quadrupole or quadrapole is one of a sequence of configurations of—for example—electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure reflecting various orders of complexity.

Magnetic quadrupole

Coils producing a quadrupole field.


quadrupole magnet


four-pole”). See also: Quadrupole magnet

All known magnetic sources give dipole fields. However, to make a magnetic quadrupole it is possible to place four identical bar magnets perpendicular to each other such that the north pole of one is next to the south of the other. Such a configuration cancels the dipole moment and gives a quadrupole moment, and its field will decrease at large distances faster than that of a dipole.

An example of a magnetic quadrupole, involving permanent magnets, is depicted on the right. Electromagnets of similar conceptual design (called quadrupole magnets) are commonly used to focus beams of charged particles in particle accelerators and beam transport lines, a method known as strong focusing. The quadrupole-dipole intersect can be found by multiplying the spin of the unpaired nucleon by its parent atom. There are four steel pole tips, two opposing magnetic north poles and two opposing magnetic south poles. The steel is magnetized by a large electric current that flows in the coils of tubing wrapped around the poles.

Changing magnetic quadrupole moments produces electromagnetic radiation.

Gravitational quadrupole

The mass quadrupole is very analogous to the electric charge quadrupole, where the charge density is simply replaced by the mass density. The gravitational potential is then expressed as:


Fermilab in Batavia, Illinois, United States. Where to begin? This is the most aesthetically pleasing laboratory building I have ever seen. They have done many incredible things: they developed the quadrupole magnet for particle accelerators, the second website ever created, they found a way to blast particles onto a local tumor as to make it disappear forever, they developed superconconductors for particle accelerators, they helped discover the muon quark, it was the largest energy particle accelerator for nearly three decades (it has shut down) before CERNs hadron collider, and they discovered the top quark. This place has so much history. It’s a major thing that it was able to cure cancerous tumors and the government shut it down forever. I went here today. The most beautiful building I have ever laid my eyes on, and the marvelous tevetron has since been shut down and is being dismantled as we speak. This breaks my heart dearly. I love this building, what it stands for, what is has contributed to society, and I aspire to work here one day.

[ Authors ]
V.O. Nesterenko, V. G. Kartavenko, W. Kleinig, R.V. Jolos, J. Kvasil, P.-G. Reinhard
[ Abstract ]
The lowest quadrupole $\gamma$-vibrational $K^{\pi}=2^+$ states in axially deformed rare-earth (Nd, Sm, Gd, Dy, Er, Yb, Hf, W) and actinide (U) nuclei are systematically investigated within the fully self-consistent separable random-phase-approximation (SRPA) based on the Skyrme functional. The energies $E_{\gamma}$ and reduced transition probabilities $B(E2)$ of $2^+_{\gamma}$-states are calculated with the Skyrme forces SV-mas10 and SkM$^*$. We demonstrate that the blocking effect in pairing plays an important role. It leads to a systematic downshift of $E_{\gamma}$ by 0.3-0.5 MeV and thus to a significant improvement of agreement with the experiment, especially in Sm, Gd, Dy, Hf, and W regions. For other isotopic chains, a noticeable overestimation of $E_{\gamma}$ and too weak collectivity of $2^+_{\gamma}$-states still persist. It is shown that domains of nuclei with a low and high $2^+_{\gamma}$-collectivity are related with the structure of the lowest 2-quasiparticle states and maintenance of the Nilsson selection rules. The description of $2^+_{\gamma}$ states with SV-mas10 and SkM$^*$ is generally similar in light rare-earth nuclei but deviates in heavier nuclei. As compared to SkM*, SV-mas10 provides better description of the quadrupole deformation and energy of the isoscalar giant quadrupole resonance. The calculations suggest that coupling with complex configurations is needed for a satisfactory description of $2^+_{\gamma}$ states in all domains.

[ Authors ]
Q. Bouton, R. Chang, A. L. Hoendervanger, F. Nogrette, A. Aspect, C. I. Westbrook, D. Clément
[ Abstract ]
We report on the Bose-Einstein condensation of metastable Helium-4 atoms using a hybrid approach, consisting of a magnetic quadrupole and a crossed optical dipole trap. In our setup we cross the phase transition with 2x10^6 atoms, and we obtain pure condensates of 5x10^5 atoms in the optical trap. This novel approach to cooling Helium-4 provides enhanced cycle stability, large optical access to the atoms and results in production of a condensate every 6 seconds - a factor 3 faster than the state-of-the-art. This speed-up will dramatically reduce the data acquisition time needed for the measurement of many particle correlations, made possible by the ability of metastable Helium to be detected individually.

[ Authors ]
Joseph M. O. Antognini
[ Abstract ]
Kozai-Lidov (KL) oscillations in hierarchical triple systems have found application to many astrophysical contexts, including planet formation, type Ia supernovae, and supermassive black hole dynamics. The period of these oscillations is known at the order-of-magnitude level, but dependences on the initial mutual inclination or inner eccentricity are not typically included. In this work I calculate the period of KL oscillations ($t_{\textrm{KL}}$) exactly in the test particle limit at quadrupole order (TPQ). I explore the parameter space of all hierarchical triples at TPQ and show that except for triples on the boundary between libration and rotation, the period of KL oscillations does not vary by more than a factor of a few. The exact period may be approximated to better than 2 per cent for triples with mutual inclinations between 60$^{\circ}$ and 120$^{\circ}$ and initial eccentricities less than $\sim$0.3. In addition, I derive an analytic expression for the period of octupole-order oscillations due to the `eccentric KL mechanism’ (EKM). I show that the timescale for EKM oscillations is proportional to $\epsilon_{\textrm{oct}}^{-½}$, where $\epsilon_{\textrm{oct}}$ measures the strength of octupole perturbations relative to quadrupole perturbations.

[ Authors ]
R. F. Garcia Ruiz, M. L. Bissell, K. Blaum, N. Frommgen, M. Hammen, J. D. Holt, M. Kowalska, K. Kreim, J. Menendez, R. Neugart, G. Neyens, W. Nortershauser, F. Nowacki, J. Papuga, A. Poves, A. Schwenk, J. Simonis, D. T. Yordanov
[ Abstract ]
High-resolution bunched-beam collinear laser spectroscopy was used to measure the optical hyperfine spectra of the $^{43-51}$Ca isotopes. The ground state magnetic moments of $^{49,51}$Ca and quadrupole moments of $^{47,49,51}$Ca were measured for the first time, and the $^{51}$Ca ground state spin $I=3/2$ was determined in a model-independent way. Our results provide a critical test of modern nuclear theories based on shell-model calculations using phenomenological as well as microscopic interactions. The results for the neutron-rich isotopes are in excellent agreement with predictions using interactions derived from chiral effective field theory including three-nucleon forces, while lighter isotopes illustrate the presence of particle-hole excitations of the $^{40}$Ca core in their ground state.

[ Authors ]
Dennis Bonatsos, Andriana Martinou, N. Minkov, S. Karampagia, D. Petrellis
[ Abstract ]
The analytic quadrupole octupole axially symmetric model, which had successfully predicted 226Ra and 226Th as lying at the border between the regions of octupole deformation and octupole vibrations in the light actinides using an infinite well potential (AQOA-IW), is made applicable to a wider region of nuclei exhibiting octupole deformation, through the use of a Davidson potential (AQOA-D). Analytic expressions for energy spectra and B(E1), B(E2), B(E3) transition rates are derived. The spectra of 222-226Ra and 224,226Th are described in terms of the two parameters phi_0 (expressing the relative amount of octupole vs. quadrupole deformation) and beta_0 (the position of the minimum of the Davidson potential), while the recently determined B(EL) transition rates of 224Ra, presenting stable octupole deformation, are successfully reproduced. A procedure for gradually determining the parameters appearing in the B(EL) transitions from a minimum set of data, thus increasing the predictive power of the model, is outlined.

Predicting the denitrification capacity of sandy aquifers from in situ measurements using push–pull 15N tracer tests
Predicting the denitrification capacity of sandy aquifers from in situ measurements using push–pull 15N tracer tests

Biogeosciences, 12, 2327-2346, 2015

Author(s): W. Eschenbach, R. Well, and W. Walther

Knowledge about the spatial variability of in situ denitrification rates (Dr(in situ)) and their relation to the denitrification capacity in nitrate-contaminated aquifers is crucial to predict the development of groundwater quality. Therefore, 28 push–pull 15N tracer tests for the measurement of in situ denitrification rates were conducted in two sandy Pleistocene aquifers in northern Germany.

The 15N analysis of denitrification-derived 15N-labelled N2 and N2O dissolved in water samples collected during the push–pull 15N tracer tests was performed using isotope ratio mass spectrometry (IRMS) in the lab and additionally for some tracer tests online in the field with a quadrupole membrane inlet mass spectrometer (MIMS) in order to test the feasibility of on-site real-time 15N analysis. Aquifer material from the same locations and depths as the push–pull injection points was incubated, and the initial and cumulative denitrification after 1 year of incubation (Dcum(365)) as well as the stock of reduced compounds (SRC) was compared with in situ measurements of denitrification. This was done to derive transfer functions suitable to predict Dcum(365) and SRC from Dr(in situ).

Dr(in situ) ranged from 0 to 51.5 μg N kg−1 d−1. Denitrification rates derived from on-site isotope analysis using MIMS satisfactorily coincided with laboratory analysis by conventional IRMS, thus proving the feasibility of in situ analysis. Dr(in situ) was significantly higher in the sulfidic zone of both aquifers compared to the zone of non-sulfidic aquifer material. Overall, regressions between the Dcum(365) and SRC of the tested aquifer material with Dr(in situ) exhibited only a modest linear correlation for the full data set. However, the predictability of Dcum(365) and SRC from Dr(in situ) data clearly increased for aquifer samples from the zone of NO3-bearing groundwater.

In the NO3-free aquifer zone, a lag phase of denitrification after NO3 injections was observed, which confounded the relationship between reactive compounds and in situ denitrification activity. This finding was attributed to adaptation processes in the microbial community after NO3 injections. It was also demonstrated that the microbial community in the NO3-free zone just below the NO3-bearing zone can be adapted to denitrification by NO3 injections into wells for an extended period. In situ denitrification rates were 30 to 65 times higher after pre-conditioning with NO3. Results from this study suggest that such pre-conditioning is crucial for the measurement of Dr(in situ) in deeper aquifer material from the NO3-free groundwater zone and thus for the prediction of Dcum(365) and SRC from Dr(in situ).

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[ Authors ]
Hong Qin, Moses Chung, Ronald C. Davidson, J. W. Burby
[ Abstract ]
It has been realized in recent years that coupled focusing lattices in accelerators and storage rings have significant advantages over conventional uncoupled focusing lattices, especially for high-intensity charged particle beams. A theoretical framework and associated tools for analyzing the spectral and structural stability properties of coupled lattices are formulated in this paper, based on the recently developed generalized Courant-Snyder theory for coupled lattices. It is shown that for periodic coupled lattices that are spectrally and structurally stable, the matrix envelope equation must admit matched solutions. Using the technique of normal form and pre-Iwasawa decomposition, a new method is developed to replace the (inefficient) shooting method for finding matched solutions for the matrix envelope equation. Stability properties of a continuously rotating quadrupole lattice are investigated. The Krein collision process for destabilization of the lattice is demonstrated.

[ Authors ]
Qiu-Yue Li, Xiao-Xiang Wang, Yan Zuo, Yu Zhang, Feng Pan
[ Abstract ]
The triaxial dynamics of the quadrupole-deformed rotor model of both the rigid and the irrotational type have been investigated in detail. The results indicate that level patterns and E2 transitional characters of the two types of the model can be matched with each other to the leading order of the deformation parameter $\beta$. Especially, it is found that the dynamical structure of the irrotational type with most triaxial deformation ($\gamma=30^\circ$) is equivalent to that of the rigid type with oblate deformation ($\gamma=60^\circ$), and the associated spectrum can be classified into the standard rotational bands obeying the rotational $L(L+1)$-law or regrouped into a new ground- and $\gamma$-band with odd-even staggering in the new $\gamma$-band commonly recognized as a signature of the triaxiality. The differences between the two types of the model in this case are emphasized especially on the E2 transitional characters.

[ Authors ]
Yin Jiang, Xu-Guang Huang, Jinfeng Liao
[ Abstract ]
We show the existence of a new gapless collective excitation in a rotating fluid system with chiral fermions, named as the Chiral Vortical Wave (CVW). The CVW has its microscopic origin at the quantum anomaly and macroscopically arises from interplay between vector and axial charge fluctuations induced by vortical effects. The wave equation is obtained both from hydrodynamic current equations and from chiral kinetic theory and its solutions show nontrivial CVW-induced charge transport from different initial conditions. Using the rotating quark-gluon plasma in heavy ion collisions as a concrete example, we show the formation of induced flavor quadrupole in QGP and estimate the elliptic flow splitting effect for Lambda baryons that may be experimentally measured.

[ Authors ]
Barun Majumder, Kent Yagi, Nicolas Yunes
[ Abstract ]
No-hair like relations between the multipole moments of the exterior gravitational field of neutron stars have recently been found to be approximately independent of the star’s internal structure. This approximate, equation-of-state universality arises after one adimensionalizes the multipole moments appropriately, which then begs the question of whether there are better ways to adimensionalize the moments to obtain stronger universality. We here investigate this question in detail by considering slowly-rotating neutron stars both in the non-relativistic limit and in full General Relativity. We find that there exist normalizations that lead to stronger equation-of-state universality in the relations among the moment of inertia and the quadrupole, octopole and hexadecapole moments of neutron stars. We determine the optimal normalization that minimizes the equation-of-state dependence in these relations. The results found here may have applications in the modeling of X-ray pulses and atomic line profiles from millisecond pulsars with NICER and LOFT.