whereas peaks corresponded to the increase or decrease in bias pressure. Evaluated with respect to the bias pressure, modulated QDT magnitude displayed a double-modulation pattern marked by a separation of the center notches. Loading/unloading of the cochlear transducer or rise/fall in bias pressure shifted the center notch to positive or negative sound pressures, indicating a mechanical hysteresis. These results suggest that QDT arises from the compression that coexists with the active hysteresis in cochlear transduction. Modulation of QDT magnitude reflects the dynamic regulation of cochlear transducer gain and compression.
An Algorithm for Solving Quadratic Programming Problems
Directory of Open Access Journals (Sweden)
V. Moraru
1997-08-01
Full Text Available Herein is investigated the method of solution of quadratic programming problems. The algorithm is based on the effective selection of constraints. Quadratic programming with constraints-equalities are solved with the help of an algorithm, so that matrix inversion is avoided, because of the more convenient organization of the Calculus. Optimal solution is determined in a finite number of iterations. It is discussed the extension of the algorithm over solving quadratic non-convex programming problems.
Various applications of Zeeman atomic absorption spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Koizumi, H.
1978-06-01
The application of the Zeeman effect to atomic absorption spectroscopy has been studied over the past several years. This technique has a larger area of application than conventional AAS because of its high degree of selectivity. The ZAA technique can be used for organometallic species determination by interfacing with a high-pressure liquid chromatograph. Various kinds of eluents can be directly introduced in the ZAA system; even organic solvents or high-concentration salt solutions. For example, the Co atom in the functional center of Vitamin B12 molecule was separately analyzed in the presence of much larger amounts of inorganic Co. In the ZAA technique, interference caused by direct spectral overlap can also be corrected. As a typical example, the Sb line at 217.02 nm overlaps the Pb absorption line at 217.00 nm. However, 1000 ppM of Pb did not cause any interference signal in the Sb analysis by ZAA. This is especially important in the analysis of gun powder residue that is often carried out by chemists working in the forensic field. In the determination of trace elements in matrices of unknown composition, the ZAA technique achieved highly reliable results by employing the standard addition method to correct for chemical interferences, because any nonspecific absorption or emission does not give rise to interference signals with this technique.
Accardi, Luigi
2009-01-01
We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. Within this semigroup we characterize the unitary and the isometric elements.
Quadratic eigenvalue problems.
Energy Technology Data Exchange (ETDEWEB)
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...
The Hanle and Zeeman polarization signals of the solar Ca II 8542 \\AA\\ line
Štěpán, Jiří
2016-01-01
We highlight the main results of a three-dimensional (3D) multilevel radiative transfer investigation about the solar disk-center polarization of the Ca {\\sc ii} 8542 \\AA\\ line. First, we investigate the linear polarization due to the atomic level polarization produced by the absorption and scattering of anisotropic radiation in a 3D model of the solar atmosphere, taking into account the symmetry breaking effects caused by its thermal, dynamic and magnetic structure. Second, we study the contribution of the Zeeman effect to the linear and circular polarization. Finally, we show examples of the Stokes profiles produced by the joint action of atomic level polarization and the Hanle and Zeeman effects. We find that the Zeeman effect tends to dominate the linear polarization signals only in the localized patches of opposite magnetic polarity where the magnetic field is relatively strong and slightly inclined, while outside such very localized patches the linear polarization is often dominated by the contribution ...
Giant dynamical Zeeman split in inverse spin valves
Wang, X. R.
2008-01-01
The inversion of a spin valve device is proposed. Opposite to a conventional spin valve of a non-magnetic spacer sandwiched between two ferromagnetic metals, an inverse spin valve is a ferromagnet sandwiched between two non-magnetic metals. It is predicted that, under a bias, the chemical potentials of spin-up and spin-down electrons in the metals split at metal-ferromagnet interfaces, a dynamical Zeeman effect. This split is of the order of an applied bias. Thus, there should be no problem o...
Modeling of Stark–Zeeman Lines in Magnetized Hydrogen Plasmas
Indian Academy of Sciences (India)
J. Rosato; H. Bufferand; H. Capes; M. Koubiti; L. Godbert-Mouret; Y. Marandet; R. Stamm
2015-12-01
The action of electric and magnetic fields on atomic species results in a perturbation of the energy level structure, which alters the shape of spectral lines. In this work, we present the Zeeman–Stark line shape simulation method and perform new calculations of hydrogen Lyman and Balmer lines, in the framework of magnetic fusion research. The role of the Zeeman effect, fine structure and the plasma's non-homogeneity along the line-of-sight are investigated. Under specific conditions, our results are applicable to DA white dwarf atmospheres.
Klein, Andreas G.; Muthen, Bengt O.
2007-01-01
In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…
Koklu, Oguz; Topcu, Abdullah
2012-01-01
Pre-existing misconceptions are serious impediments to learning in mathematics. Means for detecting and correcting them have received much attention in the literature of educational research. Dynamic geometry software has been tried at different grade levels. This quasi-experimental study investigates the effect of Cabri-assisted instruction on…
Nguyen, Trung; Kokkin, Damian L.; Steimle, Timothy; Kozyryev, Ivan; Doyle, John M.
2015-06-01
Motivated by a diverse range of applications in physics and chemistry, currently there is great interest in the cooling of molecules to very low temperatures (≤1 mK). Direct laser cooling has been previously demonstrated for the diatomic radicals SrF, YO, and CaF, and most recently a three-dimensional magneto-optical trap (MOT) of SrF molecules was achieved. To determine the possibility of laser cooling for polyatomic molecules containing three or more atoms, detailed information is required about their Franck-Condon factors (FCFs) for emission from the excited states of interest. Here we report on the high-resolution laser excitation spectra, recorded field-free and in the presence of a static magnetic field, and on the dispersed fluorescence (DF) spectra for the A^2Π1/2 ← X^2σ^+ and B^2σ^+ ← X ^2σ^+ electronic transitions of SrOH. The DF spectra were analyzed to precisely determine FCFs and compared with values predicted using a normal coordinate GF matrix approach. The recorded Zeeman spectra were analyzed to determine the magnetic moments. Implication for proposed laser cooling and trapping experiments for SrOH will be presented. E.S. Shuman, J.F. Barry and D. DeMille, Nature 467, 820 (2010) J.F. Barry, E.S. Shuman, E.B. Norrgard and D. DeMille, Phys. Rev. Lett. 108, 103002 (2012) M.T. Hummon, M. Yeo, B.K. Stuhl, A.L. Collopy, Y. Xia, and J. Ye, Phys. Rev. Lett. 110, 143001 (2013) M. Yeo, M.T. Hummon, A.L. Collopy, B. Yan, B. Hemmerling, E. Chae, J.M. Doyle, and J. Ye, arXiv:1501.04683 (2015) V. Zhelyazkova, A. Cournol, T.E. Wall, A. Matsushima, J.J. Hudson, E.A. Hinds, M.R. Tarbutt, and B.E. Sauer, Phys. Rev. A 89, 053416 (2014) J.F. Barry, D.J. McCarron, E.B. Norrgard, M.H. Steinecker and D. DeMille, Nature 512, 286 (2014) D.J. McCarron, E.B. Norrgard, M.H. Steinecker and D. DeMille, arXiv:1412.8220 (2014)
Energy Technology Data Exchange (ETDEWEB)
Revalde, Gita, E-mail: gitar@latnet.lv [Institute of Technical Physics, Riga Technical University, P.Valdena 3, Riga LV 1050 (Latvia); Sholupov, Sergey; Ganeev, Alexander; Pogarev, Sergey; Ryzhov, Vladimir [St. Petersburg State University, Universitetskaya nab., 7/9, St. Petersburg 199034 (Russian Federation); Skudra, Atis [Institute of Atomic Physics and Spectroscopy, University of Latvia, Skunu 4, Riga (Latvia)
2015-08-05
A new analytical portable system is proposed for the direct determination of benzene vapor in the ambient air and natural gas, using differential absorption spectrometry with the direct Zeeman effect and innovative radiation sources: capillary mercury lamps with different isotopic compositions ({sup 196}Hg, {sup 198}Hg, {sup 202}Hg, {sup 204}Hg, and natural isotopic mixture). Resonance emission of mercury at a wavelength of 254 nm is used as probing radiation. The differential cross section of benzene absorption in dependence on wavelength is determined by scanning of magnetic field. It is found that the sensitivity of benzene detection is enhanced three times using lamp with the mercury isotope {sup 204}Hg in comparison with lamp, filled with the natural isotopic mixture. It is experimentally demonstrated that, when benzene content is measured at the Occupational Exposure Limit (3.2 mg/m{sup 3} for benzene) level, the interference from SO{sub 2}, NO{sub 2}, O{sub 3}, H{sub 2}S and toluene can be neglected if concentration of these gases does not exceed corresponding Occupational Exposure Limits. To exclude the mercury effect, filters that absorb mercury and let benzene pass in the gas duct are proposed. Basing on the results of our study, a portable spectrometer is designed with a multipath cell of 960 cm total path length and detection limit 0.5 mg/m{sup 3} at 1 s averaging and 0.1 mg/m{sup 3} at 30 s averaging. The applications of the designed spectrometer to measuring the benzene concentration in the atmospheric air from a moving vehicle and in natural gas are exemplified. - Highlights: • Portable benzene analyser is designed for direct benzene detection in air and gas. • Zeeman effect absorption spectrometry ensures very low benzene detection limits. • The Hg 2537 nm emission line from capillary mercury lamp is used for absorption. • The best sensitivity and selectivity is found using Hg 204 isotope light source. • Mercury influence is
Multistage quadratic stochastic programming
Lau, Karen K.; Womersley, Robert S.
2001-04-01
Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.
Tuning the pseudo-Zeeman splitting in graphene cones by magnetic field
Energy Technology Data Exchange (ETDEWEB)
Kandemir, B.S.; Akay, D.
2015-06-15
The effect of a homogeneous magnetic field on the energy spectrum of gapped graphene cones with long range charged Coulomb impurity is investigated within the framework of the perturbation theory. It is found that, besides lifting the degeneracy of angular momentum channels due to topological defects, the size of the corresponding splitting is enhanced by the introduction of a homogeneous magnetic field. This indicates that the level splitting may be controlled by the strength of a magnetic field in topological cones. Therefore, our results show that the magnetic field may be used as a tool to tune the pseudo-Zeeman splitting in graphene cones. - Highlights: • The size of level splitting in angular momentum channels is enhanced by introduction of a homogenous magnetic field. • Pseudo-Zeeman splitting in graphene can be controlled by hydrogenic impurities. • Pseudo-Zeeman splitting may be controlled by the strength of magnetic field in topological cones.
Duarte, Jonathan T.
2010-01-01
Although current reform movements have stressed the importance of developing prospective middle school mathematics teachers' subject matter knowledge and understandings, there is a dearth of research studies with regard to prospective middle school teachers' confidence and knowledge with respect to quadratic functions. This study was intended to…
Polarization enhancement and suppression of four-wave mixing in multi-Zeeman levels
Institute of Scientific and Technical Information of China (English)
Zhiguo Wang; Yuxin Fu; Yue Song; Guoxian Dai; Feng Wen; Jinyan Zhao; Yanpeng Zhang
2011-01-01
Polarization dependence of the enhancement and suppression of four-wave mixing(FWM) in a multiZeeman level atomic system is investigated both theoretically and experimentally.A dressing field applied to the adjacent transition can cause energy level splitting.Therefore,it can control the enhancement and suppression of the FWM processes in the system due to the effect of electromagnetically induced transparency.The results show that the pumping beams with different polarizations select the transitions between different Zeeman levels that,in turn,affect the enhancement and suppression efficiencies of FWM.
Institute of Scientific and Technical Information of China (English)
白志斌
2011-01-01
A method for analysis of trace silver in geochemical samples by Zeeman effect graphite furnace atomic absorption spectrometry was studied. The proposed method simplified the procedure for sample processing. Satisfactory results were obtained in analysis of trace silver in geochemical reference and practical samples. The recovery was in the range of 96.2%-103.5% while the relative standard deviation was in the range of 3.04%-4.77%.The proposed method is quick ,simple and accurate.%对塞曼效应石墨炉原子吸收法对地质样中痕量银的测定进行了研究。简化了样品处理过程。对地质标样及实际样品分析获得了满意的结果加标回收率为96．2％-103．5％，相对标准偏差为3．04％-4．77％所采用的方法快速、简便，准确。
Quantum bouncer with quadratic dissipation
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, G. [NanoScience Technology Center, University of Central Florida, Orlando, FL 32826 (United States)]. e-mail: ggonzalez@physics.ucf.edu
2008-07-01
The energy loss due to a quadratic velocity-dependent force on a quantum particle bouncing off a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new, effective, phenomenological Hamiltonian which corresponds to the actual energy of the system and obtain the correction to the eigenvalues of the energy in first-order quantum perturbation theory for the case of weak dissipation. (Author)
Quantum bouncer with quadratic dissipation
González, G.
2008-02-01
The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.
Optical Zeeman Spectroscopy of Calcium Fluoride, CaF.
Steimle, Timothy; Kokkin, Damian L.; Delvin, Jack; Tarbutt, Michael
2015-06-01
Recently laser cooling has been demonstrated for the diatomic radical calcium fluoride, CaF. The mechanism of magneto-optical trapping for diatomic molecules has been elucidated recently by Tarbutt where a rate model was used to model the interaction of molecules with multiple frequencies of laser light. It was shown that the correct choice of laser polarization depends on the sign of the upper state magnetic g-factor. The magnetic tuning of the low rotational levels in the X^2σ^+, A^2Π and B^2σ^+ electronic states of CaF, have been experimentally investigated using high resolution optical Zeeman spectroscopy of a cold molecular beam sample. The observed Zeeman-induced shifts and splittings were successfully modeled using a traditional effective Hamiltonian approach to account for the interaction between the (ν=0) A^2Π and (ν=0) B^2σ^+ states. The determined magnetic g-factors for the X^2σ^+, A^2Π and B^2σ^+ states are compared to those predicted by perturbation theory. V. Zhelyazkova, A. Cournol, T.E. Wall, A. Matsushima, J.J. Hudson, E.A. Hinds, M.R. Tarbutt and B.E. Sauer, Phys. Rev. A 89, 053416 (2014) M. R. Tarbutt, New J. Phys 17, 015007 (2015)
Semidefinite programming for quadratically constrained quadratic programs
Olkin, Julia A.; Titterton, Paul J., Jr.
1995-06-01
We consider the linear least squares problem subject to multiple quadratic constraints, which is motivated by a practical application in controller design. We use the techniques of convex optimization, in particluar, interior-point methods for semi-definite programming. We reduce a quasi-convex potential function. Each iteration requires calculating a primal and dual search direction and minimizing along the plane defined by these search directions. The primal search direction requires solving a least squares problem whose matrix is composed of a block- Toeplitz portion plus other structured matrices. We make use of Kronecker products and FFTs to greatly reduce the calculation. In addition, the matrix updates and matrix inverses in the plane search are actually low-rank updates to structured matrices so we are able to further reduce the flops required. Consequently, we can design controllers for problems of considerable size.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Conventional models for fluid flow in well tests have not been consistent with material balance. According to the slightly compressible fluid assumption, the quadratic gradient term in the nonlinear partial differential equation has been usually neglected. This approach is questionable for live oil and low permeability reservoirs. We have already known that linearization by neglecting quadratic gradient terms may lead to errors for large values of well-test time. In this paper, a method that is consistent with material balance was proposed on the spherical flow system. All terms in the nonlinear partial eqiation were retained. Exact solution for the resulting nonlinear partial differential equation in an infinite reservoir was obtained by using the Laplace transform considering wellbore storage. Analytical solution for nonlinear partial differential equation are resulted by using orthogonal transforms under both closed and constant-pressure outer boundary conditions. The law of pressure changes for a fluid compressibility α and a storage coefficient CD were discussed.
DEFF Research Database (Denmark)
Esbensen, B.K.; Bache, Morten; Krolikowski, W.;
2012-01-01
We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description t...... this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions....
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
On Quadratic Differential Forms
Willems, J.C.; Trentelman, H.L.
1998-01-01
This paper develops a theory around the notion of quadratic differential forms in the context of linear differential systems. In many applications, we need to not only understand the behavior of the system variables but also the behavior of certain functionals of these variables. The obvious cases w
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2016-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
De introductie van de Zeeman atoomabsorptietechniek t.b.v. de bepaling van cadmium in grondwater
Boer; J.L.M.de
1985-01-01
Dit rapport beschrijft naast een korte theorie van het Zeeman-effect, de ontwikkeling van een procedure voor de bepaling in cadmium in grondwater m.b.v. atomaire-absorptiespectrometrie met grafietoven, waarbij speciaal aandacht werd geschonken aan de analyse van brak grondwater. Daarbij werd uit
Radiotherapy treatment planning linear-quadratic radiobiology
Chapman, J Donald
2015-01-01
Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil
Quadratic stabilization for uncertain stochastic systems
Institute of Scientific and Technical Information of China (English)
Jun'e FENG; Weihai ZHANG
2005-01-01
This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.
Successful spectral synthesis of Zeeman-split molecular bands in sunspot spectra
Berdyugina, S. V.; Frutiger, C.; Solanki, S. K.; Livingstone, W.
2000-12-01
We present the first spectral synthesis of Zeeman-split Stokes profiles of the MgH A2Pi -X2BLAigma green system and TiO gamma -system. The calculations involve different regimes of the molecular Zeeman effect, up to the complete Paschen-Back effect for individual lines. The synthetic spectra are compared with observations of Stokes I and V in sunspot umbrae. We find that although the Stokes I spectra are reasonably reproduced, some lines are obviously still missing from the employed line lists. The Stokes V spectra turn out to be much cleaner since the missing lines do not appear to be Zeeman-split. We thus provide the first good fit to Zeeman-split molecular lines, including profiles with unconventional Stokes V shapes, determined by the Paschen-Back effect. Based on observations from the Canada-France-Hawaii Telescope operated by the National Research Council of Canada, the Centre National de la Recherche Scientifique de France and the University of Hawaii
Hidden conic quadratic representation of some nonconvex quadratic optimization problems
Ben-Tal, A.; den Hertog, D.
2014-01-01
The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated S-lemma
Zeeman-Sisyphus Deceleration of Molecular Beams
Fitch, Noah; Tarbutt, Mike
2016-05-01
Ultracold molecules are useful for testing fundamental physics and studying strongly-interacting quantum systems. One production method is via direct laser cooling in a magneto-optical trap (MOT). In this endeavor, one major challenge is to produce molecules below the MOT capture velocity. Established molecular beam deceleration techniques are poorly suited because they decelerate only a small fraction of a typical molecular pulse. Direct laser cooling is a natural choice, but is also problematic due to transverse heating and the associated molecule loss. I will present a new technique that we are developing, which we call Zeeman-Sisyphus deceleration and which shows great promise for preparing molecular beams for MOT loading. This technique decelerates molecules using a linear array of permanent magnets, along with lasers that periodically optically pump molecules between weak and strong-field seeking quantum states. Being time-independent, this method is well-suited for temporally extended molecular beams. Simultaneous deceleration and transverse guiding makes this approach attractive as an alternative to direct laser cooling. I will present our development of the Zeeman-Sisyphus decelerator and its application to a molecular MOT of CaF and an ultracold fountain of YbF.
Zeeman deceleration beyond periodic phase space stability
Toscano, Jutta; Tauschinsky, Atreju; Dulitz, Katrin; Rennick, Christopher J.; Heazlewood, Brianna R.; Softley, Timothy P.
2017-08-01
In Zeeman deceleration, time-varying spatially inhomogeneous magnetic fields are used to create packets of translationally cold, quantum-state-selected paramagnetic particles with a tuneable forward velocity, which are ideal for cold reaction dynamics studies. Here, the covariance matrix adaptation evolutionary strategy is adopted in order to optimise deceleration switching sequences for the operation of a Zeeman decelerator. Using the optimised sequences, a 40% increase in the number of decelerated particles is observed compared to standard sequences for the same final velocity, imposing the same experimental boundary conditions. Furthermore, we demonstrate that it is possible to remove up to 98% of the initial kinetic energy of particles in the incoming beam, compared to the removal of a maximum of 83% of kinetic energy with standard sequences. Three-dimensional particle trajectory simulations are employed to reproduce the experimental results and to investigate differences in the deceleration mechanism adopted by standard and optimised sequences. It is experimentally verified that the optimal solution uncovered by the evolutionary algorithm is not merely a local optimisation of the experimental parameters—it is a novel mode of operation that goes beyond the standard periodic phase stability approach typically adopted.
Extended gcd of quadratic integers
Miled, Abdelwaheb
2010-01-01
Computation of the extended gcd of two quadratic integers. The ring of integers considered is principal but could be euclidean or not euclidean ring. This method rely on principal ideal ring and reduction of binary quadratic forms.
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general......., and algorithms are developed on a case by case basis. There lacks an analytical representation of a general or even a convex quadratic spline. The current paper fills this gap by providing an analytical representation of a general quadratic spline. Furthermore, for convex quadratic spline, it is shown...
Inversion of Zeeman polarization for solar magnetic field diagnostics
Derouich, M
2016-01-01
The topic of magnetic field diagnostics with the Zeeman effect is currently vividly discussed. There are some testable inversion codes available to the spectropolarimetry community and their application allowed for a better understanding of the magnetism of the solar atmosphere. In this context, we propose an inversion technique associated with a new numerical code. The inversion procedure is promising and particularly successful for interpreting the Stokes profiles in quick and sufficiently precise way. In our inversion, we fit a part of each Stokes profile around a target wavelength, and then determine the magnetic field as a function of the wavelength which is equivalent to get the magnetic field as a function of the height of line formation. To test the performance of the new numerical code, we employed "hare and hound" approach by comparing an exact solution (called input) with the solution obtained by the code (called output). The precision of the code is also checked by comparing our results to the one...
Zeeman slowers for strontium based on permanent magnets
Hill, Ian R.; Ovchinnikov, Yuri B.; Bridge, Elizabeth M.; Curtis, E. Anne; Gill, Patrick
2014-04-01
We present the design, construction, and characterization of longitudinal- and transverse-field Zeeman slowers, based on arrays of permanent magnets, for slowing thermal beams of atomic Sr. The slowers are optimized for operation with deceleration related to the local laser intensity (by the parameter ɛ), which uses more effectively the available laser power, in contrast to the usual constant deceleration mode. Slowing efficiencies of up to ≈18% are realized and compared to those predicted by modelling. We highlight the transverse-field slower, which is compact, highly tunable, light-weight, and requires no electrical power, as a simple solution to slowing Sr, well-suited to space-borne application. For 88Sr we achieve a slow-atom flux of around 6 × 109 atoms s-1 at 30 ms-1, loading approximately 5 × 108 atoms in to a magneto-optical-trap, and capture all isotopes in approximate relative natural abundances.
Zeeman Slowers for Strontium based on Permanent Magnets
Hill, Ian R; Bridge, Elizabeth M; Curtis, E Anne; Gill, Patrick
2014-01-01
We present the design, construction, and characterisation of longitudinal- and transverse-field Zeeman slowers, based on arrays of permanent magnets, for slowing thermal beams of atomic Sr. The slowers are optimised for operation with deceleration related to the local laser intensity (by the parameter $\\epsilon$), which uses more effectively the available laser power, in contrast to the usual constant deceleration mode. Slowing efficiencies of up to $\\approx$ $18$ $%$ are realised and compared to those predicted by modelling. We highlight the transverse-field slower, which is compact, highly tunable, light-weight, and requires no electrical power, as a simple solution to slowing Sr, well-suited to spaceborne application. For $^{88}$Sr we achieve a slow-atom flux of around $6\\times 10^9$ atoms$\\,$s$^{-1}$ at $30$ ms$^{-1}$, loading approximately $5\\times 10^8$ atoms in to a magneto-optical-trap (MOT), and capture all isotopes in approximate relative natural abundances.
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Factorization method of quadratic template
Kotyrba, Martin
2017-07-01
Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.
A clip-on Zeeman slower using toroidal permanent magnets.
Krzyzewski, S P; Akin, T G; Dahal, Parshuram; Abraham, E R I
2014-10-01
We present the design of a zero-crossing Zeeman slower for (85)Rb using rings of flexible permanent magnets. The design is inexpensive, requires no power or cooling, and can be easily attached and removed for vacuum maintenance. We show theoretically that such a design can reproduce a magnetic field profile of a standard zero-crossing Zeeman slower. Experimental measurements of a prototype and comparisons to theoretical simulations demonstrate the feasibility of the design and point toward future improvements. Simulations show an atom flux similar to other Zeeman slowers.
Designing Zeeman slower for strontium atoms - towards optical atomic clock
Bober, Marcin; Gawlik, Wojciech
2010-01-01
We report on design and construction of a Zeeman slower for strontium atoms which will be used in an optical atomic clock experiment. The paper describes briefly required specifications of the device, possible solutions, and concentrates on the chosen design. The magnetic field produced by the built Zeeman slower has been measured and compared with the simulations. The system consisting of an oven and Zeeman slower are designed to produce an atomic beam of 10-12 s-1 flux and final velocity of ~30 m/s.
Designing Zeeman slower for strontium atoms - towards optical atomic clock
Bober, Marcin; Zachorowski, Jerzy; Gawlik, Wojciech
2010-01-01
We report on design and construction of a Zeeman slower for strontium atoms which will be used in an optical atomic clock experiment. The paper describes briefly required specifications of the device, possible solutions, and concentrates on the chosen design. The magnetic field produced by the built Zeeman slower has been measured and compared with the simulations. The system consisting of an oven and Zeeman slower are designed to produce an atomic beam of 10-12 s-1 flux and final velocity of...
DEFF Research Database (Denmark)
Gammelgaard, Bente; Jons, O.
1997-01-01
of the species, The presence of chloride affected the stability of the selenium forms differently in aqueous solution, while there was no pronounced effect on the stabilization in plasma, Different amounts of palladium, varying from the application of 2 to 40 mu g into the graphite tube, were compared......The thermal stabilities of selenite, selenate, selenomethionine and trimethylselenonium in aqueous solution and plasma were compared, The stabilities of the four selenium forms were different in aqueous solution and plasma, The nitric acid concentration had little influence on the sensitivity......, The application of 20 mu g of palladium showed the best result in terms of sensitivity and equal stabilization of the selenium species when analysing plasma, Different amounts of magnesium nitrate, varying from the application of 0.6 to 24.3 mu g of magnesium into the graphite tube, were examined, The addition...
Zamani, A.; Azargoshasb, T.; Niknam, E.
2017-10-01
Effects of applied magnetic field, temperature and dimensions on the optical absorption coefficients (AC) and refractive index (RI) changes of a GaAs quantum ring are investigated in the presence of both Rashba and Dresselhaus spin-orbit interactions (SOI). To this end, the finite difference method (FDM) is used in order to numerically calculate the energy eigenvalues and eigenstates of the system while the compact density matrix approach is hired to calculate the optical properties. It is shown that application of magnetic field, temperature as well as the geometrical size in the presence of spin-orbit interactions, alter the electronic structure and consequently influence the linear and third-order nonlinear optical absorption coefficients as well as the refractive index changes of the system. Results show an obvious blue shift in optical curves with enhancing external magnetic field and temperature while the increment of dimensions result in red shift.
Zamani, A.; Setareh, F.; Azargoshasb, T.; Niknam, E.
2017-10-01
A wide variety of semiconductor nanostructures have been fabricated experimentally and both theoretical and experimental investigations of their features imply the great role they have in new generation technological devices. However, mathematical modeling provide a powerful means due to definitive goal of predicting the features and understanding of such structures behavior under different circumstances. Therefore, effective Hamiltonian for an electron in a quantum ring with axial symmetry in the presence of both Rashba and Dresselhaus spin-orbit interactions (SOI) is derived. Here we report our study of the electronic structure and electron g-factor in the presence of spin-orbit (SO) couplings under the influence of external magnetic field at finite temperature. This investigation shows that, when Rashba and Dresselhaus couplings are simultaneously present, the degeneracy is removed and energy levels split into two branches. Furthermore, with enhancing the applied magnetic field, separation of former degenerate levels increases and also avoided crossings (anti-crossing) in the energy spectra is detected. It is also discussed how the energy levels of the system can be adjusted with variation of temperature as well as the magnetic field and geometrical sizes.
Ovsyannikov, V. D.; Chaplygin, E. V.
2000-12-01
Analytical expressions for the dependence of the intensity of Zeeman components of doublet lines on the magnetic field are obtained. Sharp changes of these function on passing from the anomalous Zeeman effect to the Paschen-Back effect lead to the disappearance of marginal lines and the equalization of intensities of remaining lines. In the region of the complete Paschen-Back effect, a strong influence on these dependences is produced by the dynamic atom-field interaction, which weakens the paramagnetic effect in the states with a positive magnetic quantum number m and enhances the effect in the states with a negative m. Simple analytical expressions are obtained that take into account the effect of the diamagnetic interaction on line intensities. The role of the diamagnetic interaction increases in Rydberg atomic states with a large spin-orbit splitting. For the states with m > 0, it can lead to the “diamagnetic reversal” of the Paschen-Back effect, i.e., the recovery of the anomalous Zeeman effect.
PSQP: Puzzle Solving by Quadratic Programming.
Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome
2017-02-01
In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
Institute of Scientific and Technical Information of China (English)
胡光磊
2005-01-01
本文将采用两种方法对正常塞曼效应进行解释,并比较它们的异同.经比较发现两种解释所得结果一致.但经典解释从牛顿力学出发,未能反映原子内部本质;而半经典半量子解释,反映了原子内部本质.
Liu, Jihong; Qiao, Shuang; Wang, Shufang; Fu, Guangsheng
2017-01-01
We investigated the magneto-optical properties of a L21 ordered nonstoichiometric Co2Mn1.30Si0.84 film epitaxially grown on a MgO-buffered MgO (001) single-crystal substrate. Longitudinal magneto-optical Kerr effects (LMOKE) and rotating magneto-optical Kerr effect (ROT-MOKE) measurements suggest that the film exhibits a cubic magnetic anisotropy with the extracted cubic anisotropy constant of KC = 6.7 ×104 erg / cm3 . Orientation-dependent ROT-MOKE suggest that the quadratic magneto-optical Kerr effects (QMOKE) components also show fourfold symmetry with a modest amplitude of 3 mdeg, which is in accordance with complex Kerr angle expression for cubic symmetry systems. Our results suggest that ROT-MOKE is not only an efficient method to determine magnetic anisotropy parameters but also a good method to extract QMOKE components.
Bashiri, Mahdi; Karimi, Hossein
2012-07-01
Quadratic assignment problem (QAP) is a well-known problem in the facility location and layout. It belongs to the NP-complete class. There are many heuristic and meta-heuristic methods, which are presented for QAP in the literature. In this paper, we applied 2-opt, greedy 2-opt, 3-opt, greedy 3-opt, and VNZ as heuristic methods and tabu search (TS), simulated annealing, and particle swarm optimization as meta-heuristic methods for the QAP. This research is dedicated to compare the relative percentage deviation of these solution qualities from the best known solution which is introduced in QAPLIB. Furthermore, a tuning method is applied for meta-heuristic parameters. Results indicate that TS is the best in 31%of QAPs, and the IFLS method, which is in the literature, is the best in 58 % of QAPs; these two methods are the same in 11 % of test problems. Also, TS has a better computational time among heuristic and meta-heuristic methods.
A CLASS OF QUADRATIC HAMILTONIAN SYSTEMS UNDER QUADRATIC PERTURBATION
Institute of Scientific and Technical Information of China (English)
丰建文; 陈士华
2001-01-01
This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1(h) = 0 and the second order Melnikov function M2(h) ≡ 0, then the origin of the Hamiltonian system with small perturbation is a center.
Quadratic gravity: from weak to strong
Holdom, Bob
2016-01-01
More than three decades ago quadratic gravity was found to present a perturbative, renormalizable and asymptotically free theory of quantum gravity. Unfortunately the theory appeared to have problems with a spin-2 ghost. In this essay we revisit quadratic gravity in a different light by considering the case that the asymptotically free interaction flows to a strongly interacting regime. This occurs when the coefficient of the Einstein-Hilbert term is smaller than the scale $\\Lambda_{\\mathrm{QG}}$ where the quadratic couplings grow strong. Here QCD provides some useful insights. By pushing the analogy with QCD, we conjecture that the nonperturbative effects can remove the naive spin-2 ghost and lead to the emergence of general relativity in the IR.
Zeeman Doppler Maps: Always Unique, Never Spurious?
Stift, Martin J.; Leone, Francesco
2017-01-01
Numerical models of atomic diffusion in magnetic atmospheres of ApBp stars predict abundance structures that differ from the empirical maps derived with (Zeeman) Doppler mapping (ZDM). An in-depth analysis of this apparent disagreement investigates the detectability by means of ZDM of a variety of abundance structures, including (warped) rings predicted by theory, but also complex spot-like structures. Even when spectra of high signal-to-noise ratio are available, it can prove difficult or altogether impossible to correctly recover shapes, positions, and abundances of a mere handful of spots, notwithstanding the use of all four Stokes parameters and an exactly known field geometry; the recovery of (warped) rings can be equally challenging. Inversions of complex abundance maps that are based on just one or two spectral lines usually permit multiple solutions. It turns out that it can by no means be guaranteed that any of the regularization functions in general use for ZDM (maximum entropy or Tikhonov) will lead to a true abundance map instead of some spurious one. Attention is drawn to the need for a study that would elucidate the relation between the stratified, field-dependent abundance structures predicted by diffusion theory on the one hand, and empirical maps obtained by means of “canonical” ZDM, i.e., with mean atmospheres and unstratified abundances, on the other hand. Finally, we point out difficulties arising from the three-dimensional nature of the atomic diffusion process in magnetic ApBp star atmospheres.
Guises and disguises of quadratic divergences
Energy Technology Data Exchange (ETDEWEB)
Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Institute of Scientific and Technical Information of China (English)
MAO Wei; ZHANG Shu-Lian; ZHOU Lu-Fei; LIU Xiao-Yan; WANG Ming-Ming
2007-01-01
The influence of Feedback levels on the intensity and polarization properties of polarized optical feedback in a Zeeman-birefringence dual frequency laser is systematically investigated. By changing the feedback power ratio, different feedback levels are obtained. Three distinct regimes of polarized optical feedback effects are found and defined as regimes Ⅰ, Ⅱand Ⅲ. The feedback level boundaries among the regimes are acquired experimentally. The theoretical analysis is presented to be in good agreement with the experimental results.
Super-Zeeman Embedding Models on N-Supersymmetric World-Lines
Doran, C F; Gates, S J Jr; Hübsch, T; Iga, K M; Landweber, G D
2008-01-01
We construct a model of an electrically charged magnetic dipole with arbitrary N-extended world-line supersymmetry, which exhibits a supersymmetric Zeeman effect. By including supersymmetric constraint terms, the ambient space of the dipole may be tailored into an algebraic variety, and the supersymmetry broken for almost all parameter values. The so exhibited obstruction to supersymmetry breaking refines the standard one, based on the Witten index alone.
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...
Model for the overall phase-space acceptance in a Zeeman decelerator
Dulitz, Katrin; Softley, Timothy P
2015-01-01
We present a new formalism to calculate phase-space acceptance in a Zeeman decelerator. Using parameters closely mimicking previous Zeeman deceleration experiments, this approach reveals a hitherto unconsidered velocity dependence of the phase stability which we ascribe to the finite rise and fall times of the current pulses that generate the magnetic fields inside the deceleration coils. It is shown that changing the current switch-off times as the sequence progresses, so as to maintain a constant mean acceleration per pulse, can lead to a constant phase stability and hence a beam with well-defined characteristics. We also find that the time overlap between fields of adjacent coils has an influence on the phase-space acceptance. Previous theoretical and experimental results suggested unfilled regions in phase space that influence particle transmission through the decelerator. Our model provides, for the first time, a means to directly identify the origin of these effects due to coupling between longitudinal ...
Experimental results on quadratic assignment problem
Directory of Open Access Journals (Sweden)
N.P. Nikolov
1999-08-01
Full Text Available The paper presents experimental results on quadratic assignment problem. The "scanning area" method formulated for radioelectronic equipment design is applied. For all more complex tests ours results are better or coincident with the ones known in literature. Conclusion concerning the effectiveness of method are given.
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.
1971-01-01
Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.
Giant Zeeman shifts in the optical transitions of yttrium iron garnet thin films
Vidyasagar, R.; Alves Santos, O.; Holanda, J.; Cunha, R. O.; Machado, F. L. A.; Ribeiro, P. R. T.; Rodrigues, A. R.; Mendes, J. B. S.; Azevedo, A.; Rezende, S. M.
2016-09-01
We report the observation of giant Zeeman shifts in the optical transitions of high-quality very thin films of yttrium iron garnet (YIG) grown by rf sputtering on gadolinium gallium garnet substrates. The optical absorption profile measured with magneto-optical absorption spectroscopy shows dual optical transition in the UV-visible frequency region attributed to transitions from the O-2p valence band to the Fe-3d conduction band and from the O-2p valence band to Fe-2p53d6 excitonic states at the Γ-symmetry point of the YIG band structure. The application of a static magnetic field of only 0.6 kOe produces giant Zeeman shifts of ˜100 meV in the YIG band structure and ˜60 meV in the excitonic states corresponding to effective g-factors on the order of 104. The giant Zeeman effects are attributed to changes in energy levels by the large exchange fields of the Fe-3d orbitals during the magnetization process.
Symmetry-Breaking Zeeman-Coherence Parametric Wave Mixing Magnetometry
Zhou, Feng; Hagley, E W; Deng, L
2016-01-01
The nonlinear magneto-optical effect has significantly impacted modern society with prolific applications ranging from precision mapping of the Earth's magnetic field to bio-magnetic sensing. Pioneering works on collisional spin-exchange effects have led to ultra-high magnetic field detection sensitivities at the level of $fT/\\sqrt{Hz}$ using a single linearly-polarized probe light field. Here we demonstrate a nonlinear Zeeman-coherence parametric wave-mixing optical-atomic magnetometer using room temperature rubidium vapor that results in more than a three-order-of-magnitude optical signal-to-noise ratio (SNR) enhancement for extremely weak magnetic field sensing. This unprecedented enhancement was achieved with nearly a two-order-of-magnitude reduction in laser power while preserving the sensitivity of the widely-used single-probe beam optical-atomic magnetometry method. This new method opens a myriad of applications ranging from bio-magnetic imaging to precision measurement of the magnetic properties of su...
Spin 3/2 Zeeman perturbed NQR in the presence of slow sample rotation.
Panguluri, R P; Suits, B H
2006-09-01
Theoretical and experimental results are presented for the case of Zeeman perturbed nuclear quadrupole resonance (NQR) using spin-3/2 nuclei with a small Zeeman interaction, gammaB0, while the sample is very slowly rotated. It is found that the decay envelope for a simple two-pulse echo measurement can be strongly affected even though the sample may rotate only a few degrees or less during the course of the measurement. To lowest order the decay envelope can be described using a one dimensional function of the product of gammaB0, the rotation rate, and the square of the pulse spacing. Aside from an indirect and weak dependence on the quadrupole asymmetry parameter, eta, the result is independent of the NQR frequency. Identical results are expected for a stationary sample in a small rotating magnetic field. The effect seen here may be used to advantage to measure rotational motion, for example of particles in fluids, or may be an additional complication for some Zeeman perturbed NQR measurements, including some NQR detection and imaging methods.
Polarization spectra of Zeeman sublevels in Rydberg electromagnetically induced transparency
Bao, Shanxia; Zhang, Hao; Zhou, Jian; Zhang, Linjie; Zhao, Jianming; Xiao, Liantuan; Jia, Suotang
2016-10-01
The polarization spectra of electromagnetically induced transparency (EIT) for Zeeman sublevels in a cascade system with Rydberg state are demonstrated. The magnitude dependence of Rydberg-EIT on the polarizations of probe and coupling laser fields is studied, and shown mainly due to the strengths of relative dipole matrix elements between degenerate Zeeman sublevels. We further investigate the polarization spectra of Rydberg-EIT in the optimal polarization combinations of left-handed and right-handed circularly polarized fields when an external magnetic field is applied. The existence of nondegenerate Zeeman sublevels in an external magnetic field results in the splitting of Rydberg-EIT. The theoretical calculations are very consistent with the experimental spectra.
CN Zeeman observations of the NGC 2264-C protocluster
Maury, Anaëlle J; Thum, Clemens
2012-01-01
From an observational point of view, the role of magnetic fields in star formation remains unclear, and two main theoretical scenarios have been proposed so far to regulate the star-formation processes. The first model assumes that turbulence in star-forming clumps plays a crucial role, and especially that protostellar outflow-driven turbulence is crucial to support cluster-forming clumps; while the second scenario is based on the consideration of a magnetically-supported clump. Previous studies of the NGC 2264-C protocluster indicate that, in addition to thermal pressure, some extra support might effectively act against the gravitational collapse of this cluster-forming clump. We previously showed that this extra support is not due to the numerous protostellar outflows, nor the enhanced turbulence in this protocluster. Here we present the results of the first polarimetric campaign dedicated to quantifying the magnetic support at work in the NGC 2264-C clump. Our Zeeman observations of the CN(1-0) hyperfine l...
Molecular Beam Optical Zeeman Spectroscopy of Vanadium Monoxide, VO
Nguyen, Trung; Zhang, Ruohan; Steimle, Timothy
2016-06-01
Like almost all astronomical studies, exoplanet investigations are observational endeavors that rely primarily on remote spectroscopic sensing to infer the physical properties of planets. Most exoplanet related information is inferred from to temporal variation of luminosity of the parent star. An effective method of monitoring this variation is via Magnetic Doppler Imaging (MDI), which uses optical polarimetry of paramagnetic molecules or atoms. One promising paramagnetic stellar absorption is the near infrared spectrum of VO. With this in mind, we have begun a project to record and analyze the field-free and Zeeman spectrum of the band. A cold (approx. 20 K) beam of VO was probed with a single frequency laser and detected using laser induced fluorescence. The determined spectral parameters will be discussed and compared to those extracted from the analysis of a hot spectrum. Supported by the National Science Foundation under the Grant No. CHE-1265885. O. Kochukhov, N. Rusomarov, J. A. Valenti, H. C. Stempels, F. Snik, M. Rodenhuis, N. Piskunov, V. Makaganiuk, C. U. Keller and C. M. Johns-Krull, Astron. Astrophys. 574 (Pt. 2), A79/71-A79/12 (2015). S. V. Berdyugina, Astron. Soc. Pac. Conf. Ser. 437 (Solar Polarization 6), 219-235 (2011). S. V. Berdyugina, P. A. Braun, D. M. Fluri and S. K. Solanki, Astron. Astrophys. 444 (3), 947-960 (2005). A. S. C. Cheung, P. G. Hajigeorgiou, G. Huang, S. Z. Huang and A. J. Merer, J. Mol. Spectrosc. 163 (2), 443-458 (1994)
SMOOTHING BY CONVEX QUADRATIC PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Bing-sheng He; Yu-mei Wang
2005-01-01
In this paper, we study the relaxed smoothing problems with general closed convex constraints. It is pointed out that such problems can be converted to a convex quadratic minimization problem for which there are good programs in software libraries.
Quantum quadratic operators and processes
Mukhamedov, Farrukh
2015-01-01
Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels. This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.
Quadratic Tangles in Planar Algebras
Jones, Vaughan F R
2010-01-01
In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.
Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz
2015-04-01
Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. Copyright © 2015 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.
Melnichuk, Mike; Wood, Lowell T.
2017-07-01
The determination of a clear theoretical demarcation between a true or a false quadratic or higher-order low-intensity optical effect induced by an externally applied static or quasistatic (dc) vector field in anisotropic crystals is the scope of the present work. A complete set of necessary and sufficient conditions required for the practical possibility of direct detection, measurement, and tabulation of only those pure optical contributions is finally obtained. The dc electro-optic effect stands out as the most representative of all of these low-power dc optical effects. However, although the dc Kerr effect remains the main topic of application of the analytical treatment developed in this work, the current theoretical formalism is extended to include other dc conventional crystal optics effects, such as electrogyration, electroabsorption, and externally induced ray or energy propagation. Even more, the theoretical conditions are further generalized to apply to any pure higher-order crystal optics effect induced by external dc fields. These can be electric, magnetic, force, and even temperature or concentration gradient fields. The current treatment does not extend to multiple-beam high-intensity nonlinear optics effects induced by optical (ac) fields. Compared to previously published expressions, a more general Fresnel equation is also provided here together with the most general Jones vectors describing the eigenpolarizations of the single probing beam of light. All the generalizations and extensions mentioned in this article are valid as long as the field-dependent coefficients of the particular optical effect under consideration satisfy the equation of a positive-definite complex Hermitian form.
Directory of Open Access Journals (Sweden)
Chenxiao Zhang
2016-01-01
Full Text Available In this study the effect of trace elements on methanogenesis was investigated during mixed anaerobic fermentation using a single-factor experiment in the present study. The most effective concentrations of Fe0, Fe2+, Co2+ and Ni2+ that were added were 1500, 250, 0.3 and 0.6 mg/L, respectively. The optimal trace element combination was 0.58 mg/L Ni2+, 1200 mg/L Fe0 and 0.34 mg/L Co2+ by the ternary quadratic general rotary unitized design method. The degree of influence exerted by trace elements on the cumulative methane yields decreased in the order of Ni2+, Fe0 and Co2+, and the maximum CH4 yield was 241.6 mL/g volatile solids (VS, according to a regression equation. The non-dissolved organic carbon hydrolytic process showed a good fit with the first-order kinetic model. The maximum value of CH4 was 312.87 mL/g VS. Compared to the control, the bioconversion efficiencies of CH4 and CO2 production increased by 36.76% and 74.50%, respectively, at the optimal trace element combination. The obtained results provide new knowledge for improvements in the efficiency of anaerobic fermentation biogas production.
Waveguide Zeeman interferometry for thin-film chemical sensors
Energy Technology Data Exchange (ETDEWEB)
Grace, K.M.; Shrouf, K.; Johnston, R.G.; Yang, X.; Swanson, B. [Los Alamos National Lab., NM (United States); Honkanen, S.; Ayras, P.; Peyghambarian, N. [Optical Sciences Center, Univ. of Arizona, Tucson, AZ (United States); Katila, P.; Leppihalme, M. [VTT Electronics (Finland)
1997-10-01
A chemical sensor is demonstrated which is based on Si{sub 3}N{sub 4} optical waveguides coated with species-selective thin films and using Zeeman interferometry as the detection technique. Relative phase change between TE and TM modes is measured. Real time and reversible response to toluene is shown with ppm level sensitivity.
Chaotic behaviour of Zeeman machines at introductory course of mechanics
Nagy, Péter; Tasnádi, Péter
2016-05-01
Investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics into the basic course of mechanics taught to engineering students. In the present paper it will be demonstrated that Zeeman Machine can be a versatile and motivating tool for students to get introductory knowledge about chaotic motion via interactive simulations. It works in a relatively simple way and its properties can be understood very easily. Since the machine can be built easily and the simulation of its movement is also simple the experimental investigation and the theoretical description can be connected intuitively. Although Zeeman Machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also of interest with its typical chaotic features. By means of a periodically driven Zeeman Machine a wide range of chaotic properties of the simple systems can be demonstrated such as bifurcation diagrams, chaotic attractors, transient chaos and so on. The main goal of this paper is the presentation of an interactive learning material for teaching the basic features of the chaotic systems through the investigation of the Zeeman Machine.
Low Field Zeeman Magnetometry Using Rubidium Absorption Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Ram, Nibedita; Pattabiraman, M; Vijayan, C [Department of Physics, Indian Institute of Technology, Madras, Chennai 600036 (India)
2007-09-15
We report on the feasibility of utilizing the field dependence of the Doppler-free unresolved absorption line amplitude of Rubidium vapour for magnetic field measurements for fields below 50 G. The field dependence of the saturation absorption and Doppler broadened fluorescence line amplitudes have been systematically analyzed by computing the hyperfine energy eigenvalues and the transition probability among the Zeeman sublevels.
Multiline Zeeman signatures as demonstrated through the Pseudo-line
Semel, M; Stift, M J; Gonzalez, M J Martinez; Ariste, A Lopez; Leone, F
2008-01-01
In order to get a significant Zeeman signature in the polarised spectra of a magnetic star, we usually 'add' the contributions of numerous spectral lines; the ultimate goal is to recover the spectropolarimetric prints of the magnetic field in these line additions. Here we want to clarify the meaning of these techniques of line addition; in particular, we try to interpret the meaning of the 'pseudo-line' formed during this process and to find out why and how its Zeeman signature is still meaningful. We create a synthetic case of lines addition and apply well tested standard solar methods routinely used in the research on magnetism in our nearest star. The results are convincing and the Zeeman signatures well detected; Solar methods are found to be quite efficient also for stellar observations. The Zeeman signatures are unequivocally detected in this multiline approach. We may anticipate the outcome magnetic fields to be reliable well beyond the weak-field approximation. Linear polarisation in the spectra of so...
The suppression of synchronous interference NQR with Zeeman modulation
Directory of Open Access Journals (Sweden)
Politanskii L. F.
2012-04-01
Full Text Available The principles of frequency and Zeeman modulation in nuclear quadrupole resonance were considered, and the advantages of the latter were shown. The authors propose a method to eliminate the synchronous noise caused by switching of the magnetic field. Results of observations of the resonance line with 14N in the hexamethylenetetramine sample weighing 2 g were given.
A magnetic 4π goniometer for Zeeman-split NQR
Nagarajan, V.; Weiden, Norbert; Wendel, Richard; Weiss, Alarich
With the aid of three mutually perpendicular Helmholtz coils a 4π Zeeman goniometer is constructed for application in NQR spectroscopy. Details of the construction are given. The spectrometer is cheked by measuring the zero splitting cone of 35Cl NQR in a single crystal of NaClO 3 at room temperature. The precision of the goniometer is evaluated.
Shibamoto, Yuta; Otsuka, Shinya; Iwata, Hiromitsu; Sugie, Chikao; Ogino, Hiroyuki; Tomita, Natsuo
2012-01-01
Since the dose delivery pattern in high-precision radiotherapy is different from that in conventional radiation, radiobiological assessment of the physical dose used in stereotactic irradiation and intensity-modulated radiotherapy has become necessary. In these treatments, the daily dose is usually given intermittently over a time longer than that used in conventional radiotherapy. During prolonged radiation delivery, sublethal damage repair takes place, leading to the decreased effect of radiation. This phenomenon is almost universarily observed in vitro. In in vivo tumors, however, this decrease in effect can be counterbalanced by rapid reoxygenation, which has been demonstrated in a laboratory study. Studies on reoxygenation in human tumors are warranted to better evaluate the influence of prolonged radiation delivery. Another issue related to radiosurgery and hypofractionated stereotactic radiotherapy is the mathematical model for dose evaluation and conversion. Many clinicians use the linear-quadratic (LQ) model and biologically effective dose (BED) to estimate the effects of various radiation schedules, but it has been suggested that the LQ model is not applicable to high doses per fraction. Recent experimental studies verified the inadequacy of the LQ model in converting hypofractionated doses into single doses. The LQ model overestimates the effect of high fractional doses of radiation. BED is particularly incorrect when it is used for tumor responses in vivo, since it does not take reoxygenation into account. For normal tissue responses, improved models have been proposed, but, for in vivo tumor responses, the currently available models are not satisfactory, and better ones should be proposed in future studies.
Students' understanding of quadratic equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
Finite dimensional quadratic Lie superalgebras
Jarvis, Peter; Yates, Luke
2010-01-01
We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
Successive quadratic programming multiuser detector
Institute of Scientific and Technical Information of China (English)
Mu Xuewen; Zhang Yaling; Liu Sanyang
2007-01-01
Based on the semidefinite programming relaxation of the CDMA maximum likelihood multiuser detection problem,a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, the suboptimal solution of the multiuser detection problem in obtained. Compared to the interior point methods previously reported based on semidefinite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.
Integer Quadratic Quasi-polyhedra
Letchford, Adam N.
This paper introduces two fundamental families of 'quasi-polyhedra' - polyhedra with a countably infinite number of facets - that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton p...
Unramified extensions of quadratic fields
Institute of Scientific and Technical Information of China (English)
Wei Li; Dong Yang; Xianke Zhang
2008-01-01
Let K be a global quadratic field, then every unramified abelian extension of K is proved to be absolutely Galois when K is a number field or under some natural conditions when K is a function field. The absolute Galois group is also determined explicitly.
Quadratic prediction of factor scores
Wansbeek, T
1999-01-01
Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic
Quadratic function approaching method for magnetotelluric soundingdata inversion
Energy Technology Data Exchange (ETDEWEB)
Liangjun, Yan; Wenbao, Hu; Zhang, Keni
2004-04-05
The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.
Topological superconductivity in Rashba semiconductors without a Zeeman field
Energy Technology Data Exchange (ETDEWEB)
Kotetes, Panagiotis [Karlsruhe Institute of Technology (Germany)
2015-07-01
I propose new hybrid devices based on multichannel Rashba semiconductors, which harbor Majorana fermions (MFs) without a Zeeman field. In contrast, magnetic fluxes, supercurrents or electric fields can be employed, yielding an enhanced device manipulability. The generic topological phase diagram exhibits features of quantum criticality and a rich interplay of phases with 0, 1 or 2 MFs per edge. The most prominent and experimentally feasible implementation, relies on the already existing platforms of InAs-2DEG on top of a Josephson junction. Appropriate design of the latter device, allows phases with 1 or 2 MFs, both detectable in zero-bias anomaly peaks with a single or double unit of conductance. The absence of the Zeeman field in these devices could be assisting for a Kondo-peak-free interpretation of the expected MF signatures.
The Quadratic Graver Cone, Quadratic Integer Minimization, and Extensions
Lee, Jon; Romanchuk, Lyubov; Weismantel, Robert
2010-01-01
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\\em dual Graver cone}, the problem can be solved in polynomial time. We discuss the relation between this cone and the cone of positive semidefinite matrices, and show that none contains the other. So we can minimize in polynomial time some non-convex and some (including all separable) convex quadrics. We conclude by extending our results to efficient integer minimization of multivariate polynomial functions of arbitrary degree lying in suitable cones.
Consensus-ADMM for General Quadratically Constrained Quadratic Programming
Huang, Kejun; Sidiropoulos, Nicholas D.
2016-10-01
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special cases are NP-hard as well. This paper proposes a new algorithm for general QCQP. The problem is first reformulated in consensus optimization form, to which the alternating direction method of multipliers (ADMM) can be applied. The reformulation is done in such a way that each of the sub-problems is a QCQP with only one constraint (QCQP-1), which is efficiently solvable irrespective of (non-)convexity. The core components are carefully designed to make the overall algorithm more scalable, including efficient methods for solving QCQP-1, memory efficient implementation, parallel/distributed implementation, and smart initialization. The proposed algorithm is then tested in two applications: multicast beamforming and phase retrieval. The results indicate superior performance over prior state-of-the-art methods.
Quadratic and 2-Crossed Modules of Algebras
Institute of Scientific and Technical Information of China (English)
Z. Arvasi; E. Ulualan
2007-01-01
In this work, we define the quadratic modules for commutative algebras and give relations among 2-crossed modules, crossed squares, quadratic modules and simplicial commutative algebras with Moore complex of length 2.
Ballester, Ernest Alsina; Bueno, Javier Trujillo
2016-01-01
The spectral line polarization encodes a wealth of information about the thermal and magnetic properties of the solar atmosphere. Modeling the Stokes profiles of strong resonance lines is, however, a complex problem both from the theoretical and computational point of view, especially when partial frequency redistribution (PRD) effects need to be taken into account. In this work, we consider a two-level atom in the presence of magnetic fields of arbitrary intensity (Hanle-Zeeman regime) and orientation, both deterministic and micro-structured. Working within the framework of a rigorous PRD theoretical approach, we have developed a numerical code which solves the full non-LTE radiative transfer problem for polarized radiation, in one-dimensional models of the solar atmosphere, accounting for the combined action of the Hanle and Zeeman effects, as well as for PRD phenomena. After briefly discussing the relevant equations, we describe the iterative method of solution of the problem and the numerical tools that w...
Team Decision Problems with Convex Quadratic Constraints
Gattami, Ather
2015-01-01
In this paper, we consider linear quadratic team problems with an arbitrary number of quadratic constraints in both stochastic and deterministic settings. The team consists of players with different measurements about the state of nature. The objective of the team is to minimize a quadratic cost subject to additional finite number of quadratic constraints. We first consider the problem of countably infinite number of players in the team for a bounded state of nature with a Gaussian distributi...
Nikzad, Safoora; Hashemi, Bijan; Hasan, Zuhair Saraf; Mozdarani, Hossein; Baradaran-Ghahfarokhi, Milad; Amini, Payam
2016-01-01
Purpose To investigate the effect of increasing the overall treatment time as well as delivering the compensating doses on the Balb/c breast adenocarcinoma (4T1) tumor. Materials and methods A total of 72 mice were divided into two aliquots (classes A and B) based on the initial size of their induced tumor. Each class was divided into a control and several treatment groups. Among the treatment groups, group 1 was continuously exposed to 2 Gy irradiation, and groups 2 and 3 received two subfractions of 1 Gy over the total treatment times of 30 and 60 min, respectively. To investigate the effect of compensating doses, calculated based on the developed linear quadratic model (LQ) model, the remaining two groups (groups 4 and 5) received two subfractions of 1.16 and 1.24 Gy over the total treatment times of 30 and 60 min, respectively. The growing curves, Tumor Growth Time (TGT), Tumor Growth Delay Time (TGDT) and the survival of the animals were studied. Results For class A (tumor size ≤ 30 mm(3)), the average tumor size in the irradiated groups 1-5 was considerably different compared to the control group as one unit (day) change in time, by amount of -160.8, -158.9, +39.4 and +44.0, respectively. While these amounts were +22.0, +17.9, -21.7 and -0.1 for class B (tumor size ≥ 400 mm(3)). For the class A of animals, the TGT and TGDT parameters were significantly lower (0 ≤ 0.05) for the groups 2 and 3, compared to group 1. There was no significant difference (p > 0.05) between groups 1, 4 and 5 in this class. There was no significant difference (p > 0.05) between all the treated groups in class B. Conclusions Increasing total treatment time affects the radiobiological efficiency of treatment especially in small-sized tumor. The compensating doses derived from the LQ model can be used to compensate the effects of prolonged treatment times at in vivo condition.
Li, Yang; Xia, Houlin; Wu, Mingquan; Wang, Jiabo; Lu, Xiaohua; Wei, Shizhang; Li, Kun; Wang, Lifu; Wang, Ruilin; Zhao, Pan; Zhao, Yanling; Xiao, Xiaohe
2017-01-01
Skin infectious disease is a common public health problem due to the emergence of drug-resistant bacteria caused by the antibiotic misuse. Dracontomelon dao (Blanco) Merr. et Rolfe, a traditional Chinese medicine, has been used for the treatment of various skin infectious diseases over 1000 of years. Previous reports have demonstrated that the leaves of D. dao present favorable antibacterial activity against Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus, and Bacillus subtitles. The flavonoids are the main components of the ethyl acetate extract of D. dao leaf. However, the correlation between flavonoids and antibacterial activities is yet to be determined. In this study, the combined antibacterial activities of these flavonoids were investigated. Three samples with the different concentrations of flavonoids (S1–S3) were obtained. By microcalorimetric measurements, the results showed that the IC50 value of S2 was lower than those of S1 and S3. The contents of main flavonoids (including Luteolin, L-Epicatechin, Cianidanol, and Quercetin) in S1–S3 were various, confirmed by the method of the Ultra High Performance Liquid Chromatography (UPLC). Based on the method of quadratic general rotary unitized design, the antibacterial effect of single flavonoid, and the potential synergistic effects between Luteolin and Quercetin, Luteolin and Cianidanol were calculated, which were also proved by microcalorimetric analysis. The antibacterial activities of main flavonoids were Luteolin > Cianidanol > Quercetin > L-Epicatechin. Meanwhile, the synergistic effects of Luteolin and Cianidanol (PL+C = 1.425), Quercetin and Luteolin (PL+Q = 1.129) on anti-microbial activity were validated. Finally, we found that the contents of Luteolin, L-Epicatechin, Cianidanol, Quercetin were 1061.00–1061.00, 189.14–262.86, 15,990.33–16,973.62, 6799.67–7662.64 ng·ml−1 respectively, with the antibacterial rate over 60.00%. In conclusion, this study could provide
A polyhedral approach to quadratic assignment problem
Köksaldı, Ahmet Sertaç Murat
1994-01-01
Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1994. Thesis (Master's) -- Bilkent University, 1994. Includes bibliographical references. In this thesis, Quadratic Assignment Problem is considered. Since Quadratic Assignment Problem is JVP-bard, no polynomial time exact solution method exists. Proving optimality of solutions to Quadratic Assignment Problems has been limited to instances of small dimension. In...
Orthogonality preserving infinite dimensional quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Akın, Hasan [Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260 (Turkey); Mukhamedov, Farrukh [Department of Computational & Theoretical Sciences Faculty of Science, International Islamic University Malaysia P.O. Box, 141, 25710, Kuantan Pahang (Malaysia)
2015-09-18
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Extending the Scope of Robust Quadratic Optimization
Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand
2017-01-01
In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in ge
Coherent Zeeman resonance from electron spin coherence in a mixed-type GaAs/AlAs quantum well.
O'Leary, Shannon; Wang, Hailin; Prineas, John P
2007-03-01
Coherent Zeeman resonance from electron spin coherence is demonstrated in a Lambda-type three-level system, coupling electron spin states via trions. The optical control of electron density that is characteristic of a mixed-type quantum-well facilitates the study of trion formation as well as the effects of many-body interactions on the manifestation of electron spin coherence in the nonlinear optical response.
Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems
Institute of Scientific and Technical Information of China (English)
Yong XIA
2011-01-01
In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems.We show that each problem is polynomially solved.Strong duality holds if a redundant constraint is introduced.As an application,a new lower bound is proposed for the quadratic assignment problem.
Phase control of a Zeeman-split He-Ne gas laser by variation of the gaseous discharge voltage.
Shelton, W N; Hunt, R H
1992-07-20
Zeeman-split lasers are useful for precise positioning or motion control. In applications that employ such a laser to control closely the position of a moving system, phase noise in the Zeeman frequency is a serious problem. Control of low-frequency phase noise can be obtained through variation of the external magnetic field by way of a solenoid wound around the laser tube. It is the finding in this work that control of the residual higher-frequency noise of a He-Ne laser can be obtained through small variations of the high voltage that is used to effect the gaseous discharge in the laser tube. The application of the present system is to the control of the path difference in a Fourier-transform interferometric spectrometer.
Malykin, G. B.; Pozdnyakova, V. I.
2016-07-01
We consider the distributions of the scalar gravitational potential of Coriolis forces in different parts of the shoulder of a rotating equal-arms Michelson interferometer. It results in a view of the very small difference between the phases of light in the shoulders of the Michelson interferometer, in comparison with the phase difference due to the quadratic Sagnac effect. It has been shown that there is an effect, discussed earlier by P Maraner, which is a higher approximation to quadratic Sagnac effect.
A versatile dual-species Zeeman slower for caesium and ytterbium
Energy Technology Data Exchange (ETDEWEB)
Hopkins, S. A., E-mail: s.a.hopkins@durham.ac.uk; Butler, K.; Guttridge, A.; Kemp, S.; Cornish, S. L. [Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, South Road, Durham DH1 3LE (United Kingdom); Freytag, R.; Hinds, E. A.; Tarbutt, M. R. [Centre for Cold Matter, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ (United Kingdom)
2016-04-15
We describe the design, construction, and operation of a versatile dual-species Zeeman slower for both Cs and Yb, which is easily adaptable for use with other alkali metals and alkaline earths. With the aid of analytic models and numerical simulation of decelerator action, we highlight several real-world problems affecting the performance of a slower and discuss effective solutions. To capture Yb into a magneto-optical trap (MOT), we use the broad {sup 1}S{sub 0} to {sup 1}P{sub 1} transition at 399 nm for the slower and the narrow {sup 1}S{sub 0} to {sup 3}P{sub 1} intercombination line at 556 nm for the MOT. The Cs MOT and slower both use the D2 line (6{sup 2}S{sub 1/2} to 6{sup 2}P{sub 3/2}) at 852 nm. The slower can be switched between loading Yb or Cs in under 0.1 s. We demonstrate that within a few seconds the Zeeman slower loads more than 10{sup 9} Yb atoms and 10{sup 8} Cs atoms into their respective MOTs. These are ideal starting numbers for further experiments on ultracold mixtures and molecules.
A versatile dual-species Zeeman slower for caesium and ytterbium
Hopkins, S. A.; Butler, K.; Guttridge, A.; Kemp, S.; Freytag, R.; Hinds, E. A.; Tarbutt, M. R.; Cornish, S. L.
2016-04-01
We describe the design, construction, and operation of a versatile dual-species Zeeman slower for both Cs and Yb, which is easily adaptable for use with other alkali metals and alkaline earths. With the aid of analytic models and numerical simulation of decelerator action, we highlight several real-world problems affecting the performance of a slower and discuss effective solutions. To capture Yb into a magneto-optical trap (MOT), we use the broad 1S0 to 1P1 transition at 399 nm for the slower and the narrow 1S0 to 3P1 intercombination line at 556 nm for the MOT. The Cs MOT and slower both use the D2 line (62S1/2 to 62P3/2) at 852 nm. The slower can be switched between loading Yb or Cs in under 0.1 s. We demonstrate that within a few seconds the Zeeman slower loads more than 109 Yb atoms and 108 Cs atoms into their respective MOTs. These are ideal starting numbers for further experiments on ultracold mixtures and molecules.
A versatile dual-species Zeeman slower for caesium and ytterbium
Hopkins, S A; Freytag, R; Guttridge, A; Kemp, S; Hinds, E A; Tarbutt, M R; Cornish, S L
2015-01-01
We describe the design, construction and operation of a versatile dual-species Zeeman slower for both Cs and Yb, which is easily adaptable for use with other alkali metals and alkaline earths. With the aid of analytic models and numerical simulation of decelerator action, we highlight several real-world problems affecting the performance of a slower and discuss effective solutions. To capture Yb into a magneto-optical trap (MOT), we use the broad $^1S_0$ to $^1P_1$ transition at 399 nm for the slower and the narrow $^1S_0$ to $^3P_1$ intercombination line at 556 nm for the MOT. The Cs MOT and slower both use the D2 line ($6^2S_{1/2}$ to $6^2P_{3/2}$) at 852 nm. We demonstrate that within a few seconds the Zeeman slower loads more than $10^9$ Yb atoms and $10^8$ Cs atoms into their respective MOTs. These are ideal starting numbers for further experiments on ultracold mixtures and molecules.
Slow and velocity-tunable beams of metastable He2 by multistage Zeeman deceleration
Motsch, Michael; Jansen, Paul; Agner, Josef A.; Schmutz, Hansjürg; Merkt, Frédéric
2014-04-01
We report on the use of multistage Zeeman deceleration to generate beams of He2 molecules in the metastable a3Σu+ state with velocities tunable down to 100 m/s. The metastable molecules are generated by striking a discharge in a supersonic expansion of pure helium gas from a pulsed valve held at cryogenic temperature. The velocity and internal-state distributions of the metastable He2 molecules are measured for nozzle temperatures of 300, 77, and 10 K by high-resolution photoelectron and photoionization spectroscopy. The deceleration process does not exhibit any rotational state selectivity with rotational levels up to N''=21 being populated, but eliminates molecules in spin-rotational sublevels with J''=N'' from the beam, where J'' and N'' are the total and the rotational angular momentum quantum number, respectively. The lack of rotational state selectivity is attributed to the fact that the Paschen-Back regime of the Zeeman effect in the rotational levels of He2 is already reached at fields of only 0.1 T.
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Quadratic reactivity fuel cycle model
Energy Technology Data Exchange (ETDEWEB)
Lewins, J.D.
1985-11-01
For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau/sup 2/ as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau/sup 2/ in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper.
Application of Zeeman spatial beam-splitting in polarized neutron reflectometry
Kozhevnikov, S. V.; Ignatovich, V. K.; Radu, F.
2017-01-01
Neutron Zeeman spatial beam-splitting is considered at reflection from magnetically noncollinear films. Two applications of Zeeman beam-splitting phenomenon in polarized neutron reflectometry are discussed. One is the construction of polarizing devices with high polarizing efficiency. Another one is the investigations of magnetically noncollinear films with low spin-flip probability. Experimental results are presented for illustration.
On Algebraic Approach in Quadratic Systems
Directory of Open Access Journals (Sweden)
Matej Mencinger
2011-01-01
Full Text Available When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (nonchaotic dynamics. In this paper we consider homogeneous quadratic systems via the so-called Markus approach. We use the one-to-one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960. We resume some connections between the dynamics of the quadratic systems and (algebraic properties of the corresponding algebras. We consider some general connections and the influence of power-associativity in the corresponding quadratic system.
An Arecibo Survey for Zeeman Splitting in OH Megamaser Galaxies
McBride, James
2012-01-01
We present the results of a comprehensive survey using the Arecibo Observatory for Zeeman splitting of OH lines in OH megamasers (OHMs). A total of seventy-seven sources were observed with the Arecibo telescope. Of these, maser emission could not be detected for eight sources, and two sources were only ambiguously detected. Another twenty-seven sources were detected at low signal-to-noise ratios or with interference that prevented placing any useful limits on the presence of magnetic fields. In twenty-six sources, it was possible to place upper limits on the magnitude of magnetic fields, typically between 10-30 mG. For fourteen sources, the Stokes V spectra exhibit features consistent with Zeeman splitting. Eleven of these fourteen are new detections, and the remaining three are re-detections of Stokes V detections in Robishaw et al. (2008). Among confident new detections, we derive magnetic fields associated with maser regions with magnitudes ranging from 6.1-27.6 mG. The distribution of magnetic field stren...
The Random Quadratic Assignment Problem
Paul, Gerald; Shao, Jia; Stanley, H. Eugene
2011-11-01
The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.
Parametric localized modes in quadratic nonlinear photonic structures
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;
2001-01-01
We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....
A Projection Neural Network for Constrained Quadratic Minimax Optimization.
Liu, Qingshan; Wang, Jun
2015-11-01
This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.
Convergence properties of the softassign quadratic assignment algorithm.
Rangarajan, A; Vuille, A; Mjolsness, E
1999-08-15
The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.
Binary Quadratic Forms: A Historical View
Khosravani, Azar N.; Beintema, Mark B.
2006-01-01
We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost type A-source impedance network is proposed in this paper for realizing converters that demand a very high voltage gain. To achieve that, the proposed network uses an auto-transformer, whose obtained gain is quadratically dependent on the duty ratio and is presently not ma...
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance ...
Factorising a Quadratic Expression with Geometric Insights
Joarder, Anwar H.
2015-01-01
An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme sim
Low-rank quadratic semidefinite programming
Yuan, Ganzhao
2013-04-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Zeeman-Doppler Imaging : Old Problems and New Methods
Carroll, T A; Strassmeier, K G; Ilyin, I
2009-01-01
Zeeman-Doppler Imaging (ZDI) is a powerful inversion method to reconstruct stellar magnetic surface fields. The reconstruction process is usually solved by translating the inverse problem into a regularized least-square or optimization problem. In this contribution we will emphasize that ZDI is an inherent non-linear problem and the corresponding regularized optimization is, like many non-linear problems, potentially prone to local minima. We show how this problem will be exacerbated by using an inadequate forward model. To facilitate a more consistent full radiative transfer driven approach to ZDI we describe a two-stage strategy that consist of a principal component analysis (PCA) based line profile reconstruction and a fast approximate polarized radiative transfer method to synthesize local Stokes profiles. Moreover, we introduce a novel statistical inversion method based on artificial neural networks (ANN) which provide a fast calculation of a first guess model and allows to incorporate better physical co...
Zeeman-Doppler imaging: old problems and new methods
Carroll, Thorsten A.; Kopf, Markus; Strassmeier, Klaus G.; Ilyin, Ilya
2009-04-01
Zeeman-Doppler Imaging (ZDI) is a powerful inversion method to reconstruct stellar magnetic surface fields. The reconstruction process is usually solved by translating the inverse problem into a regularized least-square or optimization problem. In this contribution we will emphasize that ZDI is an inherent non-linear problem and the corresponding regularized optimization is, like many non-linear problems, potentially prone to local minima. We show how this problem will be exacerbated by using an inadequate forward model. To facilitate a more consistent full radiative transfer driven approach to ZDI we describe a two-stage strategy that consist of a principal component analysis (PCA) based line profile reconstruction and a fast approximate polarized radiative transfer method to synthesize local Stokes profiles. Moreover, we introduce a novel statistical inversion method based on artificial neural networks (ANN) which provide a fast calculation of a first guess model and allows to incorporate better physical constraints into the inversion process.
Zeeman Doppler maps: the true and the spurious
Stift, Martin J
2016-01-01
Numerical models of atomic diffusion in magnetic atmospheres of ApBp stars predict abundance structures that differ from the empirical abundance maps derived with (Zeeman) Doppler mapping (ZDM). Whereas both equilibrium abundance stratification calculations and stationary solutions to the time-dependent diffusion equations predict (warped) rings about the magnetic equator in dipole-like magnetic geometries, spot-like structures dominate published maps. An in-depth analysis of this apparent disagreement investigates the detectability by means of ZDM of a variety of abundance structures, including (warped) rings predicted by theory, but also some complex spot-like structures. As it turns out, a number of published maps have to be considered spurious either because strong magnetic fields have been neglected or because they are based on spectra where photon noise dominates over the signal of the alleged abundance structures. Even when spectra of high signal to noise ratio are available, it can prove altogether im...
An inverted crossover resonance within one Zeeman manifold
Salter, Liam A
2016-01-01
We detect and describe inverted crossover resonances in $\\pi$-driven four-level systems where $\\Delta F$ can be zero. The signal is observed through sub-Doppler frequency modulation spectroscopy of the $(6s^{2})$ $^{1}S_{0}$ $-$ $(6s6p)$ $^{3}P_{1}$ transition in $^{171}$Yb, where the nuclear spin $I=1/2$. The resonance is inherently insensitive to first-order Zeeman shifts. Optical frequency measurements of the $F'=1/2$ hyperfine line recorded over several weeks demonstrate a statistical uncertainty of $2\\times10^{-11}$. The inverted crossover resonance found with the $F'=3/2$ line is used for 556 nm laser frequency stabilization and this light cools $^{171}$Yb atoms in a two-stage magneto-optical trap. We test the atomic cloud temperatures on the frequency instability of the light.
Solving quadratic programming problems by delayed projection neural network.
Yang, Yongqing; Cao, Jinde
2006-11-01
In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.
Stochastic level-value approximation for quadratic integer convex programming
Institute of Scientific and Technical Information of China (English)
PENG Zheng; WU Dong-hua
2008-01-01
We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and re-port some numerical results to illuminate its effectiveness.
MODIFICATION OF THE MOOG SPECTRAL SYNTHESIS CODES TO ACCOUNT FOR ZEEMAN BROADENING OF SPECTRAL LINES
Energy Technology Data Exchange (ETDEWEB)
Deen, Casey P. [Max Planck Institut fuer Astronomie, Koenigstuhl 17, D-69117 Heidelberg, GermanyAND (Germany); Department of Astronomy, University of Texas at Austin, 1 University Station, Austin, TX 78712 (United States)
2013-09-15
In an attempt to widen access to the study of magnetic fields in stellar astronomy, I present MOOGStokes, a version of the MOOG one-dimensional local thermodynamic equilibrium radiative transfer code, overhauled to incorporate a Stokes vector treatment of polarized radiation through a magnetic medium. MOOGStokes is a suite of three complementary programs, which together can synthesize the disk-averaged emergent spectrum of a star with a magnetic field. The first element (a pre-processing script called CounterPoint) calculates for a given magnetic field strength, wavelength shifts, and polarizations for the components of Zeeman-sensitive lines. The second element (a MOOG driver called SynStokes derived from the existing MOOG driver Synth) uses the list of Zeeman-shifted absorption lines together with the existing machinery of MOOG to synthesize the emergent spectrum at numerous locations across the stellar disk, accounting for stellar and magnetic field geometry. The third and final element (a post-processing script called DiskoBall) calculates the disk-averaged spectrum by weighting the individual emergent spectra by limb darkening and projected area, and applying the effects of Doppler broadening. All together, the MOOGStokes package allows users to synthesize emergent spectra of stars with magnetic fields in a familiar computational framework. MOOGStokes produces disk-averaged spectra for all Stokes vectors ( I, Q, U, V ), normalized by the continuum. MOOGStokes agrees well with the predictions of INVERS10 a polarized radiative transfer code with a long history of use in the study of stellar magnetic fields. In the non-magnetic limit, MOOGStokes also agrees with the predictions of the scalar version of MOOG.
Quadratic Hedging of Basis Risk
Directory of Open Access Journals (Sweden)
Hardy Hulley
2015-02-01
Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.
On Quadratic Variation of Martingales
Indian Academy of Sciences (India)
Rajeeva L Karandikar; B V Rao
2014-08-01
We give a construction of an explicit mapping $$\\Psi: D([0,∞),\\mathbb{R})→ D([0,∞),\\mathbb{R}),$$ where $D([0,∞), \\mathbb{R})$ denotes the class of real valued r.c.l.l. functions on $[0,∞)$ such that for a locally square integrable martingale $(M_t)$ with r.c.l.l. paths, $$\\Psi(M.())=A.()$$ gives the quadratic variation process (written usually as $[M,M]_t$) of $(M_t)$. We also show that this process $(A_t)$ is the unique increasing process $(B_t)$ such that $M_t^2-B_t$ is a local martingale, $B_0=0$ and $$\\mathbb{P}(( B)_t=[( M)_t]^2, 0 < ∞)=1.$$ Apart from elementary properties of martingales, the only result used is the Doob’s maximal inequality. This result can be the starting point of the development of the stochastic integral with respect to r.c.l.l. martingales.
Picconi, David; Ferrer, Francisco José Avila; Improta, Roberto; Lami, Alessandro; Santoro, Fabrizio
2013-01-01
We present mixed quantum-classical simulation of the internal conversion between the lowest energy pipi* (S(La)) and npi* (S(n)) excited electronic states in adenine in the gas phase, adopting a quadratic vibronic model (QVC), parametrized with the help of PBE0 density functional calculations. Our approach is based on a hierarchical representation of the QVC Hamiltonian and a subsequent treatment of the most relevant coordinates at accurate time-dependent quantum level and of the other 'bath' modes at classical level. We predict an ultrafast transfer (-30 fs) of approximately 75% of the initial population excited on S(La) to S(n). Within an adiabatic picture, on the same timescale the wave packet concentrates almost completely on the lowest S1 state, where however it shows a very broad distribution with different characteristics (due to the different 'diabatic' character). It is shown that the proposed methodology offers a practicable route to describe the quantum dynamics of internal conversion processes in large semi-rigid systems.
Radar Rainfall Estimation using a Quadratic Z-R equation
Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan
2016-04-01
The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.
The Pure Virtual Braid Group Is Quadratic
Lee, Peter
2011-01-01
If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra gr_I K need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a criterion which is equivalent to gr_I K being quadratic. We apply this criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic.
Specialization of Quadratic and Symmetric Bilinear Forms
Knebusch, Manfred
2010-01-01
The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed for fields of characteristic different from 2, are explored here without this restriction. In addition to chapters on specialization theory, generic splitting t
Quadratic stabilization of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
DONG YaLi; FAN JiaoJiao; MEI ShengWei
2009-01-01
In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.
Numerical model of Zeeman splitting of ro-vibrational lines in the fundamental band of NO molecule
Borkov, Yu. G.; Sulakshina, O. N.; Klimachev, Yu. M.
2016-07-01
This paper presents the results of calculation the LMR spectrograms of NO molecule in a variable magnetic field with maximum induction up to 6 T for probed CO laser lines. For the simulation of the LMR spectrum a numerical model was developed. This model is based on the numerical diagonalization the matrix of the effective molecular Hamiltonian, which includes Zeeman operator corresponding to interaction an external magnetic field with NO molecule. The comparison of calculated and experimental spectrograms has shown that the numerical model is very reliable and can reproduce the location of absorption peaks measured in a damped oscillating magnetic field.
Quantum electroweak symmetry breaking through loop quadratic contributions
Directory of Open Access Journals (Sweden)
Dong Bai
2015-06-01
Full Text Available Based on two postulations that (i the Higgs boson has a large bare mass mH≫mh≃125 GeV at the characteristic energy scale Mc which defines the Standard Model (SM in the ultraviolet region, and (ii quadratic contributions of Feynman loop diagrams in quantum field theories are physically meaningful, we show that the SM electroweak symmetry breaking is induced by the quadratic contributions from loop effects. As the quadratic running of Higgs mass parameter leads to an additive renormalization, which distinguishes from the logarithmic running with a multiplicative renormalization, the symmetry breaking occurs once the sliding energy scale μ moves from Mc down to a transition scale μ=ΛEW at which the additive renormalized Higgs mass parameter mH2(Mc/μ gets to change the sign. With the input of current experimental data, this symmetry breaking energy scale is found to be ΛEW≃760 GeV, which provides another basic energy scale for the SM besides Mc. Studying such a symmetry breaking mechanism could play an important role in understanding both the hierarchy problem and naturalness problem. It also provides a possible way to explore the experimental implications of the quadratic contributions as ΛEW lies within the probing reach of the LHC and the future Great Collider.
Alsina Ballester, E.; Belluzzi, L.; Trujillo Bueno, J.
2017-02-01
The spectral line polarization encodes a wealth of information about the thermal and magnetic properties of the solar atmosphere. Modeling the Stokes profiles of strong resonance lines is, however, a complex problem both from a theoretical and computational point of view, especially when partial frequency redistribution (PRD) effects need to be taken into account. In this work, we consider a two-level atom in the presence of magnetic fields of arbitrary intensity (Hanle–Zeeman regime) and orientation, both deterministic and micro-structured. Working within the framework of a rigorous PRD theoretical approach, we have developed a numerical code that solves the full non-LTE radiative transfer problem for polarized radiation, in one-dimensional models of the solar atmosphere, accounting for the combined action of the Hanle and Zeeman effects, as well as for PRD phenomena. After briefly discussing the relevant equations, we describe the iterative method of solution of the problem and the numerical tools that we have developed and implemented. We finally present some illustrative applications to two resonance lines that form at different heights in the solar atmosphere, and provide a detailed physical interpretation of the calculated Stokes profiles. We find that magneto-optical effects have a strong impact on the linear polarization signals that PRD effects produce in the wings of strong resonance lines. We also show that the weak-field approximation has to be used with caution when PRD effects are considered.
Structure of Solvable Quadratic Lie Algebras
Institute of Scientific and Technical Information of China (English)
ZHU Lin-sheng
2005-01-01
@@ Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras.
Compression limits in cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw;
2008-01-01
Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency.......Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency....
Cascaded quadratic soliton compression at 800 nm
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey;
2007-01-01
We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion.......We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
A NEW INEXACT SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM
Institute of Scientific and Technical Information of China (English)
倪勤
2002-01-01
This paper represents an inexact sequential quadratic programming (SQP ) algorithm which can solve nonlinear programming (NLP ) problems. An inexact solution of the quadratic programming subproblem is determined by a projection and contraction method such that only matrix-vector product is required. Some truncated criteria are chosen such that the algorithm is suitable to large scale NLP problem. The global convergence of the algorithm is proved.
The explicit dependence of quadrat variance on the ratio of clump size to quadrat size.
Ferrandino, Francis J
2005-05-01
ABSTRACT In the past decade, it has become common practice to pool mapped binary epidemic data into quadrats. The resultant "quadrat counts" can then be analyzed by fitting them to a probability distribution (i.e., betabinomial). Often a binary form of Taylor's power law is used to relate the quadrat variance to the quadrat mean. The fact that there is an intrinsic dependence of such analyses on quadrat size and shape is well known. However, a clear-cut exposition of the direct connection between the spatial properties of the two-dimensional pattern of infected plants in terms of the geometry of the quadrat and the results of quadrat-based analyses is lacking. This problem was examined both empirically and analytically. The empirical approach is based on a set of stochastically generated "mock epidemics" using a Neyman-Scott cluster process. The resultant spatial point-patterns of infected plants have a fixed number of disease foci characterized by a known length scale (monodisperse) and saturated to a known disease level. When quadrat samples of these epidemics are fit to a beta-binomial distribution, the resulting measures of aggregation are totally independent of disease incidence and most strongly dependent on the ratio of the length scale of the quadrat to the length scale of spatial aggregation and to a lesser degree on disease saturation within individual foci. For the analytical approach, the mathematical form for the variation in the sum of random variates is coupled to the geometry of a quadrat through an assumed exponential autocorrelation function. The net result is an explicit equation expressing the intraquadrat correlation, quadrat variance, and the index of dispersion in terms of the ratio of the quadrat length scale to the correlative length scale.
Zeeman-Doppler imaging of active young solar type stars
Hackman, Thomas; Rosén, Lisa; Kochukhov, Oleg; Käpylä, Maarit J
2015-01-01
By studying young magnetically active late-type stars, i.e. analogues to the young Sun, one can draw conclusions on the evolution of the solar dynamo. We determine the topology of the surface magnetic field and study the relation between the magnetic field and cool photospheric spots in three young late-type stars. High-resolution spectropolarimetry of the targets were obtained with the HARPSpol instrument mounted at the ESO 3.6 m telescope. The signal-to-noise ratio of the Stokes IV measurements were boosted by combining the signal from a large number of spectroscopic absorption lines through the least squares deconvolution technique. Surface brightness and magnetic field maps were calculated using the Zeeman-Doppler imaging technique. All the three targets show clear signs of both magnetic fields and cool spots. Only one of the targets, namely V1358 Ori, shows evidence of the dominance of non-axisymmetric modes. In two of the targets, the poloidal field is significantly stronger than the toroidal one, indic...
Energy Technology Data Exchange (ETDEWEB)
Casabianca, T.; Bitonte, R.; Epifani, M.; Ubaldi, C. [ENEA, Divisione Tecnologie Ingegneria e Servizi Ambientali, Centro Ricerche Trisaia, MT (Italy)
2001-07-01
In the framework of SIMOA project have been investigated methods to evaluate the level of soil contamination due to heavy metals. In this wok, it is discussed a procedure to measure topsoil bioavailable fraction of seven heavy metals (Cd, Cu, Pb, Ni, Cr, Hg). The adopted procedure is based on acid digestion followed by instrumental detection by means of graphite furnace atomic-absorption spectrophotometry (GFAAS) using Zeeman effect to reduce background contribution. Details of samples preparation and analysis, experimental setup optimization and statistical data analysis are presented, together with a discussion on method accuracy and data interpretation. [Italian] Nell'ambito del progetto SIMOA (Sistema Integrato di Monitoraggio Ambientale) per il monitoraggio ambientale nel bacino del Basento (Regione Basilicata, Italia), vengono investigati i metodi per il controllo dei livelli di inquinamento del suolo da parte di metalli pesanti. Nel presente lavoro viene proposta una procedura per determinare il livello di concentrazione della frazione biodisponibile di sette metalli pesanti (Cadmio, Rame, Piombo, Nickel, Cromo, Mercurio) in campion di suolo superficiale. Il metodo e' basato su di un trattamento di digestione acida in forno a microonde cui segue la rivelazione strumentale mediante spettrofotometria di assorbimento atomico in fornetto di grafite (GFAAS) con effetto Zeeman per la correzione del fondo. Si descrivono in dettaglio le fasi di preparazione dei campioni, la metodologia di misura e l'analisi statistica dei dati, oltre ad una discussione sull'attendibilita' del metodo e sui futuri sviluppi.
Hu, Jin; Tang, Zhijie; Liu, Jinyu; Zhu, Yanglin; Wei, Jiang; Mao, Zhiqiang
2017-07-01
Topological semimetals represent a new class of quantum materials hosting Dirac/Weyl fermions. The essential properties of topological fermions can be revealed by quantum oscillations. Here we present systematic de Haas-van Alphen (dHvA) oscillation studies on the recently discovered topological Dirac nodal-line semimetal ZrSiS. From the angular dependence of dHvA oscillations, we have revealed the anisotropic Dirac bands in ZrSiS and found surprisingly strong Zeeman splitting at low magnetic fields. The Landé g factor estimated from the separation of Zeeman splitting peaks is as large as 38. From the analyses of dHvA oscillations, we also revealed nearly zero effective mass and exceptionally high quantum mobility for Dirac fermions in ZrSiS. These results shed light on the nature of novel Dirac fermion physics of ZrSiS.
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2006-01-01
This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...
Linear-quadratic control and quadratic differential forms for multidimensional behaviors
Napp, D.; Trentelman, H.L.
2011-01-01
This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look
Xia, Yong; Han, Ying-Wei
2014-01-01
In this paper, we propose a mixed-binary convex quadratic programming reformulation for the box-constrained nonconvex quadratic integer program and then implement IBM ILOG CPLEX 12.6 to solve the new model. Computational results demonstrate that our approach clearly outperform the very recent state-of-the-art solvers.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard
2015-05-04
In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
Linear quadratic regulator for laser beam shaping
Escárate, Pedro; Agüero, Juan C.; Zúñiga, Sebastián; Castro, Mario; Garcés, Javier
2017-07-01
The performance of an adaptive optics system depends on multiple factors, including the quality of the laser beam before being projected to the mesosphere. In general, cumbersome procedures are required to optimize the laser beam in terms of amplitude and phase. However, aberrations produced by the optics of the laser beam system are still detected during the operations due to, for example, uncertainty in the utilized models. In this paper we propose the use of feedback to overcome the presence of model uncertainty and disturbances. In particular we use a Linear Quadratic Regulator (LQR) for closed loop laser beam shaping using a setup of two deformable mirrors. The proposed method is studied and simulated to provide an automatic optimization of the Amplitude of the laser beam. The performance of the LQR control algorithm is evaluated via numerical simulations using the root mean square error (RMSE). The results show an effective amplitude correction of the laser system aberrations after 20 iterations of the algorithm, a RMSE less than 0.7 was obtained, with about 140 actuators per mirror and a separation of z=3 [m] among the mirrors.
Laurent, Devenoges; André, Stefanov; Antoine, Jallageas; Jacques, Morel; Thomas, Südmeyer; Pierre, Thomann
2016-01-01
We report the evaluation of the second order Zeeman shift in the continuous atomic fountain clock FoCS-2. Because of the continuous operation and its geometrical constraints, the methods used in pulsed fountain are not applicable. We use here time-resolved Zeeman spectroscopy to probe the magnetic field profile in the clock. The pulses of ac magnetic excitation allow us to measure the Zeeman frequency with spatial resolution and to evaluate the Zeeman shift with an uncertainty smaller than 10E-16 in relative units.
Zeeman Effect in the Electronic Spectrum of Solid CS2
Hochstrasser, Robin M.; Wiersma, Douwe A.
1971-01-01
The lowest-energy 3A2←1Σg+ singlet-triplet transition of CS2 has been studied in the CS2 crystal at 4.2°K. The spectrum consists mainly of progressions in the bending mode ν2'. The following values for the upper state frequencies have been obtained (v1'=677 cm–1, ν2'=309 cm–1) and the unobserved B2
Quantum coherent effects in multi-Zeeman-sublevel atomic systems
Institute of Scientific and Technical Information of China (English)
Dong Ya-Bin; Gao Jiang-Rui; Dong You-Er
2008-01-01
This paper reports the experimental results on electromagnetically induced absorption(EIA)spectra observed in the system which does not satisfy completely the conditions given by Lezama et al[1999 Phys.Rev.A 59 4732].EIA signals on the transitions in the Cs D2 line are able to be observed,where Fg (→)F3=Fg-1 as open systems.Theoretical model of Lezama et al is good for the case Fg(→)=Fg+1,considering spontaneous transfer of atomic coherences or populations this model is not able to explain our experimental results obtained in the case Fg(→)Fe=Fg-1.This paper offers a theoretical model which is able to well explain the case Fg(→)Fe=Fg-1.It also uses this theoretical model to explain the split and shift of EIA peaks,which have been obtained in experiments.
Indian Academy of Sciences (India)
DEEPAK KUMAR; A G RAMAKRISHNAN
2016-03-01
Particle swarm optimization (PSO) is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The central idea is to use PSO to move in the direction towards optimal solution rather than searching the entire feasibleregion. Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or classification boundary for a data set. Our results on the Iris, Pima, Wine, Thyroid, Balance, Bupa, Haberman, and TAE datasets show that the proposed method works better than a neural network and the performance is close to that of a support vector machine
Studying stellar spin-down with Zeeman-Doppler magnetograms
See, V.; Jardine, M.; Vidotto, A. A.; Donati, J.-F.; Boro Saikia, S.; Fares, R.; Folsom, C. P.; Hébrard, É. M.; Jeffers, S. V.; Marsden, S. C.; Morin, J.; Petit, P.; Waite, I. A.; BCool Collaboration
2017-04-01
Magnetic activity and rotation are known to be intimately linked for low-mass stars. Understanding rotation evolution over the stellar lifetime is therefore an important goal within stellar astrophysics. In recent years, there has been increased focus on how the complexity of the stellar magnetic field affects the rate of angular-momentum loss from a star. This is a topic that Zeeman-Doppler imaging (ZDI), a technique that is capable of reconstructing the large-scale magnetic field topology of a star, can uniquely address. Using a potential field source surface model, we estimate the open flux, mass-loss rate and angular-momentum-loss rates for a sample of 66 stars that have been mapped with ZDI. We show that the open flux of a star is predominantly determined by the dipolar component of its magnetic field for our choice of source surface radius. We also show that, on the main sequence, the open flux, mass-loss and angular-momentum-loss rates increase with decreasing Rossby number. The exception to this rule is stars less massive than 0.3 M⊙. Previous work suggests that low-mass M dwarfs may possess either strong, ordered and dipolar fields or weak and complex fields. This range of field strengths results in a large spread of angular-momentum-loss rates for these stars and has important consequences for their spin-down behaviour. Additionally, our models do not predict a transition in the mass-loss rates at the so-called wind-dividing line noted from Lyα studies.
Zhang, J.-Z.; Galbraith, I.
2008-05-01
Using perturbation theory, intraband magneto-optical absorption is calculated for InAs/GaAs truncated pyramidal quantum dots in a magnetic field applied parallel to the growth direction z . The effects of the magnetic field on the electronic states as well as the intraband transitions are systematically studied. Selection rules governing the intraband transitions are discussed based on the symmetry properties of the electronic states. While the broadband z -polarized absorption is almost insensitive to the magnetic field, the orbital Zeeman splitting is the dominant feature in the in-plane polarized spectrum. Strong in-plane polarized magneto-absorption features are located in the far-infrared region, while z -polarized absorption occurs at higher frequencies. This is due to the dot geometry (the base length is much larger than the height) yielding different quantum confinement in the vertical and lateral directions. The Thomas-Reiche-Kuhn sum rule, including the magnetic field effect, is applied together with the selection rules to the absorption spectra. The orbital Zeeman splitting depends on both the dot size and the confining potential—the splitting decreases as the dot size or the confining potential decreases. Our calculated Zeeman splittings are in agreement with experimental data.
Fusion arrest and collapse phenomena due to Kerr-nonlinearity in quadratic media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole; Sørensen, Mads Peter
2000-01-01
Emphasizing collapse phenomena it is investigated to what extend the always present cubic nonlinearity affects the properties of soliton interaction in quadratic bulk media. An effective particle approach is applied and verified by numerical simulations....
Fast approximate quadratic programming for graph matching.
Directory of Open Access Journals (Sweden)
Joshua T Vogelstein
Full Text Available Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs, we find that it efficiently achieves performance.
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.
Quadratic Interpolation Algorithm for Minimizing Tabulated Function
Directory of Open Access Journals (Sweden)
E. A. Youness
2008-01-01
Full Text Available Problem statement: The problem of finding the minimum value of objective function, when we know only some values of it, is needed in more practical fields. Quadratic interpolation algorithms are the famous tools deal with this kind of these problems. These algorithms interested with the polynomial space in which the objective function is approximated. Approach: In this study we approximated the objective function by a one dimensional quadratic polynomial. This approach saved the time and the effort to get the best point at which the objective is minimized. Results: The quadratic polynomial in each one of the steps of the proposed algorithm, accelerate the convergent to the best value of the objective function without taking into account all points of the interpolation set. Conclusion: Any n-dimensional problem of finding a minimal value of a function, given by some values, can be converted to one dimensional problem easier in deal.
The Wiener maximum quadratic assignment problem
Cela, Eranda; Woeginger, Gerhard J
2011-01-01
We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time solution for the following problem from chemical graph theory: Find a tree that maximizes the Wiener index among all trees with a prescribed degree sequence. This settles an open problem from the literature.
A CART extention using Quadratic Decision Borders
DEFF Research Database (Denmark)
Hartelius, Karsten
1999-01-01
In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...
A CART extension using Quadratic Decision Borders
DEFF Research Database (Denmark)
Hartelius, Karsten
1999-01-01
In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...
Quintessence with quadratic coupling to dark matter
Boehmer, Christian G; Chan, Nyein; Lazkoz, Ruth; Maartens, Roy
2009-01-01
We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
On orthogonality preserving quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Discrete fractional Radon transforms and quadratic forms
Pierce, Lillian B
2010-01-01
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove sharp results for this class of discrete operators in all dimensions, providing necessary and sufficient conditions for them to extend to bounded operators from $\\ell^p$ to $\\ell^q$. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of Hardy and Littlewood. Techniques from harmonic analysis, in particular Fourier transform methods and oscillatory integrals, as well as the number theoretic structure of quadratic forms, exponential sums, and theta functions, play key roles in the proof.
MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION
Institute of Scientific and Technical Information of China (English)
Zhong-Zhi Bai; Yong-Hua Gao
2007-01-01
We construct a modified Bernoulli iteration method for solving the quadratic matrix equation AX2+BX+C=0,where A,B and C are square matrices.This method is motivated from the Gauss-Seidel iteration for solving linear systems and the ShermanMorrison-Woodbury formula for updating matrices.Under suitable conditions, we prove the local linear convergence of the Dew method.An algorithm is presented to find the solution of the quadratic matrix equation and some numerical results are given to show the feasibility and the effectiveness of the algorithm.In addition,we also describe and analyze the block version of the modified Bernoulli iteration method.
π Berry phase and Zeeman splitting of Weyl semimetal TaP
Hu, J.; Liu, J. Y.; Graf, D.; Radmanesh, S. M. A.; Adams, D. J.; Chuang, A.; Wang, Y.; Chiorescu, I.; Wei, J.; Spinu, L.; Mao, Z. Q.
2016-01-01
The recent breakthrough in the discovery of Weyl fermions in monopnictide semimetals provides opportunities to explore the exotic properties of relativistic fermions in condensed matter. The chiral anomaly-induced negative magnetoresistance and π Berry phase are two fundamental transport properties associated with the topological characteristics of Weyl semimetals. Since monopnictide semimetals are multiple-band systems, resolving clear Berry phase for each Fermi pocket remains a challenge. Here we report the determination of Berry phases of multiple Fermi pockets of Weyl semimetal TaP through high field quantum transport measurements. We show our TaP single crystal has the signatures of a Weyl state, including light effective quasiparticle masses, ultrahigh carrier mobility, as well as negative longitudinal magnetoresistance. Furthermore, we have generalized the Lifshitz-Kosevich formula for multiple-band Shubnikov-de Haas (SdH) oscillations and extracted the Berry phases of π for multiple Fermi pockets in TaP through the direct fits of the modified LK formula to the SdH oscillations. In high fields, we also probed signatures of Zeeman splitting, from which the Landé g-factor is extracted. PMID:26726050
Test-assignment: a quadratic coloring problem
Duives, Jelle; Lodi, Andrea; Malaguti, Enrico
2013-01-01
We consider the problem of assigning the test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. The problem is a generalization of the Vertex Coloring and we model it as a binary quadratic problem. Exact solution methods bas
Institute of Scientific and Technical Information of China (English)
谭亚茹
2016-01-01
The quadratic Higher Algebra is an important part of this paper, the definition of quadratic forms, introduces the second type of representation, and then describes how to use the allocation method, elementary transformation, orthogonal transformation method, etc. II second type into the standard form, and the second type of normal form, finally introduced posi-tive definite quadratic form and method for determining positive definite quadratic form.%二次型是高等代数的重要组成部分，本文从二次型的定义出发，介绍了二次型的表示方法，然后介绍了如何用配方法、初等变换法、正交变换法等将二次型化为标准形，以及二次型的规范形，最后介绍了正定二次型和判定正定二次型的方法。
On Quadratic Programming with a Ratio Objective
Bhaskara, Aditya; Manokaran, Rajsekar; Vijayaraghavan, Aravindan
2011-01-01
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \\sum_ij a_ij x_i x_j. QP captures many known combinatorial optimization problems and SDP techniques have given optimal approximation algorithms for many of these problems. We extend this body of work by initiating the study of Quadratic Programming problems where the variables take values in the domain {-1,0,1}. The specific problem we study is: QP-Ratio: max_{-1,0,1}^n (x^T A x) / (x^T x). This objective function is a natural relative of several well studied problems. Yet, it is a good testbed for both algorithms and complexity because the techniques used for quadratic problems for the {-1,1} and {0,1} domains do not seem to carry over to the {-1,0,1} domain. We give approximation algorithms and evidence for the hardness of approximating the QP-Ratio problem. We consider an SDP relaxation obtained by adding constraints to the natural SDP relaxation for this problem and obtain an O(n^{2/7}) algorithm for...
Distortion control of conjugacies between quadratic polynomials
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We use a new type of distortion control of univalent functions to give an alternative proof of Douady-Hubbard’s ray-landing theorem for quadratic Misiurewicz polynomials. The univalent maps arise from Thurston’s iterated algorithm on perturbation of such polynomials.
Target manifold formation using a quadratic SDF
Hester, Charles F.; Risko, Kelly K. D.
2013-05-01
Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.
The GCD property and irreduciable quadratic polynomials
Directory of Open Access Journals (Sweden)
Saroj Malik
1986-01-01
Full Text Available The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a Prüfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.
Modulational instability in periodic quadratic nonlinear materials
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...
Integration of the Quadratic Function and Generalization
Mitsuma, Kunio
2011-01-01
We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families...
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
In this paper, we propose using realized range-based estimation to draw inference about the quadratic variation of jump-diffusion processes. We also construct a new test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the test...
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient...
Interactions of space-variant polarization beams with Zeeman-shifted rubidium vapor
Szapiro, Anat; Levy, Uriel
2015-01-01
Space variant beams are of great importance as a variety of applications have emerged in recent years. As such, manipulation of their degrees of freedom is highly desired. Here, by exploiting the circular dichroism and circular birefringence in a Zeeman-shifted Rb medium, we study the general interaction of space variant beams with such a medium. We present two particular cases of radial polarization and hybrid polarization beams where the control of the polarization states is demonstrated experimentally. Moreover, we show that a Zeeman-shifted atomic system can be used as an analyzer for such space variant beams
Malykin, G. B.; Pozdnyakova, V. I.
2015-04-01
It is shown that when an equal-arm Michelson interferometer is involved in rotation (for example, Earth's rotation around its axis or around the Sun) and its arms are oriented differently with respect to the plane of rotation, a phase difference arises between the light rays that pass through different arms. This phase difference is due to the fact that the arms experience variously the Newtonian (nonrelativistic) scalar gravitational potential of the Coriolis forces. It is shown that the phase difference is proportional to the length of the interferometer arm, the square of the angular velocity of the rotation, and the square of the distance from the center of rotation — hence, the proposal to call this phenomenon the quadratic Sagnac effect. In the present paper, we consider, as an illustrative example, the results of the once well-known experiments of D C Miller, who claimed to observe the translational motion of Earth relative to the hypothetical ‘luminiferous ether’. It is shown that this claim can actually be explained by the fact that, because of the orbital revolution of Earth, the time dilations in the orthogonal arms of the Michelson interferometer are influenced differently by the scalar gravitational potential of the Coriolis forces.
Quadratically constrained quadratic programs on acyclic graphs with application to power flow
Bose, Subhonmesh; Low, Steven H; Chandy, K Mani
2012-01-01
This paper proves that non-convex quadratically constrained quadratic programs have an exact semidefinite relaxation when their underlying graph is acyclic, provided the constraint set satisfies a certain technical condition. When the condition is not satisfied, we propose a heuristic to obtain a feasible point starting from a solution of the relaxed problem. These methods are then demonstrated to provide exact solutions to a richer class of optimal power flow problems than previously solved.
EXACT SOLUTIONS FOR NONLINEAR TRANSIENT FLOW MODEL INCLUDING A QUADRATIC GRADIENT TERM
Institute of Scientific and Technical Information of China (English)
曹绪龙; 同登科; 王瑞和
2004-01-01
The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform. Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.
Directory of Open Access Journals (Sweden)
M. Safaei
2016-12-01
Full Text Available This study aimed to investigate the spatial patterns of Acanthophyllum microcephalum Boiss, Nepeta glomerulosa Boiss and Hertia angustifolia and evaluate the effects of study scale on spatial patterns of three range plant species in Ghale-Gharak research-station located in Shahr-e-Kord. 40 points with a distance of five meters from each other were selected for sampling of vegetation along four 50 m transects using a random-systematic approach. The species spatial patterns were measured by 6 different distance-based methods including Hopkines, Johnson-and-Zimer, Eberhardt, Holgate, Hines and T-Square-index. A 100 m2 reference site (10 by 10 m was selected to record the species co-ordinates and conduct point pattern analysis. The spatial patterns of the species were determined in 3 scales of 10×10, 5×10 and 5×5 meters to highlight the effects of scale on spatial patterns of vegetation. According to the results, H. angustifolia showed randomized spatial patterns due to its seed dispersal ability. N. glomerulosa and A. microcephalum showed a clustered spatial pattern beacuse their seed are in achene form and fall next to these species. All the 3 species had a clustered pattern when the scale of point pattern analysis was decreased. Identifying these plant spatial patterns and their controlling factors such as seed dispersal mechanisms of the species and sampling scale are required to select the best sampling strategy in rangeland assessment programs.
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Bianchi $VII_A$ solutions of quadratic gravity
de Deus, Juliano A
2011-01-01
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model $H^ 3$ for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity.
SPEECH EMOTION RECOGNITION USING MODIFIED QUADRATIC DISCRIMINATION FUNCTION
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Quadratic Discrimination Function(QDF)is commonly used in speech emotion recognition,which proceeds on the premise that the input data is normal distribution.In this Paper,we propose a transformation to normalize the emotional features,then derivate a Modified QDF(MQDF) to speech emotion recognition.Features based on prosody and voice quality are extracted and Principal Component Analysis Neural Network (PCANN) is used to reduce dimension of the feature vectors.The results show that voice quality features are effective supplement for recognition.and the method in this paper could improve the recognition ratio effectively.
On quadratic residue codes and hyperelliptic curves
Directory of Open Access Journals (Sweden)
David Joyner
2008-01-01
Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''
Higgsed Stueckelberg vector and Higgs quadratic divergence
Directory of Open Access Journals (Sweden)
Durmuş Ali Demir
2015-01-01
Full Text Available Here we show that, a hidden vector field whose gauge invariance is ensured by a Stueckelberg scalar and whose mass is spontaneously generated by the Standard Model Higgs field contributes to quadratic divergences in the Higgs boson mass squared, and even leads to its cancellation at one-loop when Higgs coupling to gauge field is fine-tuned. In contrast to mechanisms based on hidden scalars where a complete cancellation cannot be achieved, stabilization here is complete in that the hidden vector and the accompanying Stueckelberg scalar are both free from quadratic divergences at one-loop. This stability, deriving from hidden exact gauge invariance, can have important implications for modeling dark phenomena like dark matter, dark energy, dark photon and neutrino masses. The hidden fields can be produced at the LHC.
Linear quadratic output tracking and disturbance rejection
Karimi-Ghartemani, Masoud; Khajehoddin, S. Ali; Jain, Praveen; Bakhshai, Alireza
2011-08-01
This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.
Estimating quadratic variation using realized variance
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Shephard, N.
2002-01-01
This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process is a semimar......This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process...... have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data and some stock data. We show that even with large values of M the RV is sometimes a quite noisy estimator of integrated variance. Copyright © 2002 John Wiley & Sons, Ltd....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2003-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Quaternion orders, quadratic forms, and Shimura curves
Alsina, Montserrat
2004-01-01
Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...
Institute of Scientific and Technical Information of China (English)
肖峰; 郭瑞民; 陈帅; 张宇; 李路明; 陈徐宗
2003-01-01
We observed electromagnetically induced transparency (EIT) in a Zeeman-sublevel system using rubidium atomic vapour at the temperature of 75℃, in which the width of the EIT signal is only 0.6 MHz. Two different methods were performed to observe the EIT signal in our experiment.
Designing and building a permanent magnet Zeeman slower for calcium atoms using a 3D printer
Parsagian, Alexandria; Kleinert, Michaela
2015-10-01
We present the design of a Zeeman slower for calcium atoms using permanent magnets instead of more traditional electromagnets and the novel technique of 3D printing to create a very robust and flexible structure for these magnets. Zeeman slowers are ideal tools to slow atoms from several hundreds of meters per second to just a few tens of meters per second. These slower atoms can then easily be trapped in a magneto-optical trap, making Zeeman slowers a very valuable tool in many cold atom labs. The use of permanent magnets and 3D printing results in a highly stable and robust slower that is suitable for undergraduate laboratories. In our design, we arranged 28 magnet pairs, 2.0 cm apart along the axis of the slower and at varying radial distances from the axis. We determined the radial position of the magnets by simulating the combined field of all magnet pairs using Mathematica and comparing it to the ideal theoretical field for a Zeeman slower. Finally, we designed a stable, robust, compact, and easy-to-align mounting structure for the magnets in Google Sketchup, which we then printed using a commercially available 3D printer by Solidoodle. The resulting magnetic field is well suited to slow calcium atoms from the 770 m/s rms velocity at a temperature of 950 K, down to the capture velocity of the magneto-optical trap.
Neutron Zeeman beam-splitting for the investigation of magnetic nanostructures
Kozhevnikov, S. V.; Ott, F.; Semenova, E.
2016-01-01
The Zeeman spatial splitting of a neutron beam takes place during a neutron spin-flip in magnetically non-collinear systems at grazing incidence geometry. We apply the neutron beam-splitting method for the investigation of magnetically non-collinear clusters of submicron size in a thin film. The experimental results are compared with ones obtained by other methods.
Neutron Zeeman beam-splitting for the investigation of magnetic nanostructures
Energy Technology Data Exchange (ETDEWEB)
Kozhevnikov, S.V., E-mail: kozhevn@nf.jinr.ru [Frank Laboratory of Neutron Physics, JINR, 141980, Dubna (Russian Federation); Ott, F. [Laboratoire Léon Brillouin CEA/CNRS, IRAMIS, Université Paris-Saclay, F-91191, Gif sur Yvette (France); Semenova, E. [Condensed Matter Department, Faculty of Physics, Tver State University, 170002, Tver (Russian Federation)
2017-03-01
Zeeman spatial splitting of a neutron beam takes place during a neutron spin-flip in magnetically non-collinear systems at grazing incidence geometry. We apply the neutron beam-splitting method for the investigation of magnetically non-collinear clusters of submicron size in a thin film. The experimental results are compared with ones obtained by other methods.
Zeeman Relaxation of Cold Atomic Iron and Nickel in Collisions with 3He
Johnson, Cort; Brahms, Nathan; Doyle, John M; Kleppner, Daniel; Greytak, Thomas J
2010-01-01
We have measured the ratio of the diffusion cross-section to the angular momentum reorientation cross-section in the colliding Fe-3He and Ni-3He systems. Nickel (Ni) and iron (Fe) atoms are introduced via laser ablation into a cryogenically cooled experimental cell containing cold (< 1 K) 3He buffer gas. Elastic collisions rapidly cool the translational temperature of the ablated atoms to the helium temperature. The cross-section ratio is extracted by measuring the decays of the atomic Zeeman sublevels. For our experimental conditions, thermal energy is comparable to the Zeeman splitting. As a result, thermal excitations between Zeeman sublevels significantly impact the observed decay. To determine the cross-section ratio accurately, we introduce a model of Zeeman state dynamics that includes thermal excitations. We find the cross-section ratio for Ni-3He = 5 x 10^3 and Fe-3He <= 3 x 10^3 at 0.75 K in a 0.8 T magnetic field. These measurements are interpreted in the context of submerged shell suppressio...
Hernandez, R A Vargas
2015-01-01
We show that Zeeman excitations in an ensemble of highly magnetic atoms trapped in an optical lattice lead to interacting Frenkel excitons described by a tunable $t$-$V$ model. The dispersion of the excitons and the interactions between excitons can be tuned in a wide range by transferring atoms to different Zeeman states. We show that these parameters are insensitive to an external magnetic field, which leads to an interesting possibility of engineering lattice models with significant particle-non-conserving terms. We consider the coupling of the Zeeman excitations to the translational motion of atoms in the lattice and show that the resulting Hamiltonian is equivalent to a polaron Hamiltonian, where the mathematical form of the particle - phonon interaction can be tuned by transferring atoms to different Zeeman states. We calculate the model parameters for the specific system of Dy atoms on an optical lattice with the lattice site separation 266 nm and show that the exciton interaction parameters can be tun...
New diagnostic technique for Zeeman-compensated atomic beam slowing: technique and results
Molenaar, P.A.; Straten, P. van der; Heideman, H.G.M.; Metcalf, H.
2001-01-01
We have developed a new diagnostic tool for the study of Zeeman-compensated slowing of an alkali atomic beam. Our time-of-flight technique measures the longitudinal veloc- ity distribution of the slowed atoms with a resolution below the Doppler limit of 30 cm/s. Furthermore, it can map the position
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...
Elementary Components of the Quadratic Assignment Problem
Chicano, Francisco; Alba, Enrique
2011-01-01
The Quadratic Assignment Problem (QAP) is a well-known NP-hard combinatorial optimization problem that is at the core of many real-world optimization problems. We prove that QAP can be written as the sum of three elementary landscapes when the swap neighborhood is used. We present a closed formula for each of the three elementary components and we compute bounds for the autocorrelation coefficient.
Cubic Lienard Equations with Quadratic Damping (Ⅱ)
Institute of Scientific and Technical Information of China (English)
Yu-quan Wang; Zhu-jun Jing
2002-01-01
Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation.
Characterization of a Quadratic Function in Rn
Xu, Conway
2010-01-01
It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.
Tahir, Muhammad
2013-05-01
We show that the surface states of magnetic topological insulators realize an activated behavior and Shubnikov de Haas oscillations. Applying an external magnetic field perpendicular to the surface of the topological insulator in the presence of Zeeman interaction, we investigate the opening of a gap at the Dirac point, making the surface Dirac fermions massive, and the effects on the transport properties. Analytical expressions are derived for the collisional conductivity for elastic impurity scattering in the first Born approximation. We also calculate the Hall conductivity using the Kubo formalism. Evidence for a transition from gapless to gapped surface states at n = 0 and activated transport is found from the temperature and magnetic-field dependence of the collisional and Hall conductivities. © Copyright EPLA, 2013.
Chen, R Y; Chen, Z G; Song, X-Y; Schneeloch, J A; Gu, G D; Wang, F; Wang, N L
2015-10-23
We present a magnetoinfrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ZrTe(5). We observe clear transitions between Landau levels and their further splitting under a magnetic field. Both the sequence of transitions and their field dependence follow quantitatively the relation expected for 3D massless Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ZrTe(5) is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitting of the Landau levels provides direct, bulk spectroscopic evidence that a relatively weak magnetic field can produce a sizable Zeeman effect on the 3D Dirac fermions, which lifts the spin degeneracy of Landau levels. Our analysis indicates that the compound evolves from a Dirac semimetal into a topological line-node semimetal under the current magnetic field configuration.
McKenna, Frederick W; Ahmad, Salahuddin
2011-04-01
The linear quadratic is the standard model for calculating isoeffects in the range of conventional dose per fraction. However, the use of hypofractionation and stereotactic body radiation therapy can call for isoeffect calculations for large doses per fraction. The purpose of this work is to investigate the linear quadratic at large doses per fraction. The linear quadratic is compared to models that incorporate effects such as dose protraction, whose purpose is to extend the useful range of the linear quadratic to larger doses. The linear quadratic and extended linear quadratic models are fit to 4 data sets. The model-predicted isoeffects for these data sets are calculated. It is found that the linear quadratic and extended linear quadratic predict different isoeffect curves for certain data sets. However, for these data sets, by appropriate selection of a α/β ratio, the linear quadratic can well approximate the extended linear quadratic models. In particular, it is found that a α/β ratio of 0.5 well approximates the extended linear quadratic isoeffect curve for 2 prostate cell lines for conventional and moderate doses per fraction.
Directory of Open Access Journals (Sweden)
Frederick W McKenna
2011-01-01
Full Text Available The linear quadratic is the standard model for calculating isoeffects in the range of conventional dose per fraction. However, the use of hypofractionation and stereotactic body radiation therapy can call for isoeffect calculations for large doses per fraction. The purpose of this work is to investigate the linear quadratic at large doses per fraction. The linear quadratic is compared to models that incorporate effects such as dose protraction, whose purpose is to extend the useful range of the linear quadratic to larger doses. The linear quadratic and extended linear quadratic models are fit to 4 data sets. The model-predicted isoeffects for these data sets are calculated. It is found that the linear quadratic and extended linear quadratic predict different isoeffect curves for certain data sets. However, for these data sets, by appropriate selection of a α/β ratio, the linear quadratic can well approximate the extended linear quadratic models. In particular, it is found that a α/β ratio of 0.5 well approximates the extended linear quadratic isoeffect curve for 2 prostate cell lines for conventional and moderate doses per fraction.
Quadratic forms representing all odd positive integers
Rouse, Jeremy
2011-01-01
We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove that an arbitrary, positive-definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451. This result is analogous to Bhargava and Hanke's celebrated 290-theorem. In addition, we prove that these three remaining ternaries represent all positive odd integers, assuming the generalized Riemann hypothesis. This result is made possible by a new analytic method for bounding the cusp constants of integer-valued quaternary quadratic forms $Q$ with fundamental discriminant. This method is based on the analytic properties of Rankin-Selberg $L$-functions, and we use it to prove...
Optimal Approximation of Quadratic Interval Functions
Koshelev, Misha; Taillibert, Patrick
1997-01-01
Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.
Restart-Based Genetic Algorithm for the Quadratic Assignment Problem
Misevicius, Alfonsas
The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.
Neural network for solving convex quadratic bilevel programming problems.
He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie
2014-03-01
In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.
Quadratic models of AC-DC power flow and optimal reactive power flow with HVDC and UPFC controls
Energy Technology Data Exchange (ETDEWEB)
Yu, Juan; Yan, Wei; Wen, Lili [The Key Laboratory of High Voltage Engineering and Electrical New Technology, Ministry of Education, Electrical Engineering College of Chongqing University, Chongqing 400030 (China); Li, Wenyuan [British Columbia Transmission Corporation (BCTC), Suite 1100, Four Bentall Center, 1055 Dunsmuir Street, P.O. Box 49260, Vancouver, BC (Canada)
2008-03-15
Quadratic models of power flow (PF) and optimal reactive power flow (ORPF) for AC-DC power systems are proposed in the paper. Voltage magnitudes at the two sides of ideal converter transformers are used as additional state variables to build the quadratic models. Effects of converter controls on equality constraints are considered. The quadratic expression of unified power flow controller (UPFC) is also developed and incorporated into the proposed models. The proposed PF model retaining nonlinearity has a better convergence feature and requires less CPU time compared to traditional PF models. The Hessian matrices in the quadratic AC-DC ORPF model are constant and need to be calculated only once in the entire optimization process, which speeds up the calculation greatly. Results obtained from the four IEEE test systems and an actual utility system indicate that the proposed quadratic models achieve a superior performance than conventional models. (author)
Hansen, Mikkel Bo; Christiansen, Ove; Hättig, Christof
2009-10-21
Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H(2)O, CH(2)O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented.
Research and application of air mercury measurement based on transverse Zeeman background correction
Zhang, Yong; Si, Fuqi; Zeng, Yi; Li, Chuangxin; Liu, Wenqing
2016-10-01
Mercury is known as a highly toxic metal, which will have a significant health hazard to the human body. To monitor the trace mercury pollution in air, the development of monitoring instruments has been conducted. In this paper the mercury analyzer is developed based on the cold atomic absorption spectrometry theory by exploiting the transverse Zeeman-Effect background correction technology. The experiments have been done to test the performance of the system. At the same time, the same experiments with RA-915 mercury analyzer have been done to compare with the results. First, zero gas was measured for an hour and high concentration mercury sample gas was measured for four days. The results of zero gas shows that the detection limit of the system is 2.19ng/m3 and the standard deviation is 0.73. The concentration fluctuation is within a tight range of +/-1.5ng/m3. The results of high concentration sample gas are in good agreement with the results of RA-915, and the correlation coefficient is 0.95. Second, laboratory air was measured for 12 hours. The results compared with RA-915 are in good agreement and have the same variation trend. Additionally, the atmospheric mercury concentration near the non-ferrous metal smelter in Tongling city has been measured by the system and the RA-915. The measurement results from two analyzers have a good linear correlation with correlation coefficient of 0.98 and slope of 1.027. It indicates that the system has accurate background correction ability, low detection limit and is applicable to long-term air mercury on-line monitoring.
Zeeman-Doppler imaging of active young solar-type stars
Hackman, T.; Lehtinen, J.; Rosén, L.; Kochukhov, O.; Käpylä, M. J.
2016-03-01
Context. By studying young magnetically active late-type stars, i.e. analogues to the young Sun, we can draw conclusions on the evolution of the solar dynamo. Aims: We determine the topology of the surface magnetic field and study the relation between the magnetic field and cool photospheric spots in three young late-type stars. Methods: High-resolution spectropolarimetry of the targets was obtained with the HARPSpol instrument mounted at the ESO 3.6 m telescope. The signal-to-noise ratios of the Stokes IV measurements were boosted by combining the signal from a large number of spectroscopic absorption lines through the least squares deconvolution technique. Surface brightness and magnetic field maps were calculated using the Zeeman-Doppler imaging technique. Results: All three targets show clear signs of magnetic fields and cool spots. Only one of the targets, V1358 Ori, shows evidence of the dominance of non-axisymmetric modes. In two of the targets, the poloidal field is significantly stronger than the toroidal one, indicative of an α2-type dynamo, in which convective turbulence effects dominate over the weak differential rotation. In two of the cases there is a slight anti-correlation between the cool spots and the strength of the radial magnetic field. However, even in these cases the correlation is much weaker than in the case of sunspots. Conclusions: The weak correlation between the measured radial magnetic field and cool spots may indicate a more complex magnetic field structure in the spots or spot groups involving mixed magnetic polarities. Comparison with a previously published magnetic field map shows that on one of the stars, HD 29615, the underlying magnetic field changed its polarity between 2009 and 2013. Based on observations made with the HARPSpol instrument on the ESO 3.6 m telescope at La Silla (Chile), under the program ID 091.D-0836.
Vestibular integrator neurons have quadratic functions due to voltage dependent conductances.
Magnani, Christophe; Eugène, Daniel; Idoux, Erwin; Moore, Lee E
2013-12-01
The nonlinear properties of the dendrites of the prepositus hypoglossi nucleus (PHN) neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel system of frequency probing, namely quadratic sinusoidal analysis (QSA), was used to decode the intrinsic nonlinear behavior of these neurons under voltage clamp conditions. Voltage clamp currents were measured at harmonic and interactive frequencies using specific nonoverlapping stimulation frequencies. Eigenanalysis of the QSA matrix reduces it to a remarkably compact processing unit, composed of just one or two dominant components (eigenvalues). The QSA matrix of rat PHN neurons provides signatures of the voltage dependent conductances for their particular dendritic and somatic distributions. An important part of the nonlinear response is due to the persistent sodium conductance (gNaP), which is likely to be essential for sustained effects needed for a neural integrator. It was found that responses in the range of 10 mV peak to peak could be well described by quadratic nonlinearities suggesting that effects of higher degree nonlinearities would add only marginal improvement. Therefore, the quadratic response is likely to sufficiently capture most of the nonlinear behavior of neuronal systems except for extremely large synaptic inputs. Thus, neurons have two distinct linear and quadratic functions, which shows that piecewise linear + quadratic analysis is much more complete than just piecewise linear analysis; in addition quadratic analysis can be done at a single holding potential. Furthermore, the nonlinear neuronal responses contain more frequencies over a wider frequency band than the input signal. As a consequence, they convert limited amplitude and bandwidth input signals to wider bandwidth and more complex output responses. Finally, simulations at subthreshold membrane potentials with realistic PHN neuron models
Constrained neural approaches to quadratic assignment problems.
Ishii, S; Sato, M
1998-08-01
In this paper, we discuss analog neural approaches to the quadratic assignment problem (QAP). These approaches employ a hard constraints scheme to restrict the domain space, and are able to obtain much improved solutions over conventional neural approaches. Since only a few strong heuristics for QAP have been known to date, our approaches are good alternatives, capable of obtaining fairly good solutions in a short period of time. Some of them can also be applied to large-scale problems, say of size N>/=300.
Automatic differentiation for reduced sequential quadratic programming
Institute of Scientific and Technical Information of China (English)
Liao Liangcai; Li Jin; Tan Yuejin
2007-01-01
In order to slove the large-scale nonlinear programming (NLP) problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming (rSQP) and automatic differentiation (AD) is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.
Linear Stability Analysis of Dynamical Quadratic Gravity
Ayzenberg, Dimitry; Yunes, Nicolas
2013-01-01
We perform a linear stability analysis of dynamical, quadratic gravity in the high-frequency, geometric optics approximation. This analysis is based on a study of gravitational and scalar modes propagating on spherically-symmetric and axially-symmetric, vacuum solutions of the theory. We find dispersion relations that do no lead to exponential growth of the propagating modes, suggesting the theory is linearly stable on these backgrounds. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
In this paper, we propose using realized range-based estimation to draw inference about the quadratic variation of jump-diffusion processes. We also construct a new test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the te...... is well-sized and more powerful than a return-based t-statistic for sampling frequencies normally used in empirical work. Applied to equity data, we find that the intensity of the jump process is not as high as previously reported....
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the ......, the test is well-sized and more powerful than a return-based t-statistic for sampling frequencies normally used in empirical work. Applied to equity data, we show that the intensity of the jump process is not as high as previously reported....
Quadratic forms for Feynman-Kac semigroups
Energy Technology Data Exchange (ETDEWEB)
Hibey, Joseph L. [Department of Electrical Engineering, University of Colorado at Denver, Campus Box 110, Denver, CO 80217 (United States)]. E-mail: joseph.hibey@cudenver.edu; Charalambous, Charalambos D. [Electrical and Computer Engineering Department, University of Cyprus, 75 Kallipoleos Avenue, Nicosia (Cyprus)]. E-mail: chadcha@ucy.ac.cy
2006-05-15
Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions.
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2004-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...
Zeeman-Field-Tuned Topological Phase Transitions in a Two-Dimensional Class-DIII Superconductor.
Deng, W Y; Geng, H; Luo, W; Sheng, L; Xing, D Y
2016-01-01
We investigate the topological phase transitions in a two-dimensional time-reversal invariant topological superconductor in the presence of a Zeeman field. Based on the spin Chern number theory, we find that the system exhibits a number of topologically distinct phases with changing the out-of-plane component of the Zeeman field, including a quantum spin Hall-like phase, quantum anomalous Hall-like phases with total Chern number C = -2, -1, 1 and 2, and a topologically trivial superconductor phase. The BdG band gap closes at each boundary of the phase transitions. Furthermore, we demonstrate that the zero bias conductance provides clear transport signatures of the different topological phases, which are robust against symmetry-breaking perturbations.
Zeeman nuclear quadrupole resonance study of a germanium tetrachloride single crystal
Sengupta, S.; Litzistorf, G.; Lucken, E. A. C.
Zeeman studies of a single crystal of GeCl 4 have been carried out on a previously described pulsed FT NQR spectrometer. The technique for growing single crystals from liquid samples is described. The Zeeman-split spectrum for each of the resonances at μ1 = 25.4493, μ2 = 25.7133, μ3 = 25.7354, and μ4 = 25.7457 MHz reveals four quadruplets. The asymmetry parameters found lie in two groups of average values η = 0.035 and η = 0.078, much lower than the previously reported value of η = 0.35 obtained from a polycrystalline sample. The crystal of GeCl 4 is found to be orthorhombic with mmm or D2 h symmetry. From the directions of the field gradient axes the interbond angles have been calculated and show that the GeCl 4 molecule is a slightly distorted tetrahedron.
Raman sideband cooling of a 138Ba+ ion using a Zeeman interval
Seck, Christopher M; Dietrich, Matthew R; Odom, Brian C
2016-01-01
Motional ground state cooling and internal state preparation are important elements for quantum logic spectroscopy (QLS), a class of quantum information processing. Since QLS does not require the high gate fidelities usually associated with quantum computation and quantum simulation, it is possible to make simplifying choices in ion species and quantum protocols at the expense of some fidelity. Here, we report sideband cooling and motional state detection protocols for $^{138}$Ba$^+$ of sufficient fidelity for QLS without an extremely narrowband laser or the use of a species with hyperfine structure. We use the two S$_{1/2}$ Zeeman sublevels of $^{138}$Ba$^+$ to Raman sideband cool a single ion to the motional ground state. Because of the small Zeeman splitting, near-resonant Raman sideband cooling of $^{138}$Ba$^+$ requires only the Doppler cooling lasers and two additional AOMs. Observing the near-resonant Raman optical pumping fluorescence, we estimate a final average motional quantum number $\\bar{n}\\appro...
Directory of Open Access Journals (Sweden)
Yong Li
2014-01-01
Full Text Available The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.
Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu
2014-01-27
The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.
Electroweak vacuum stability and finite quadratic radiative corrections
Energy Technology Data Exchange (ETDEWEB)
Masina, Isabella [Ferrara Univ. (Italy). Dipt. di Fisica e Scienze della Terra; INFN, Sezione di Ferrara (Italy); Southern Denmark Univ., Odense (Denmark). CP3-Origins; Southern Denmark Univ., Odense (Denmark). DIAS; Nardini, Germano [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Quiros, Mariano [Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); IFAE-IAB, Barcelona (Spain)
2015-07-15
If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff Λ{sub i}. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λ{sub i}, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.
STRUCTURE OPTIMIZATION OF RESERVATION BY PRECISE QUADRATIC REGULARIZATION
Directory of Open Access Journals (Sweden)
KOSOLAP A. I.
2015-11-01
Full Text Available The problem of optimization of the structure of systems redundancy elements. Such problems arise in the design of complex systems. To improve the reliability of operation of such systems of its elements are duplicated. This increases system cost and improves its reliability. When optimizing these systems is maximized probability of failure of the entire system while limiting its cost or the cost is minimized for a given probability of failure-free operation. A mathematical model of the problem is a discrete backup multiextremal. To search for the global extremum of currently used methods of Lagrange multipliers, coordinate descent, dynamic programming, random search. These methods guarantee a just and local solutions are used in the backup tasks of small dimension. In the work for solving redundancy uses a new method for accurate quadratic regularization. This method allows you to convert the original discrete problem to the maximization of multi vector norm on a convex set. This means that the diversity of the tasks given to the problem of redundancy maximize vector norm on a convex set. To solve the problem, a reformed straightdual interior point methods. Currently, it is the best method for local optimization of nonlinear problems. Transformed the task includes a new auxiliary variable, which is determined by dichotomy. There have been numerous comparative numerical experiments in problems with the number of redundant subsystems to one hundred. These experiments confirm the effectiveness of the method of precise quadratic regularization for solving problems of redundancy.
Electroweak vacuum stability and finite quadratic radiative corrections
Masina, Isabella; Nardini, Germano; Quiros, Mariano
2015-08-01
If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales, the cutoff is not unique and each SM sector has its own UV cutoff Λi. We have performed this calculation assuming the minimal supersymmetric standard model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λi, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the focus point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.
The Nonlinear Analytical Envelope Equation in quadratic nonlinear crystals
Bache, Morten
2016-01-01
We here derive the so-called Nonlinear Analytical Envelope Equation (NAEE) inspired by the work of Conforti et al. [M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, "Interaction between optical fields and their conjugates in nonlinear media," Opt. Express 21, 31239-31252 (2013)], whose notation we follow. We present a complete model that includes $\\chi^{(2)}$ terms [M. Conforti, F. Baronio, and C. De Angelis, "Nonlinear envelope equation for broadband optical pulses in quadratic media," Phys. Rev. A 81, 053841 (2010)], $\\chi^{(3)}$ terms, and then extend the model to delayed Raman effects in the $\\chi^{(3)}$ term. We therefore get a complete model for ultrafast pulse propagation in quadratic nonlinear crystals similar to the Nonlinear Wave Equation in Frequency domain [H. Guo, X. Zeng, B. Zhou, and M. Bache, "Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media," J. Opt. Soc. Am. B 30, 494-504 (2013)], but where the envelope is...
On a general class of quadratic hopping sequences
Institute of Scientific and Technical Information of China (English)
JIA HuaDing; YUAN Ding; PENG DaiYuan; GUO Ling
2008-01-01
Based upon quadratic polynomials over the finite field, a new class of frequency hopping sequences with large family size suitable for applications in time/frequency hopping CDMA systems, multi-user radar and sonar systems is proposed and investigated. It is shown that the new time/frequency hopping sequences have at most one hit in their autocorrelation functions and at most two hits in their crosscorrelation functions except for a special case, and their family size is much larger than the conventional quadratic hopping sequences. The percentage of full collisions for the new quadratic hopping sequences is discussed. In addition, the average number of hits for the new quadratic hopping sequences, quadratic congruence sequences, extended quadratic congruence sequences and the general linear hopping sequences are also derived.
Quadratic residues and non-residues selected topics
Wright, Steve
2016-01-01
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
Zeeman and orbital limiting magnetic fields in cuprates: The pseudogap connection
Indian Academy of Sciences (India)
Lia Krusin-Elbaum; Takasada Shibauchi; Gianni Blatter
2006-01-01
In cuprates, in a view where pairing correlations set in at the pseudogap energy scale * and acquire global coherence at a lower temperature c, the region c ≤ ≤ * is a vast fluctuation regime. c and * vary differently with doping and the question remains about the doping trends of the relevant magnetic field scales: the field c2 bounding the superconducting response and the pseudogap closing field pg. In-plane thermal (Nernst) and our interlayer (tunneling) transport experiments in Bi2Sr2CaCu2O8+ report hugely different limiting magnetic fields. Here, based on pairing (and the uncertainty principle) combined with the definitions of the Zeeman energy and the magnetic length, we show that both fields convert to the same pseudogap scale * upon transformation as orbital and Zeeman critical fields, respectively. The region of superconducting coherence is confined to the `dome' that coincides with the usual unique upper critical field c2 on the strongly overdoped side. We argue that the distinctly different orbital and the Zeeman limiting fields can co-exist owing to charge and spin degrees of freedom separated to different parts of the strongly anisotropic Fermi surface.
On Quadratic BSDEs with Final Condition in L2
Yang, Hanlin
2015-01-01
This thesis consists of three parts. In the first part, we study $\\mathbb{L}^p$ solutions of a large class of BSDEs. Existence, comparison theorem, uniqueness and a stability result are proved. In the second part, we establish the solvability of quadratic semimartingale BSDEs. In contrast to current literature, we use Lipschitz-quadratic regularization and obtain the existence and uniqueness results with minimal assumptions. The third part is a brief summary of quadratic semimartingales and t...
Quadratic forms and Clifford algebras on derived stacks
Vezzosi, Gabriele
2013-01-01
In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We define the associated notion of derived Clifford algebra, in all these contexts, and compare it with its classical version, when they both apply. Finally, we prove three main existence results for derived shifted quadratic forms over derived stacks, define ...
Robust Solutions of Uncertain Complex-valued Quadratically Constrained Programs
Institute of Scientific and Technical Information of China (English)
Da Chuan XU; Zheng Hai HUANG
2008-01-01
In this paper,we discuss complex convex quadratically constrained optimization with uncertain data.Using S-Lemma,we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program.By exploring the approximate S-Lemma,we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set.
Some Aspects of Quadratic Generalized White Noise Functionals
Si, Si; Hida, Takeyuki
2009-02-01
We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.
Quadratic dynamical decoupling with nonuniform error suppression
Energy Technology Data Exchange (ETDEWEB)
Quiroz, Gregory; Lidar, Daniel A. [Department of Physics and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States); Departments of Electrical Engineering, Chemistry, and Physics, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States)
2011-10-15
We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.
The Quadratic Selective Travelling Salesman Problem
DEFF Research Database (Denmark)
Thomadsen, Tommy; Stidsen, Thomas K.
2003-01-01
complication that each pair of nodes have an associated profit which can be gained only if both nodes are visited. The QSTSP is a subproblem when constructing hierarchical ring networks. We describe an integer linear programming model for the QSTSP. The QSTSP is solved by two construction heuristics...... solutions at a cost of much higher running time. All problems with up to 50 nodes are solved within one hour.......A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...
Compact stars with quadratic equation of state
Ngubelanga, Sifiso A; Ray, Subharthi
2015-01-01
We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.
Directed animals, quadratic and rewriting systems
Marckert, Jean-François
2011-01-01
A directed animal is a percolation cluster in the directed site percolation model. The aim of this paper is to exhibit a strong relation between in one hand, the problem of computing the generating function $\\G$ of directed animals on the square lattice, counted according to the area and the perimeter, and on the other hand, the problem to find a solution to a system of quadratic equations involving unknown matrices. The matrices solution of this problem can be finite or infinite. We were unable to find finite solutions. We present some solid clues that some infinite explicit matrices, fix points of a rewriting like system are the natural solutions of this system of equations: some strong evidences are given that the problem of finding $\\G$ reduces then to the problem of finding an eigenvector to an explicit infinite matrix. Similar properties are shown for other combinatorial questions concerning directed animals, and for different lattices.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...
A SPLITTING METHOD FOR QUADRATIC PROGRAMMING PROBLEM
Institute of Scientific and Technical Information of China (English)
魏紫銮
2001-01-01
A matrix splitting method is presented for minimizing a quadratic programming (QP)problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
Linear ultrasonic motor using quadrate plate transducer
Institute of Scientific and Technical Information of China (English)
Jiamei JIN; Chunsheng ZHAO
2009-01-01
A linear ultrasonic motor using a quadrate plate transducer was developed for precision positioning. This motor consists of two pairs of Pb(Zr, Ti)O3 piezo-electric ceramic elements, which are piezoelectrically excited into the second-bending mode of the motor stator's neutral surface in two orthogonal directions, on which the tops of four projections move along an elliptical trajectory, which in turn drives a contacted slider into linear motion via frictional forces. The coincident frequency of the stator is easily obtained for its coincident characteristic dimen-sion in two orthogonal directions. The performance characteristics achieved by the motor are: 1) a maximum linear speed of more than 60 mm/s; 2) a stroke of more than 150 mm; 3) a driving force of more than 5.0 N; and 4) a response time of about 2 ms.
Large-scale sequential quadratic programming algorithms
Energy Technology Data Exchange (ETDEWEB)
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
A smoothing Newton method for a type of inverse semi-definite quadratic programming problem
Xiao, Xiantao; Zhang, Liwei; Zhang, Jianzhong
2009-01-01
We consider an inverse problem arising from the semi-definite quadratic programming (SDQP) problem. We represent this problem as a cone-constrained minimization problem and its dual (denoted ISDQD) is a semismoothly differentiable (SC1) convex programming problem with fewer variables than the original one. The Karush-Kuhn-Tucker conditions of the dual problem (ISDQD) can be formulated as a system of semismooth equations which involves the projection onto the cone of positive semi-definite matrices. A smoothing Newton method is given for getting a Karush-Kuhn-Tucker point of ISDQD. The proposed method needs to compute the directional derivative of the smoothing projector at the corresponding point and to solve one linear system per iteration. The quadratic convergence of the smoothing Newton method is proved under a suitable condition. Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this type of inverse quadratic programming problems.
Maraner, P.
2016-07-01
It is argued that the 'quadratic Sagnac effect' recently put forward by G B Malykin and V I Pozdnyakova is the consequence of an incorrect estimation of second-order relativistic corrections and not a real physical phenomenon. The correct expression for the phase shift induced by rotations in a Michelson interferometer is presented.
Bai, Zheng-Jian; Yang, Jin-Ku; Datta, Biswa Nath
2016-12-01
In this paper, we consider the robust partial quadratic eigenvalue assignment problem in vibration by active feedback control. Based on the receptance measurements and the system matrices, we propose an optimization method for the robust and minimum norm partial quadratic eigenvalue assignment problem. We provide a new cost function and the closed-loop eigenvalue sensitivity and the feedback norms can be minimized simultaneously. Our method is also extended to the case of time delay between measurements of state and actuation of control. Numerical tests demonstrate the effectiveness of our method.
Institute of Scientific and Technical Information of China (English)
钟伟民; 何国龙; 皮道映; 孙优贤
2005-01-01
A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.
Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps
Directory of Open Access Journals (Sweden)
Minsong Zhang
2014-01-01
Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.
New Heuristic Rounding Approaches to the Quadratic Assignment Problem
Gharibi, Wajeb
2011-01-01
Quadratic assignment problem is one of the great challenges in combinatorial optimization. It has many applications in Operations research and Computer Science. In this paper, the author extends the most-used rounding approach to a one-parametric optimization model for the quadratic assignment problems. A near-optimum parameter is also predestinated. The numerical experiments confirm the efficiency.
Binary GCD like Algorithms for Some Complex Quadratic Rings
DEFF Research Database (Denmark)
Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg
2004-01-01
binary gcd like algorithms for the ring of integers in and , one now has binary gcd like algorithms for all complex quadratic Euclidean domains. The running time of our algorithms is O(n 2) in each ring. While there exists an O(n 2) algorithm for computing the gcd in quadratic number rings by Erich...
Geometric quadratic stochastic operator on countable infinite set
Energy Technology Data Exchange (ETDEWEB)
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar [Department of Computational and Theoretical Sciences, Kulliyyah of Science, International Islamic University, Jalan Sultan Ahmad Shah, Bandar InderaMahkota, 25200 Kuantan, Pahang (Malaysia)
2015-02-03
In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.
Quadratic Twists of Rigid Calabi–Yau Threefolds Over
DEFF Research Database (Denmark)
Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko
2013-01-01
We consider rigid Calabi–Yau threefolds defined over Q and the question of whether they admit quadratic twists. We give a precise geometric definition of the notion of a quadratic twists in this setting. Every rigid Calabi–Yau threefold over Q is modular so there is attached to it a certain newfo...
Immunizing Conic Quadratic Optimization Problems Against Implementation Errors
Ben-Tal, A.; den Hertog, D.
2011-01-01
We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonali
A Constructive Transition from Linear to Quadratic Functions.
Movshovitz-Hadar, Nitsa
1993-01-01
Presents an approach to quadratic functions that draws upon knowledge of linear functions by looking at the product of two linear functions. Then considers the quadratic function as the sum of three monomials. Potential advantages of each approach are discussed. (Contains 17 references.) (MDH)
Approximate *-derivations and approximate quadratic *-derivations on C*-algebras
Directory of Open Access Journals (Sweden)
Park Choonkil
2011-01-01
Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.
AdS Waves as Exact Solutions to Quadratic Gravity
Gullu, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram
2011-01-01
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity.
A combined strategy for solving quadratic assignment problem
Ahyaningsih, Faiz
2017-08-01
The quadratic assignment problem is a combinatorial problem of deciding the placement of facilities in specified locations in such a way as to minimize a nonconvex objective function expressed in terms of flow between facilities, and distance between location. Due to the non-convexity nature of the problem, therefore to get a `good' starting point is necessary in order to obtain a better optimal solution. In this paper we propose a combined strategy (random point strategy to get initial starting point and then use forward exchange strategy and backward exchange strategy to get `optimal' solution). As a computational experience we've solved the problem of Esc 16b, Esc 16c and Esc 16h from QAPLIB. Finally, we present a comparative study between Combined Strategy and Data -Guided Lexisearch Algorithm. The computational study shows the effectiveness of our proposed combined strategy.
Qualitative analysis of certain generalized classes of quadratic oscillator systems
Energy Technology Data Exchange (ETDEWEB)
Bagchi, Bijan, E-mail: bbagchi123@gmail.com; Ghosh, Samiran, E-mail: sran-g@yahoo.com; Pal, Barnali, E-mail: barrna.roo@gmail.com; Poria, Swarup, E-mail: swarupporia@gmail.com [Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009 (India)
2016-02-15
We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56, 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ, the other points to a centre for λ < 0 but a saddle λ > 0. On the other hand, the second potential reveals only a center for both the signs of λ from a linear stability analysis. We carry out our study by extending Quesne’s scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term fcosωt.
Repopulation Kinetics and the Linear-Quadratic Model
O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.
2009-08-01
The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.
Threshold Signature Scheme Based on Discrete Logarithm and Quadratic Residue
Institute of Scientific and Technical Information of China (English)
FEI Ru-chun; WANG Li-na
2004-01-01
Digital signature scheme is a very important research field in computer security and modern cryptography.A(k,n) threshold digital signature scheme is proposed by integrating digital signature scheme with Shamir secret sharing scheme.It can realize group-oriented digital signature, and its security is based on the difficulty in computing discrete logarithm and quadratic residue on some special conditions.In this scheme, effective digital signature can not be generated by any k-1 or fewer legal users, or only by signature executive.In addition, this scheme can identify any legal user who presents incorrect partial digital signature to disrupt correct signature, or any illegal user who forges digital signature.A method of extending this scheme to an Abelian group such as elliptical curve group is also discussed.The extended scheme can provide rapider computing speed and stronger security in the case of using shorter key.
Few-cycle nonlinear mid-IR pulse generated with cascaded quadratic nonlinearities
DEFF Research Database (Denmark)
Bache, Morten; Liu, Xing; Zhou, Binbin
change Δn = ncascI, where ncase ∝ −d2eff/Δk, and deff is the effective quadratic nonlinearity. Due to competing material nonlinearities nKerr the total nonlinear refractive is ncubic = ncasc + nKerr. Interestingly ncubic can become negative (self-defocusing), elegantly avoiding self-focusing problems...
QUADRATIC ADMISSIBLE ESTIMATE OF COVARIANCE IN PSEUDO-ELLIPTICAL CONTOURED DISTRIBUTION
Institute of Scientific and Technical Information of China (English)
Hengjian CUI; Xiuhong GAO
2006-01-01
This article mainly discusses the admissibility of quadratic estimate of covariance in pseudoelliptical distribution. Under the quadratic loss function, the necessary and sufficient conditions that a quadratic estimator is an admissible estimator of covariance in the class of quadratic estimators are obtained. A complete class of the quadratic estimator class is also given.
Directory of Open Access Journals (Sweden)
Rocío Meza-Moreno
2015-01-01
Full Text Available Let p=4k+1 be a prime number and Fp the finite field with p elements. For x∈1,n, Nx will denote the set of quadratic nonresidues less than or equal to x. In this work we calculate the number of quadratic nonresidues in the shifted set N(p-1/2+a.
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
A Quadratic Closure for Compressible Turbulence
Energy Technology Data Exchange (ETDEWEB)
Futterman, J A
2008-09-16
We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.
Optimal power flow using sequential quadratic programming
Nejdawi, Imad M.
1999-11-01
Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.
Energy Technology Data Exchange (ETDEWEB)
Hey, J.D.; Chu, C.C. [Plasma Physics Research Institute, University of Natal, Durban (South Africa)]. E-mails: hey@nu.ac.za; chu@nu.ac.za; Brezinsek, S.; Unterberg, B.; Mertens, Ph. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Juelich (Germany)]. E-mail: ph.mertens@fz-juelich.de
2002-03-28
Oxygen ion impurity radiation is a potential source of inaccuracy in ion temperature determination with the aid of the commonly used C VI transition n=8{yields}n'=7, produced by charge-exchange recombination (CXR) of C{sup 6+} ions, since the corresponding transition in O VI cannot be resolved under typical plasma conditions in the tokamak. In order to demonstrate the possible importance of oxygen ion impurity radiation, we have selected a convenient spectroscopic 'window' (about 8 A wide) containing the major Zeeman components of two prominent lines in the visible (multiplet 1), one emitted by C{sup 2+} and one by O{sup +}. Observations have been performed in this wavelength range, both tangentially and perpendicularly to the magnetic flux surfaces, in the second case with the aid of a special graphite test limiter. Measurements include the case of special plasma discharges in which oxygen gas was introduced from the test limiter. The temperatures of both species are evaluated from the Doppler broadening of the respective Zeeman components, and compared with the results from a model for collisional heating by impact with hot protons (deuterons) in the plasma edge. The spectra and derived results show that impurity identification in tokamak edge plasmas should not be carried out with the aid of spectral lines from highly excited levels populated by CXR, but using lines corresponding to much more species-specific transitions from lower ionization stages. The identification and quantitative analysis should be performed with the aid of carefully measured and calculated Zeeman-(Paschen-Back-) broadened line profiles, since these have features practically unique to the species under investigation. Some allowance may, however, be required for deviation, from a statistical distribution, of population among fine-structure sublevels. (author)
The potential characteristics analysis of probing signal with the quadratic frequency modulation
Directory of Open Access Journals (Sweden)
O. D. Mrachkovsky
2012-12-01
Full Text Available Introduction: Complex signals with the button ambiguity function can provide the distance and speed of target independent estimation. The signal with the symmetrical linear frequency modulation has this property in the class of signal with frequency modulation. Problem statement: To show that in the class of signals frequency-shift is signal with button ambiguity function. Such signal is a signal with the quadratic frequency intra-modulation. The potential characteristics research of signal with the quadratic frequency intra-modulation: The signal with quadratic frequency modulation and its properties are considered, analytic form of signal and its spectrum are shown, figures of amplitude spectra of signal are drawn, and figures of ambiguity diagram, cross-correlation functions and response ambiguity function in strong and weak fields are shown. The comparison of the signal with the quadratic frequency intra-modulation and the signal with the symmetrical linear frequency modulation are shown. The result of research is that the ambiguity function form of a signal with the quadratic frequency intra-modulation comes nearer to button in the strong correlation field and it has X – for min the weak correlation field. The autocorrelation function of the signal with the quadratic frequency intra-modulation has some constant level which decreases with signal base increasing. It is revealed that autocorrelation function of the signal has no side lobes. It improves resolution capability of a weak signal against the strong signal. The pedestal level of the autocorrelation function of this signal is a little lower than pedestal level of the autocorrelation function of the signal with the symmetrical linear frequency modulation. Properties of section of cross-correlation function to two peaks and effect of these properties are considered. Signals with the quadratic frequency intra-modulation are expedient for using in the sonar of submarines, because in
Energy Technology Data Exchange (ETDEWEB)
Kuramoto, H.; Hiraki, N. [Kyushu Inst. of Tech., Kitakyushu, Fukuoka (Japan); Toi, K. [and others
1997-01-01
The toroidal current penetration is studied in current ramp experiments of the JIPP T-IIU tokamak. The poloidal magnetic field profile in the peripheral region of a plasma (0.5 {<=} {rho} {<=} 1.0) has been measured directly with a newly developed fast response Zeeman polarimeter. The experimental results indicate that an obvious skin effect of toroidal current density is clearly observed during both the current ramp-up and ramp-down experiments. The experimentally obtained toroidal current density profiles are well described by the profiles calculated on the assumption of the neoclassical electrical conductivity. Quasi-linear {Delta}`-analysis of tearing modes for the measured current density profile is consistent with time behaviour of coherent MHD modes such as m=4/n=1 or m=3/n=1 (m: poloidal mode number, n: toroidal mode number) often observed during the current ramp-up phase. The effect of these MHD modes on current penetration during the current ramp-up discharges is studied. (author)
Dynamically configurable and optimizable Zeeman slower using permanent magnets and servomotors
Reinaudi, G; Bega, K; Zelevinsky, T
2011-01-01
We report on the implementation of a dynamically configurable, servomotor-controlled, permanent magnet Zeeman slower for quantum optics experiments with ultracold atoms and molecules. This atom slower allows for switching between magnetic field profiles that are designed for different atomic species. Additionally, through feedback on the atom trapping rate, we demonstrate that computer-controlled genetic optimization algorithms applied to the magnet positions yield traps several times larger than those obtained with the calculated design field, hence accounting for experimental circumstances not present in the design model. The device is lightweight, remotely controlled, and consumes no power in steady state.
Investigation of different magnetic field configurations using an electrical, modular Zeeman slower
Energy Technology Data Exchange (ETDEWEB)
Ohayon, Ben; Ron, Guy, E-mail: gron@racah.phys.huji.ac.il [Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2015-10-15
We present a method of constructing an automatically reconfigurable, modular, electronic Zeeman slower, which is remotely controlled. This setup is used to investigate the ability of different magnetic field profiles to slow thermal atoms to the capture velocity of a magneto-optical-trap. We show that a simple numerical optimization process yields better results than the commonly used approach for deciding on the appropriate field and comes close to the optimum field, found by utilizing a fast feedback loop which uses a genetic algorithm. Our new numerical method is easily adaptable to a variety of existing slower designs and may be beneficial where feedback is unavailable.
New diagnostic technique for Zeeman-compensated atomic beam slowing: technique and results
Molenaar, P.A.; Van Der Straten, P.; Heideman, H.G.M.; Metcalf, H
2001-01-01
We have developed a new diagnostic tool for the study of Zeeman-compensated slowing of an alkali atomic beam. Our time-of-flight technique measures the longitudinal veloc- ity distribution of the slowed atoms with a resolution below the Doppler limit of 30 cm/s. Furthermore, it can map the position and velocity distribution of atoms in either ground hyperfine level inside the solenoid without any devices inside the solenoid. The technique reveals the optical pumping ef- fects, and shows in de...
Experimental realization of two-isotope collision-assisted Zeeman cooling
Hamilton, Mathew
The work presented in this thesis focuses on the demonstration and initial evaluation of a novel non-evaporative cooling method called collision-assisted Zeeman cooling. For this realization, an ultracold gas consisting of a mixture of 87Rb and 85Rb was used. Cooling was accomplished through interisotope inelastic spin-exchange collisions that converted kinetic energy into magnetic energy. Continual optical pumping spin polarized the 85Rb which ensured that only kinetic energy reducing collisions occurred and the scattered pump photons carried entropy out of the system. Thus, cooling of the ultracold gas can be achieved without requiring the loss of any atoms in order to do so. This represents a theoretical advantage over forced evaporative cooling, which is the current state-of-the-art cooling technique in most experiments. This thesis discusses the details of collision-assisted Zeeman cooling, as well as how the theory of the technique has been extended from cooling a single species to cooling with two species. There are many predicted advantages from using two rather than one species of atom in this type of cooling: greater flexibility in finding favorable spin-exchange collision rates, easier requirements on the magnetic fields that must be used, and an additional means to mitigate reabsorption (the primary limitation in many if not most non-evaporative cooling techniques). The experimental considerations needed to prepare a system that simultaneously trapped two isotopes to be able to perform collision-assisted Zeeman cooling are discussed. Because this cooling scheme is highly reliant on the initial conditions of the system, a focused experiment examining the loading of the optical trap with both isotopes of Rb was conducted and the results of that experiment are described here. The first experimental observations of spin-exchange collisions in an ultracold gas mixture of Rb are described as a part of this work. The experiments where collision-assisted Zeeman
On nondecomposable positive definite Hermitian forms over imaginary quadratic fields
Institute of Scientific and Technical Information of China (English)
ZHU; Fuzu
2001-01-01
［1］Mordell, L. J., The representation of a definite quadratic form as a sum of two others, Ann. of Math., 937, 38: 75.［2］Erds, P., Ko Chao, On definite quadratic forms, which are not the sum of two definite or semidefinite forms, Acta Arith., 939, 3: 02.［3］Erds, P., Ko Chao, Some results on definite quadratic forms, J. London Math. Soc., 938, 3: 27.［4］Zhu Fu-zu, Construction of nondecomposable positive definite quadratic forms, Sci. Sinica, Ser. A, 987, 30(): 9.［5］Zhu Fuzu, On nondecomposability and indecomposability of quadratic forms, Sci. Sinica, Ser. A, 988, 3(3): 265.［6］Pleskin, W., Additively indecomposable positive integral quadratic forms, J. Number Theory, 994, 47: 273.［7］Zhu Fuzu, An existence theorem on positive definite unimodular even Hermitian forms, Chinese Ann. of Math., Ser. A, 984, 5: 33.［8］Zhu Fu-Zu, On the construction of positive definite indecomposable unimodular even Hermitian forms, J. Number Theory, 995, 30: 38.［9］O'Meara, O. T., Introduction to Quadratic Forms, Berlin, New York: Springer-Verlag, 973.［10］Zhu Fuzu, Construction of indecomposable definite Hermitian forms, Chinese Ann. of Math., Ser. B, 994, 5: 349.［11］Zhu Fuzu, On nondecomposable Hermitian forms over Gaussian domain, Acta Math. Sinica, New Ser., 998, 4: 447.
Zeeman shift--a tool for assignment of 14N NQR lines of nonequivalent 14N atoms in powder samples.
Luznik, J; Jazbinsek, V; Pirnat, J; Seliger, J; Trontelj, Z
2011-09-01
The use of Zeeman perturbed 14N nuclear quadrupole resonance (NQR) to determine the ν+ and ν-14N lines in polycrystalline samples with several nonequivalent nitrogen atoms was investigated. The 14N NQR line shift due to a weak external Zeeman magnetic field was calculated, assuming isotropic distribution of EFG tensor directions. We calculated the broad line distribution of the ν+ and ν- line shifts and experimentally confirmed the calculated Zeeman field dependence of singularities (NQR peaks) in cyclotrimethylenetrinitramine (RDX) and aminotetrazole monohydrate (ATMH). The calculated and measured frequency shifts agreed well. The proposed measurement method enabled determination of which 14N NQR lines in ATMH belong to ν+ and which to ν- transitions.
The Cyclicity of the Period Annulus Around the Quadratic Isochronous Center
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The number of the limit cycles bifurcating in small quadratic perturbations of quadratic systems with an isochronous center is studied, it turns out that the cyclicity of the period annulus around one kind of quadratic isochronous center is two.
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems. The u....... The unique path generated by the minimizers of these problems yields the solution to the original problem for finite values of the approximation parameter. Thus, a finite continuation algorithm is designed. Results of extensive computational experiments are reported....
Directory of Open Access Journals (Sweden)
Linlin Gao
2015-11-01
Full Text Available From the perspective of vehicle dynamics, the four-wheel independent steering vehicle dynamics stability control method is studied, and a four-wheel independent steering varying parameter linear quadratic regulator control system is proposed with the help of expert control method. In the article, a four-wheel independent steering linear quadratic regulator controller for model following purpose is designed first. Then, by analyzing the four-wheel independent steering vehicle dynamic characteristics and the influence of linear quadratic regulator control parameters on control performance, a linear quadratic regulator control parameter adjustment strategy based on vehicle steering state is proposed to achieve the adaptive adjustment of linear quadratic regulator control parameters. In addition, to further improve the control performance, the proposed varying parameter linear quadratic regulator control system is optimized by genetic algorithm. Finally, simulation studies have been conducted by applying the proposed control system to the 8-degree-of-freedom four-wheel independent steering vehicle dynamics model. The simulation results indicate that the proposed control system has better performance and robustness and can effectively improve the stability and steering safety of the four-wheel independent steering vehicle.
OH AND CN ZEEMAN OBSERVATIONS OF MAGNETIC FIELDS IN MOLECULAR CLOUDS
Directory of Open Access Journals (Sweden)
R. M. Crutcher
2009-01-01
Full Text Available Observations of the Zeeman e ect in OH and CN provide valuable information about magnetic eld strengths and directions in molecular clouds in the density range 103 < n(cm-3 < 106 that these species sample. These data make it possible to test predictions of weak eld, turbulence driven star formation and strong eld, ambipolar di usion driven star formation. Here we discuss exactly what information Zeeman observations provide and how those data may be analyzed to yield meaningful results. The data imply that the mean mass-to-ux ratio in molecular cores is - 2 - 3 times critical, which means that magnetic elds are generally not strong enough to prevent gravitational collapse. However, this information about mean eld strengths is not de nitive in excluding one or the other of the two models of star formation. Present data do suggest that magnetic elds play a very signi cant role in the evolution of molecular clouds and in the star formation process. Finally, very preliminary results are discussed from two in-progress studies; these studies have the potential to be signi cantly more de nitive in testing the predictions of star formation theory, and perhaps in discriminating between the two theories.
Measuring 10-20 T magnetic fields in single wire explosions using Zeeman splitting.
Banasek, J T; Engelbrecht, J T; Pikuz, S A; Shelkovenko, T A; Hammer, D A
2016-10-01
We have shown that the Zeeman splitting of the sodium (Na) D-lines at 5890 Å and 5896 Å can be used to measure the magnetic field produced by the current flowing in an exploding wire prior to wire explosion. After wire explosion, the lines in question are either not visible in the strong continuum from the exploding wire plasma, or too broad to measure the magnetic field by methods discussed in this paper. We have determined magnetic fields in the range 10-20 T, which lies between the small field and Paschen-Back regimes for the Na D-lines, over a period of about 70 ns on a 10 kA peak current machine. The Na source is evaporated drops of water with a 0.171 M NaCl solution deposited on the wire. The Na desorbs from the wire as it heats up, and the excited vapor atoms are seen in emission lines. The measured magnetic field, determined by the Zeeman splitting of these emission lines, estimates the average radial location of the emitting Na vapor as a function of time under the assumption the current flows only in the wire during the time of the measurement.
Measuring 10-20 T magnetic fields in single wire explosions using Zeeman splitting
Banasek, J. T.; Engelbrecht, J. T.; Pikuz, S. A.; Shelkovenko, T. A.; Hammer, D. A.
2016-10-01
We have shown that the Zeeman splitting of the sodium (Na) D-lines at 5890 Å and 5896 Å can be used to measure the magnetic field produced by the current flowing in an exploding wire prior to wire explosion. After wire explosion, the lines in question are either not visible in the strong continuum from the exploding wire plasma, or too broad to measure the magnetic field by methods discussed in this paper. We have determined magnetic fields in the range 10-20 T, which lies between the small field and Paschen-Back regimes for the Na D-lines, over a period of about 70 ns on a 10 kA peak current machine. The Na source is evaporated drops of water with a 0.171 M NaCl solution deposited on the wire. The Na desorbs from the wire as it heats up, and the excited vapor atoms are seen in emission lines. The measured magnetic field, determined by the Zeeman splitting of these emission lines, estimates the average radial location of the emitting Na vapor as a function of time under the assumption the current flows only in the wire during the time of the measurement.
Quadratic partial eigenvalue assignment problem with time delay for active vibration control
Pratt, J. M.; Singh, K. V.; Datta, B. N.
2009-08-01
Partial pole assignment in active vibration control refers to reassigning a small set of unwanted eigenvalues of the quadratic eigenvalue problem (QEP) associated with the second order system of a vibrating structure, by using feedback control force, to suitably chosen location without altering the remaining large number of eigenvalues and eigenvectors. There are several challenges of solving this quadratic partial eigenvalue assignment problem (QPEVAP) in a computational setting which the traditional pole-placement problems for first-order control systems do not have to deal with. In order to these challenges, there has been some work in recent years to solve QPEVAP in a computationally viable way. However, these works do not take into account of the practical phenomenon of the time-delay effect in the system. In this paper, a new "direct and partial modal" approach of the quadratic partial eigenvalue assignment problem with time-delay is proposed. The approach works directly in the quadratic system without requiring transformation to a standard state-space system and requires the knowledge of only a small number of eigenvalues and eigenvectors that can be computed or measured in practice. Two illustrative examples are presented in the context of active vibration control with constant time-delay to illustrate the success of our proposed approach. Future work includes generalization of this approach to a more practical complex time-delay system and extension of this work to the multi-input problem.
Combinatorics on Words in Symbolic Dynamics: The Quadratic Map
Institute of Scientific and Technical Information of China (English)
Wan Ji DAI; Kebo L(U); Jun WANG
2008-01-01
This paper is contributed to the combinatorial properties of the MSS sequences, which are the periodic kneading words of quadratic maps denned on a interval. An explicit expression of adjacency relations on MSS sequences of given lengths is established.
Modulational stability and dark solitons in periodic quadratic nonlinear media
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....
Reconsideration on Homogeneous Quadratic Riemann Boundary Value Problem
Institute of Scientific and Technical Information of China (English)
Lu Jian-ke
2004-01-01
The homogeneous quadratic Riemann boundary value problem (1) with Hǒlder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its general method of solution is obtained.
A Trust-region-based Sequential Quadratic Programming Algorithm
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....
Geometric structure of pseudo-plane quadratic flows
Sun, Che
2017-03-01
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous applications focused on two-dimensional homogeneous fluid, this study examines the geometric structure of three-dimensional quadratic flows in stratified fluid by solving a steady-state pseudo-plane flow model. The complete set of exact solutions reveals that steady quadratic flows have an invariant conic type in the non-rotating frame and a non-rotatory vertical structure in the rotating frame. Three baroclinic solutions with vertically non-aligned formulation disprove an earlier conjecture. All elliptic and hyperbolic solutions, except for the inertial ones, exhibit vertical concentricity. The rich geometry of quadratic flows stands in contrast to the depleted geometry of high-degree polynomial flows. A paradox in the steady solutions of shallow-water reduced-gravity models is also explained.
Finite dimensional semigroup quadratic algebras with minimal number of relations
Iyudu, Natalia
2011-01-01
A quadratic semigroup algebra is an algebra over a field given by the generators $x_1,...,x_n$ and a finite set of quadratic relations each of which either has the shape $x_jx_k=0$ or the shape $x_jx_k=x_lx_m$. We prove that a quadratic semigroup algebra given by $n$ generators and $d\\leq \\frac{n^2+n}{4}$ relations is always infinite dimensional. This strengthens the Golod--Shafarevich estimate for the above class of algebras. Our main result however is that for every $n$, there is a finite dimensional quadratic semigroup algebra with $n$ generators and $\\delta_n$ generators, where $\\delta_n$ is the first integer greater than $\\frac{n^2+n}{4}$. This shows that the above Golod-Shafarevich type estimate for semigroup algebras is sharp.
Quadratic measurement and conditional state preparation in an optomechanical system
DEFF Research Database (Denmark)
A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.;
2014-01-01
We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....
An Interval Maximum Entropy Method for Quadratic Programming Problem
Institute of Scientific and Technical Information of China (English)
RUI Wen-juan; CAO De-xin; SONG Xie-wu
2005-01-01
With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.
On wave-packet dynamics in a decaying quadratic potential
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Henriksen, Niels Engholm
1997-01-01
We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....
DERIVATIVES OF EIGENPAIRS OF SYMMETRIC QUADRATIC EIGENVALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Derivatives of eigenvalues and eigenvectors with respect to parameters in symmetric quadratic eigenvalue problem are studied. The first and second order derivatives of eigenpairs are given. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the quadratic eigenvalue problem, and the use of state space representation is avoided, hence the cost of computation is greatly reduced. The efficiency of the presented method is demonstrated by considering a spring-mass-damper system.
Scale-Invariant Rotating Black Holes in Quadratic Gravity
Directory of Open Access Journals (Sweden)
Guido Cognola
2015-07-01
Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
Ideal Class Groups and Subgroups of Real Quadratic Function Fields
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n, and obtained eight series of such fields. The ideal class numbers h(OK) of K in the series all have a factor n.
Burgers' turbulence problem with linear or quadratic external potential
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.
2005-01-01
We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....
On Integers, Primes and UniqueFactorization in Quadratic Fields
Hedenlund, Alice
2013-01-01
Abstract. This thesis will deal with quadratic elds. The prob- lem is to study such elds and their properties including, but not limited to, determining integers, nding primes and deciding which quadratic elds have unique factorization. The goal is to get famil- iar with these concepts and to provide a starting point for students with an interest in algebra to explore eld extensions and inte- gral closures in relation to elementary number theory. The reader will be assumed to have a basic kn...
Stability of a Generalized Quadratic Functional Equation in Schwartz Distributions
Institute of Scientific and Technical Information of China (English)
Jae-Young CHUNG
2009-01-01
We consider the Hyers-Ulam stability problem of the generalized quadratic functional equation u(o)A+v(o)B-2w(o)P1-2k(o)P2=0, which is a distributional version of the classical generalized quadratic functional equation f(x + y) + g(x - y) - 2h(x) - 2k(y) = 0.
On the use of simplex methods in constructing quadratic models
Institute of Scientific and Technical Information of China (English)
Qing-hua ZHOU
2007-01-01
In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of function evaluations have been reduced obviously through our algorithms.
Institute of Scientific and Technical Information of China (English)
陈进国; 曾垂焕; 柯宗枝; 谢星云; 林兴
2013-01-01
Objective:To develop a method for direct determination of lead in urine by GF-AAS.Methods:Lead in urine samples was determined by GF-AAS with the dynamic thimagnetic field Zeeman correction technique at wavelength of 283.3 nm,with palladium chloride as the matrix modifier.Results:With dynamic trimagnetic field mode,data and the correction curve of two magnetic field can also be obtained,the standard curve (0 pg/L ～ 80 μg/L) was y =0.0048x + 0.0145,r =0.9997 ; while the standard curve (80 μg/L ～ 600 μg/L) of 3-magnetic field was y =0.0013x +0.0308,r =0.9998.The detection limit was 2.0μg/L; the recovery rate was 94.6％ ～ 104.8％; RSD was 0.60％ ～3.72％.Conclusion:The method includes advantages of the two kinds of magnetic field models:low detection limit,rapidity (sample without dilution again),accuracy,wide linear range (0 μg/L ～ 600 μg/L).The method can be used in the occupation exposure and non-occupation exposure of lead deter mination in urine.Low-concentration data was processed by the 2-magnetic field standard curve,while high-concentration data was processed by the 3-magnetic field standard curve.%目的:建立石墨炉原子吸收光谱法同时测定尿中铅(浓度变化范围大)的检测方法.方法:应用动态三磁场塞曼校正技术的石墨炉原子吸收光谱仪,通过磁场优化,采用氯化钯作基体改进剂,在283.3 nm波长下进行测定.结果:采用动态3-磁场模式测定时,还可同时得到2-磁场模式的数据和校正曲线,2-磁场标准曲线段(0.0 μg/L～80.0μg/L):y=0.0048x +0.0145,r=0.9997;3-磁场标准曲线段(80.0μg/L～600.0 μg/L):y=0.0013x +0.0308,r=0.9998；最低检出浓度2.0μg/L；回收率94.6％～104.8％；RSD为0.60％ ～ 3.72％.结论:该方法保持两种磁场模式的优点:检出限低、快速(样品无需再稀释)、准确、线性范围宽(0.0 μg/L ～600.0 μg/L)；可应用于职业接触和非职业接触尿中铅的同时测定,低浓度采用灵敏度较高的2
Reddy, Narsimha; Bhavsar, Arun; Narasimhan, P. T.
1986-02-01
A simple microprocessor-controlled pulsed NQR spectrometer system has been developed with the capability to acquire Zeeman perturbed spin echo envelope modulations (ZSEEM). The CPU of the system is based on the Intel Corporation 8085 A microprocessor. The performance of the spectrometer is illustrated with the presentation of ZSEEM spectra of NaClO3 and KClO3.
Brice, Joseph T.; Liang, Tao; Raston, Paul L.; McCoy, Anne B.; Douberly, Gary E.
2016-09-01
Sequential capture of OH and CO by superfluid helium droplets leads exclusively to the formation of the linear, entrance-channel complex, OH-CO. This species is characterized by infrared laser Stark and Zeeman spectroscopy via measurements of the fundamental OH stretching vibration. Experimental dipole moments are in disagreement with ab initio calculations at the equilibrium geometry, indicating large-amplitude motion on the ground state potential energy surface. Vibrational averaging along the hydroxyl bending coordinate recovers 80% of the observed deviation from the equilibrium dipole moment. Inhomogeneous line broadening in the zero-field spectrum is modeled with an effective Hamiltonian approach that aims to account for the anisotropic molecule-helium interaction potential that arises as the OH-CO complex is displaced from the center of the droplet.
Personal Pornography Viewing and Sexual Satisfaction: A Quadratic Analysis.
Wright, Paul J; Bridges, Ana J; Sun, Chyng; Ezzell, Matthew; Johnson, Jennifer A
2017-09-08
Personal pornography viewing has been associated with lower sexual satisfaction in both experimental and observational research. The language used to hypothesize this relationship typically suggests that it is frequent viewing, rather than infrequent or only occasional viewing, that is responsible for any adverse effects. When the nature of the relationship between a predictor and a criterion depends on the levels of the predictor, a curvilinear relationship is indicated. Nevertheless, studies have assumed linearity in their analytical approach. Curvilinear relationships will go undetected unless they are specifically tested. This article presents results from a survey of approximately 1,500 U.S. adults. Quadratic analyses indicated a curvilinear relationship between personal pornography viewing and sexual satisfaction in the form of a predominately negative, concave downward curve. The nature of the curvilinearity did not differ as a function of participants' gender, relationship status, or religiosity. But the negative acceleration was slightly more pronounced for men than for women, for people not in a relationship than for people in a relationship, and for religious people than for nonreligious people. For all groups, negative simple slopes were present when viewing reached once a month or more. These results are correlational only. However, if an effects perspective were adopted, they would suggest that consuming pornography less than once a month has little or no impact on satisfaction, that reductions in satisfaction tend to initiate once viewing reaches once a month, and that additional increases in the frequency of viewing lead to disproportionately larger decrements in satisfaction.
A transient, quadratic nodal method for triangular-Z geometry
Energy Technology Data Exchange (ETDEWEB)
DeLorey, T.F.
1993-06-01
Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.
Quadratic 0-1 programming: Geometric methods and duality analysis
Liu, Chunli
The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems.
Tokamak Plasmas : Internal magnetic ﬁeld measurement in tokamak plasmas using a Zeeman polarimeter
Indian Academy of Sciences (India)
M Jagadeeshwari; J Govindarajan
2000-11-01
In a tokamak plasma, the poloidal magnetic ﬁeld proﬁle closely depends on the current density proﬁle. We can deduce the internal magnetic ﬁeld from the analysis of circular polarization of the spectral lines emitted by the plasma. The theory of the measurement and a detailed design of the Zeeman polarimeter constructed to measure the poloidal ﬁeld proﬁle in the ADITYA tokamak are presented. The Fabry-Perot which we have employed in our design, with photodiode arrays followed by lock-in detection of the polarization signal, allows the measurement of the fractional circular polarization. In this system He-II line with wavelength 4686 Å is adopted as the monitoring spectral line. The line emission used in the present measurement is not well localized in the plasma, necessiating the use of a spatial inversion procedure to obtain the local values of the ﬁeld.
Zeeman-Doppler Imaging of II Peg - The magnetic field restructuring from 2004 to 2007
Carroll, T A; Strassmeier, K G; Ilyin, I; Tuominen, I
2009-01-01
We present Zeeman-Doppler images of the active K2 star II Peg for the years 2004 and 2007. The surface magnetic field was reconstructed with our new ZDI code "iMap" which provides a full polarized radiative transfer driven inversion to simultaneously reconstruct the surface temperature and magnetic vector field distribution. II Peg shows a remarkable large scale magnetic field structure for both years. The magnetic field is predominantly located at high latitudes and is arranged in active longitudes. A dramatic evolution in the magnetic field structure is visible for the two years, where a dominant and largely unipolar field in 2004 has developed into two distinct and large scale bipolar structures in 2007.
A Zeeman slower design with permanent magnets in a Halbach configuration.
Cheiney, P; Carraz, O; Bartoszek-Bober, D; Faure, S; Vermersch, F; Fabre, C M; Gattobigio, G L; Lahaye, T; Guéry-Odelin, D; Mathevet, R
2011-06-01
We describe a simple Zeeman slower design using permanent magnets. Contrary to common wire-wound setups, no electric power and water cooling are required. In addition, the whole system can be assembled and disassembled at will. The magnetic field is however transverse to the atomic motion and an extra repumper laser is necessary. A Halbach configuration of the magnets produces a high quality magnetic field and no further adjustment is needed. After optimization of the laser parameters, the apparatus produces an intense beam of slow and cold (87)Rb atoms. With typical fluxes of (1-5) × 10(10) atoms/s at 30 m s(-1), our apparatus efficiently loads a large magneto-optical trap with more than 10(10) atoms in 1 s, which is an ideal starting point for degenerate quantum gas experiments.
Experimental studies of a zeeman-tuned xenon laser differential absorption apparatus.
Linford, G J
1973-06-01
A Zeeman-tuned cw xenon laser differential absorption device is described. The xenon laser was tuned by axial magnetic fields up to 5500 G generated by an unusually large water-cooled dc solenoid. Xenon laser lines at 3.37 micro, 3.51 micro, and 3.99 micro were tuned over ranges of 6 A, 6 A, and 11 A, respectively. To date, this apparatus has been used principally to study the details of formaldehyde absorption lines lying near the 3 .508-micro xenon laser transition. These experiments revealed that the observed absorption spectrum of formaldehyde exhibits a sufficiently unique spectral structure that the present technique may readily be used to measure relative concentrations of formaldehyde in samples of polluted air.
First Zeeman Doppler imaging of a cool star using all four Stokes parameters
Rosén, Lisa; Wade, Gregg A
2015-01-01
Magnetic fields are ubiquitous in active cool stars but they are in general complex and weak. Current Zeeman Doppler imaging (ZDI) studies of cool star magnetic fields chiefly employ circular polarization observations because linear polarization is difficult to detect and requires a more sophisticated radiative transfer modeling to interpret. But it has been shown in previous theoretical studies, and in the observational analyses of magnetic Ap stars, that including linear polarization in the magnetic inversion process makes it possible to correctly recover many otherwise lost or misinterpreted magnetic features. We have obtained phase-resolved observations in all four Stokes parameters of the RS CVn star II Peg at two separate epochs. Here we present temperature and magnetic field maps reconstructed for this star using all four Stokes parameters. This is the very first such ZDI study of a cool active star. Our magnetic inversions reveal a highly structured magnetic field topology for both epochs. The strengt...
Zeeman study of 35Cl NQR in tetrachlorocyclopentene-1,3-dione
Mano, K.; Sengupta, S.; Giezendanner, D.; Lucken, E. A. C.
1983-01-01
The 35Cl NQR Zeeman spectrum in a single crystal of tetrachlorocyclopentene-1,3-dione has been studied for the two lines, 38734.1 (H) and 35667.0 (L) KHz at 21°C by a pulsed FT NQR spectrometer equipped for automatic measurements. Each line yields 12 efgt's in a magnetic field. Their directional symmetry (three two-fold and four three-fold axes) indicates that the crystal system is cubic. This is confirmed by its X-ray powder pattern and inspection with the polarization microscope; space group Fd3 or Fm3, a = 21.910 Å, Z = 48, D c = 1.78, D o = 1.75 . The molecular structure and the molecular orientations in the unit cell are determined from the results. The η-values are 5.8 and 21.6% for H and L, respectively.
Two simple approximations to the distributions of quadratic forms.
Yuan, Ke-Hai; Bentler, Peter M
2010-05-01
Many test statistics are asymptotically equivalent to quadratic forms of normal variables, which are further equivalent to T = sigma(d)(i=1) lambda(i)z(i)(2) with z(i) being independent and following N(0,1). Two approximations to the distribution of T have been implemented in popular software and are widely used in evaluating various models. It is important to know how accurate these approximations are when compared to each other and to the exact distribution of T. The paper systematically studies the quality of the two approximations and examines the effect of the lambda(i) and the degrees of freedom d by analysis and Monte Carlo. The results imply that the adjusted distribution for T can be as good as knowing its exact distribution. When the coefficient of variation of the lambda(i) is small, the rescaled statistic T(R) = dT/(sigma(d)(i=1) lambda(i)) is also adequate for practical model inference. But comparing T(R) against chi2(d) will inflate type I errors when substantial differences exist among the lambda(i), especially, when d is also large.
Linear versus quadratic portfolio optimization model with transaction cost
Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah
2014-06-01
Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.
Quadratic MOKE on Co-based Heusler compounds
Energy Technology Data Exchange (ETDEWEB)
Wolf, Georg; Leven, Britta; Hillebrands, Burkard [FB Physik, Landesforschungszentrum OPTIMAS, TU Kaiserslautern, 67663 Kaiserslautern (Germany); Hamrle, Jaroslav [Institute of Physics, VSB, Technical University, Ostrava (Czech Republic); Ebke, Daniel; Thomas, Andy; Reiss, Guenter [Thin Films and Physics of Nanostructures, Physics Department, Bielefeld University (Germany)
2011-07-01
The intensive research on Co-based Heusler compounds revealed that some of these materials show a large quadratic magneto-optical Kerr effect (QMOKE). The presence of QMOKE strongly depends on the electronic band structure. In the case of Heusler compounds the electronic bands can be modified by changing the composition or improving the crystalline structure. This work presents a systematic study on several Heusler compounds (Co{sub 2}FeSi, Co{sub 2}Fe{sub 0.5}Mn{sub 0.5}Si, Co{sub 2}MnSi and Co{sub 2}FeAl{sub 0.5}Si{sub 0.5}). The amplitude of the QMOKE is investigated as a function of the post deposition annealing temperature, which is known to improve the crystal ordering. We find that the QMOKE is increasing with the annealing temperature. From this we conclude that there is a strong correlation between the presence of QMOKE and the high crystalline ordering in Heusler compounds.
Gravity Waves From Non-Minimal Quadratic Inflation
Pallis, Constantinos
2015-01-01
We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter cR, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index ns, tensor-to-scalar ratio r=(2-4)x10^-3, and an inflaton mass close to 3x10^13 GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kahler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniqu...
Energy Technology Data Exchange (ETDEWEB)
Deshpande, Avinash A. [Raman Research Institute, Sadashivanagar, Bangalore 560080 (India); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801 (United States); Mendoza-Torres, J. E., E-mail: desh@rri.res.in, E-mail: mgoss@aoc.nrao.edu, E-mail: mend@inaoep.mx [Instituto Nacional de Astrofísica Optica y Electrónica, Tonantzintla, Puebla 72840 (Mexico)
2013-09-20
Our analysis of a Very Long Baseline Array 12 hr synthesis observation of the OH masers in the well-known star-forming region W49N has yielded valuable data that enable us to probe distributions of magnetic fields in both the maser columns and the intervening interstellar medium (ISM). The data, consisting of detailed high angular resolution images (with beam width ∼20 mas) of several dozen OH maser sources, or spots, at 1612, 1665, and 1667 MHz, reveal anisotropic scatter broadening with typical sizes of a few tens of milliarcseconds and axial ratios between 1.5 and 3. Such anisotropies have been reported previously by Desai et al. and have been interpreted as being induced by the local magnetic field parallel to the Galactic plane. However, we find (1) apparent angular sizes of, on average, a factor of about 2.5 less than those reported by Desai et al., indicating significantly less scattering than inferred previously, and (2) a significant deviation in the average orientation of the scatter-broadened images (by ∼10°) from that implied by the magnetic field in the Galactic plane. More intriguingly, for a few Zeeman pairs in our set, significant differences (up to 6σ) are apparent in the scatter-broadened images for the two hands of circular polarization, even when the apparent velocity separation is less than 0.1 km s{sup –1}. This may possibly be the first example of a Faraday rotation contribution to the diffractive effects in the ISM. Using the Zeeman pairs, we also study the distribution of the magnetic field in the W49N complex, finding no significant trend in the spatial structure function. In this paper, we present the details of our observations and analysis leading to these findings, discuss implications of our results for the intervening anisotropic magneto-ionic medium, and suggest possible implications for the structure of magnetic fields within this star-forming region.
A GPU implementation of the Simulated Annealing Heuristic for the Quadratic Assignment Problem
Paul, Gerald
2012-01-01
The quadratic assignment problem (QAP) is one of the most difficult combinatorial optimization problems. An effective heuristic for obtaining approximate solutions to the QAP is simulated annealing (SA). Here we describe an SA implementation for the QAP which runs on a graphics processing unit (GPU). GPUs are composed of low cost commodity graphics chips which in combination provide a powerful platform for general purpose parallel computing. For SA runs with large numbers of iterations, we fi...
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.
2015-09-03
Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
Spectra of fiber Bragg grating and long period fiber grating undergoing linear and quadratic strain
Institute of Scientific and Technical Information of China (English)
YUAN Yin-quan; LIANG Lei; ZHANG Dong-eheng
2009-01-01
The effects of linear and quadratic strain on the reflective spectrum of FBG and the transmission spectrum of LPFG have been numerically investigated based on the coupled -mode equations. The results show that for the FBG or LPFG undergo-ing only linear strain, the reflection or transmission spectrum is symmetrical about its central wavelength, the dependence relationships of the central wavelength shift, full-width-at-half-maximum, peak intensity upon the strain gradient have been obtained.
ACTIVE CONTROL OF QUARTER-CAR SUSPENSION SYSTEM USING LINEAR QUADRATIC REGULATOR
V M NANDEDKAR; K.R. Borole; G.J Vikhe; M.P. Nagarkar
2011-01-01
The automobile is composed of many systems. One of these is the suspension system. The main functions of the automotive suspension system are to provide vehicle support, stability and directional control during handling manoeuvres and to provide effective isolation from road disturbances. The suspension system has to balance the tradeoff between ride comfort and handling performance. This paper analyses the passive suspension system and active suspension system using a Linear Quadratic Regula...
Analytical Solution of Linear, Quadratic and Cubic Model of PTT Fluid
Directory of Open Access Journals (Sweden)
Naeem Faraz
2015-07-01
Full Text Available An attempt is made for the first time to solve the quadratic and cubic model of magneto hydrodynamic Poiseuille flow of Phan-Thein-Tanner (PTT. Series solution of magneto hydrodynamic (MHD flow is developed by using homotopy perturbation method (HPM. Results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. The results obtained reveals many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.
Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M.
2016-06-01
Context. In the case of unresolved solar structures or stray light contamination, inversion techniques using four Stokes parameters of Zeeman profiles cannot disentangle the combined contributions of magnetic and nonmagnetic areas to the observed Stokes I. Aims: In the framework of a two-component model atmosphere with filling factor f, we propose an inversion method restricting input data to Q , U, and V profiles, thus overcoming ambiguities from stray light and spatial mixing. Methods: The V-moments inversion (VMI) method uses shifts SV derived from moments of V-profiles and integrals of Q2, U2, and V2 to determine the strength B and inclination ψ of a magnetic field vector through least-squares polynomial fits and with very few iterations. Moment calculations are optimized to reduce data noise effects. To specify the model atmosphere of the magnetic component, an additional parameter δ, deduced from the shape of V-profiles, is used to interpolate between expansions corresponding to two basic models. Results: We perform inversions of HINODE SOT/SP data for inclination ranges 0 <ψ< 60° and 120 <ψ< 180° for the 630.2 nm Fe i line. A damping coefficient is fitted to take instrumental line broadening into account. We estimate errors from data noise. Magnetic field strengths and inclinations deduced from VMI inversion are compared with results from the inversion codes UNNOFIT and MERLIN. Conclusions: The VMI inversion method is insensitive to the dependence of Stokes I profiles on the thermodynamic structure in nonmagnetic areas. In the range of Bf products larger than 200 G, mean field strengths exceed 1000 G and there is not a very significant departure from the UNNOFIT results because of differences between magnetic and nonmagnetic model atmospheres. Further improvements might include additional parameters deduced from the shape of Stokes V profiles and from large sets of 3D-MHD simulations, especially for unresolved magnetic flux tubes.
The generalized quadratic knapsack problem. A neuronal network approach.
Talaván, Pedro M; Yáñez, Javier
2006-05-01
The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Energy Technology Data Exchange (ETDEWEB)
Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar
2016-06-15
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.
The quadratic reciprocity law a collection of classical proofs
Baumgart, Oswald
2015-01-01
This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.
On Volterra quadratic stochastic operators with continual state space
Energy Technology Data Exchange (ETDEWEB)
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar [Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University, Jalan Sultan Ahmad Shah, Bandar Indera Mahkota, 25200 Kuantan, Pahang (Malaysia)
2015-05-15
Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.
Amalgamated Products of Ore and Quadratic Extensions of Rings
Johnson, Garrett
2012-01-01
We study the ideal theory of amalgamated products of Ore and quadratic extensions over a base ring R. We prove an analogue of the Hilbert Basis theorem for an amalgamated product Q of quadratic extensions and determine conditions for when the one-sided ideals of Q are principal or doubly-generated. We also determine conditions that make Q a principal ideal ring. Finally, we show that the double affine Hecke algebra $H_{q,t}$ associated to the general linear group GL_2(k) (here, k is a field with characteristic not 2) is an amalgamated product of quadratic extensions over a three-dimensional quantum torus and give an explicit isomorphism. In this case, it follows that $H_{q,t}$ is a noetherian ring.
Robust quadratic assignment problem with budgeted uncertain flows
Directory of Open Access Journals (Sweden)
Mohammad Javad Feizollahi
2015-12-01
Full Text Available We consider a generalization of the classical quadratic assignment problem, where material flows between facilities are uncertain, and belong to a budgeted uncertainty set. The objective is to find a robust solution under all possible scenarios in the given uncertainty set. We present an exact quadratic formulation as a robust counterpart and develop an equivalent mixed integer programming model for it. To solve the proposed model for large-scale instances, we also develop two different heuristics based on 2-Opt local search and tabu search algorithms. We discuss performance of these methods and the quality of robust solutions through extensive computational experiments.
Selectable linear or quadratic coupling in an optomechanical system
Xuereb, André
2012-01-01
There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyse here the situation when one of the mirrors of the cavity itself is also allowed to move. We reveal that the interplay between the two oscillators yields a cross-coupling that results in, e.g., appreciable cooling and squeezing of the motion of the sphere, despite its nominal quadratic coupling. We also discuss a simple modification that would allow this cross-coupling to be removed at will, thereby yielding a purely quadratic coupling for the sphere.
The size of quadratic $p$-adic linearization disks
Lindahl, Karl-Olof
2013-01-01
We find the exact radius of linearization disks at indifferent fixed points of quadratic maps in $\\mathbb{C}_p$. We also show that the radius is invariant under power series perturbations. Localizing all periodic orbits of these quadratic-like maps we then show that periodic points are not the only obstruction for linearization. In so doing, we provide the first known examples in the dynamics of polynomials over $\\mathbb{C}_p$ where the boundary of the linearization disk does not contain any ...
On the use of simplex methods in constructing quadratic models
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper,we investigate the quadratic approximation methods.After studying the basic idea of simplex methods,we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces.And the quadratic model is solved in the new subspaces.The motivation is to use the information disclosed by the former steps to construct more promising directions.For most tested problems,the number of function evaluations have been reduced obviously through our algorithms.
New robust chaotic system with exponential quadratic term
Institute of Scientific and Technical Information of China (English)
Bao Bo-Cheng; Li Chun-Biao; Xu Jian-Peing; Liu Zhong
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term.This system can display a double-scroll chaotic attractor with only two equilibria,and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent.Some basic dynamical properties and chaotic behaviour of novel attractor are studied.By numerical simulation,this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviottrs by a constant controller.
Approximation algorithms for indefinite complex quadratic maximization problems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper,we consider the following indefinite complex quadratic maximization problem: maximize zHQz,subject to zk ∈ C and zkm = 1,k = 1,...,n,where Q is a Hermitian matrix with trQ = 0,z ∈ Cn is the decision vector,and m 3.An (1/log n) approximation algorithm is presented for such problem.Furthermore,we consider the above problem where the objective matrix Q is in bilinear form,in which case a 0.7118 cos mπ 2approximation algorithm can be constructed.In the context of quadratic optimization,various extensions and connections of the model are discussed.
Simultaneous quadratic performance stabilization for linear time-delay systems
Institute of Scientific and Technical Information of China (English)
Chen Yuepeng; Zhou Zude; Liu Huanbin; Zhang Qingling
2006-01-01
A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained in terms of linear matrix inequalities (LMIs) which are independent of time delays such that the resultant collection of discrete time-delay systems are stable with an upper bound of the quadratic performance index. Subsequently, controllers are designed such that the resultant closed-loop discrete time-delay systems are simultaneously stabilized with the upper bound of the quadratic performance index. Finally,a numerical example is given to illustrate the design method.
PORTAL SUPPLY TO CAUDATE LOBE AND QUADRATE LOBE OF LIVER
Directory of Open Access Journals (Sweden)
Maheswari
2015-09-01
Full Text Available The precise knowledge of intra hepatic branching pattern of portal vein to caudate lobe and quadrate lobe is important for Gastroenterologist during hepatic segmental and subsegmental resection. The study was done in 47 adult human liver specimens. In this study methods like Manual dissection and Contrast study were used. During this study the portal branches to caudate l obe, Quadrate lobe and accessory branches to segment IV in addition to its branches were observed. The results were compared with previous studies
Sparse Signal Recovery from Quadratic Measurements via Convex Programming
Li, Xiaodong; Voroninski, Vladislav
2012-01-01
In this paper we consider a system of quadratic equations ||^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be underdetermined, i.e., m < n. We prove that if there exists a sparse solution x, i.e., at most k components of x are non-zero, then by solving a convex optimization program, we can solve for x up to a multiplicative constant with high probability, provided that k
Exact solutions to quadratic gravity generated by a conformal method
Pravda, Vojtech; Podolsky, Jiri; Svarc, Robert
2016-01-01
We study the role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one non-linear partial differential equation for the conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. We show that all spacetimes conformal to Kundt are either Kundt or Robinson--Trautmann, and we provide explicit Kundt and Robinson--Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.
Vladimirov, Igor G
2012-01-01
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of its observables which corresponds to the Hamiltonian of a quantum harmonic oscillator. This approximation is carried out in a mean square optimal sense with respect to a Gaussian reference quantum state and leads to a self-consistent linearization procedure where the mean vector and quantum covariance matrix of the system observables evolve in time according to the effective linear dynamics. We demonstrate the proposed Hamiltonian-based Gaussian linearization for the quantum Duffing oscillator whose Hamiltonian is a quadro-quartic polynomial of the momentum and position operators. The results of the paper are applicable t...
Stochastic resonance in a fractional oscillator driven by multiplicative quadratic noise
Ren, Ruibin; Luo, Maokang; Deng, Ke
2017-02-01
Stochastic resonance of a fractional oscillator subject to an external periodic field as well as to multiplicative and additive noise is investigated. The fluctuations of the eigenfrequency are modeled as the quadratic function of the trichotomous noise. Applying the moment equation method and Shapiro–Loginov formula, we obtain the exact expression of the complex susceptibility and related stability criteria. Theoretical analysis and numerical simulations indicate that the spectral amplification (SPA) depends non-monotonicly both on the external driving frequency and the parameters of the quadratic noise. In addition, the investigations into fractional stochastic systems have suggested that both the noise parameters and the memory effect can induce the phenomenon of stochastic multi-resonance (SMR), which is previously reported and believed to be absent in the case of the multiplicative noise with only a linear term.
Fitting timeseries by continuous-time Markov chains: A quadratic programming approach
Crommelin, D. T.; Vanden-Eijnden, E.
2006-09-01
Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows.
Interval-parameter robust quadratic programming for water quality management under uncertainty
Li, Y. P.; Huang, G. H.; Nie, S. L.; Mo, D. W.
2008-07-01
Effective planning of water quality management is important for facilitating sustainable socio-economic development in watershed systems. An interval-parameter robust quadratic programming (IRQP) method is developed by incorporating techniques of robust programming and interval quadratic programming within a general optimization framework. The IRQP improves upon existing quadratic programming methods, and can tackle uncertainties presented as interval numbers and fuzzy sets as well as their combinations. Moreover, it can deal with nonlinearities in the objective function such that economies-of-scale effects can be reflected. The developed method is applied to a case study of a water quality management under uncertainty. A number of decision alternatives are generated based on the interval solutions as well as the projected applicable conditions. They represent multiple decision options with various environmental and economic considerations. Willingness to accept a low economic revenue will guarantee satisfying the water quality requirements. A strong desire to acquire a high benefit will run the risk of violating environmental criteria.
Liu, Q; Wang, J
2008-04-01
In this paper, a one-layer recurrent neural network with a discontinuous hard-limiting activation function is proposed for quadratic programming. This neural network is capable of solving a large class of quadratic programming problems. The state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints. In addition, a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming. Simulation results on numerical examples and support vector machine (SVM) learning show the effectiveness and performance of the neural network.
Comparison Between Normal Zeeman Effect and Abnormal Zeeman Effect%正常塞曼效应与反常塞曼效应的比较
Institute of Scientific and Technical Information of China (English)
李兴鳌; 杨建平; 周震
2004-01-01
从磁场的强弱、朗德g因子取值、量子力学微扰论等三个方面对正常塞曼效应和反常塞曼效应进行了比较,揭示了正常塞曼效应和反常塞曼效应之间的区别和联系.
Clustered Self Organising Migrating Algorithm for the Quadratic Assignment Problem
Davendra, Donald; Zelinka, Ivan; Senkerik, Roman
2009-08-01
An approach of population dynamics and clustering for permutative problems is presented in this paper. Diversity indicators are created from solution ordering and its mapping is shown as an advantage for population control in metaheuristics. Self Organising Migrating Algorithm (SOMA) is modified using this approach and vetted with the Quadratic Assignment Problem (QAP). Extensive experimentation is conducted on benchmark problems in this area.
Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.
Wang, Di; Kleinberg, Robert D
2009-11-28
Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.
A new heuristic for the quadratic assignment problem
Zvi Drezner
2002-01-01
We propose a new heuristic for the solution of the quadratic assignment problem. The heuristic combines ideas from tabu search and genetic algorithms. Run times are very short compared with other heuristic procedures. The heuristic performed very well on a set of test problems.
HOMOCLINIC CYCLES OF A QUADRATIC SYSTEM DESCRIBED BY QUARTIC CURVES
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
This paper is devoted to discussing the topological classification of the quartic invariant algebraic curves for a quadratic system. We obtain sufficient and necessary conditions which ensure that the homoclinic cycle of the system is defined by the quartic invariant algebraic curve. Finally, the corresponding global phase diagrams are drawn.
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
Positivity and storage functions for quadratic differential forms
Trentelman, Hendrikus; Willems, Jan C.
1996-01-01
Differential equations and one-variable polynomial matrices play an essential role in describing dynamics of systems. When studying functions of the dynamical variables or specifying performance criteria in optimal control, we invariably encounter quadratic expressions in the variables and their der
Canonical realization of Bondi-Metzner-Sachs symmetry: Quadratic Casimir
Gomis, Joaquim; Longhi, Giorgio
2016-01-01
We study the canonical realization of Bondi-Metzner-Sacks symmetry for a massive scalar field introduced by Longhi and Materassi [J. Math. Phys. 40, 480 (1999)]. We construct an invariant scalar product for the generalized momenta. As a consequence we introduce a quadratic Casimir with the supertranslations.
A Unified Approach to Teaching Quadratic and Cubic Equations.
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
Second Order Backward Stochastic Differential Equations with Quadratic Growth
Dylan, Possamai
2012-01-01
We prove the existence and uniqueness of a solution for one-dimensionnal second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2010), with a bounded terminal condition and a generator which is continuous with quadratic growth in z. We also prove a Feyman-Kac formula and a probabilistic representation for fully nonlinear PDEs in this setting.
Bandit-Inspired Memetic Algorithms for Solving Quadratic Assignment Problems
Puglierin, Francesco; Drugan, Madalina M.; Wiering, Marco
2013-01-01
In this paper we propose a novel algorithm called the Bandit-Inspired Memetic Algorithm (BIMA) and we have applied it to solve different large instances of the Quadratic Assignment Problem (QAP). Like other memetic algorithms, BIMA makes use of local search and a population of solutions. The novelty
The Quadratic Assignment Problem is Easy for Robinsonian Matrices
Laurent, M.; Seminaroti, M.
2014-01-01
We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form QAP(A;B), by showing that the identity permutation is optimal when A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B is a Toeplitz matrix. A Robinson (dis)
A bilinear programming solution to the quadratic assignment problem
J.F. Kaashoek (Johan); J.H.P. Paelinck (Jean)
1999-01-01
textabstractThe quadratic assignment problem (QAP) or maximum acyclical graph problem is well documented (see e.g. Pardalos and Wolkowicz, 1994). One of the authors has published some material, in which it was tried, by structuring the problem additionally, to bring it as closely as possible in the
The quadratic assignment problem is easy for robinsonian matrices
Laurent, M.; Seminaroti, M.
2015-01-01
We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans–Beckman form QAP(A,B), by showing that the identity permutation is optimal when AA and BB are respectively a Robinson similarity and dissimilarity matrix and one of AA or BB is a Toeplitz matrix. A Robinson (
A Result on Output Feedback Linear Quadratic Control
Engwerda, J.C.; Weeren, A.J.T.M.
2006-01-01
In this note we consider the static output feedback linear quadratic control problem.We present both necessary and sufficient conditions under which this problem has a solution in case the involved cost depend only on the output and control variables.This result is used to present both necessary and
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS
Directory of Open Access Journals (Sweden)
E. L. Shishkina
2016-12-01
Full Text Available In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with the Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with the Bessel operator.