Manifestations of the roton mode in dipolar Bose-Einstein condensates

We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that a small perturbation in the trapping potential can lead to dramatic changes in the condensate's density profile for sufficiently large dipolar interaction strengths and trap aspect ratios. By employing perturbation theory, we relate these oscillations to a previously identified "rotonlike" mode in dipolar BECs. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been predicted previously.     

The role of dipolar interactions for the magnetic properties of ferromagnetic nanoring

We investigate numerically the effects of the dipolar interactions on magnetic properties in small ferromagnetic nanorings using a Monte Carlo technique. Our simulated results show that the strength of dipolar interaction in the magnetic nanoring has an important influence on the magnetization reversal processes and further the coercivity and the remanence. As the dipolar interaction increases, the transition of magnetization reversal processes from the onion-rotation state to the vortex state can occur, which results in an increase in coercivity and a decrease in remanence. On the other hand, it is found that the coercivity and the remanence depend more strongly on the strength of dipolar coupling for the relatively small size nanoring than for the large size nanoring in width. This can be attributed to the stable vortex state without core in smaller width nanoring in contrast to the metastable vortex state with core in larger width nanoring, induced by strong dipolar interactions. Additionally, the temperature dependence of coercivity and remanence in magnetic nanoring is also studied at a fixed dipolar interaction.     

Ordering in nematic liquid crystals from NMR cross-polarization studies

The measurement of dipolar couplings between nuclei is a convenient way of obtatining directly liquid crystalline ordering through NMR since the coupling is dependent on the average orientation of the dipolar vector in the magnetic field which also aligns the liquid crystal. However, measurement of the dipolar coupling between a pair of selected nuclei is beset with problems that require special solutions. In this article the use of cross polarization for measuring dipolar couplings in liquid crystals is illustrated. Transient oscillations observed during cross polarization provide the dipolar couplings between essentially isolated nearest neighbour spins which can be extracted for several sites simultaneously by employing two-dimensional NMR techniques. The use of the method for obtaining heteronuclear dipolar couplings and hence the order parameters of liquid crystals is presented. Several modifications to the basic experiment are considered and their utility illustrated. A method for obtaining proton-proton dipolar couplings, by utilizing cross polarization from the dipolar reservoir, is also presented.     

Shape and magnetic moment dependence of the dipolar field in Mn_(12)-acetate

There is a small fraction of fast-relaxation species in Mn12-acetate, which is utilized to determine the dipolar field of Mn12. Here we report an easier way to precisely obtain the dipolar field by measuring the M-H curves above the blocking temperature of fastrelaxation species. We found that there is a simple linear relationship between the magnetic moment and dipolar field; besides the dipolar field is also dependent on the sample shape, which is consistent with the numerical calculation.     

Simultaneous measurement of D and T2 using the distant dipolar field

The presence of long-range dipolar fields in liquids is known to introduce a non-linear term in the Bloch-Torrey equations which is responsible for many interesting effects in nuclear magnetic resonance as well as in magnetic resonance imaging. We show here, for the first time, that the diffusion coefficient D and the spin-spin relaxation time T2 can be obtained simultaneously from the time evolution profile of the long-range dipolar field refocused signal. In a COSY Revamped by Z-asymmetric Echo Detection sequence, the analytical first-order approximation solution of the Bloch-Torrey equations modified to include the effect of the distant dipolar field is used to demonstrate the technique in an experiment using doped water.     

Clean TOCSY transfer through residual dipolar couplings

The transfer efficiency of cross-relaxation compensated (Clean) TOCSY sequences is analyzed for applications to residual dipolar couplings. Surprisingly most conventional Clean TOCSY sequences are very inefficient for dipolar transfer. It is shown theoretically, that this is a general property of all phase-alternating mixing sequences, i.e., for such sequences the suppression of cross-relaxation excludes dipolar transfer in the spin-diffusion limit. A new family of clean dipolar TOCSY sequences is derived which provides excellent transfer efficiencies for a broad range of offset frequencies.     

Magnetic microstructure of the spin reorientation transition: a computer experiment

The scenario of the spin reorientation in two-dimensional films within first-order anisotropy approximation is theoretically studied by means of Monte Carlo simulations. The magnetic microstructure is investigated as a function of the ratio of the perpendicular anisotropy energy to the dipolar one. If the anisotropy dominates, out-of-plane domains will be found while in-plane vortices appear for a vanishing anisotropy. In the range of comparable anisotropy and dipolar energies a complex domain pattern evolves yielding a continuous transition between the two structures. The structure with equally distributed magnetic moment orientations is stable at the point where anisotropy and dipolar energies cancel each other.     

Induced dipole contributions to the potential in the surface region of an ionic solid

The theory of the electric potential near the surface of an ionic solid is extended to include induced dipolar effects. Numerical results are given for the {100} and {110} faces of several solids having the NaCl structure. General matrices are given which allow the determination of the dipolar contribution for any ionic solid of the NaCl type. It is shown that the contribution is small for the two surface planes considered.     

Proton residual dipolar couplings by NMR magnetization exchange in cross-linked elastomers: determination and imaging.

Proton nuclear magnetic resonance (NMR) magnetization exchange is used to investigate residual dipolar couplings in a series of cross-linked poly(styrene-cobutadiene) elastomers. A new model for the dipolar unit is used for the evaluation of the signal decay in magnetization exchange experiments. It takes into account an extended residual dipolar coupling network along the polymer chain. It is shown that in the regime of short mixing times, information about the residual dipolar coupling between methine and methylene protons can be obtained which is not affected by other inter- and intramolecular dipolar couplings. The dynamic order parameter of methine-methylene protons is measured and correlated with cross-link density. This study certifies the quality of a filter for magnetization from residual dipolar couplings which exploit magnetization exchange. The filter can be used to generate contrast in NMR images of heterogeneous elastomers. The first proton NMR parameter image of a dynamic order parameter is presented for a phantom made from poly(styrene-cobutadiene) samples with different cross-link densities.     

Efficient numerical methods for computing ground states and dynamics of dipolar Bose–Einstein condensates

New efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar Bose–Einstein condensates (BECs) described by a three-dimensional (3D) Gross–Pitaevskii equation (GPE) with a dipolar interaction potential. Due to the high singularity in the dipolar interaction potential, it brings significant difficulties in mathematical analysis and numerical simulations of dipolar BECs. In this paper, by decoupling the two-body dipolar interaction potential into short-range (or local) and long-range interactions (or repulsive and attractive interactions), the GPE for dipolar BECs is reformulated as a Gross–Pitaevskii–Poisson type system. Based on this new mathematical formulation, we prove rigorously existence and uniqueness as well as nonexistence of the ground states, and discuss the existence of global weak solution and finite time blow-up of the dynamics in different parameter regimes of dipolar BECs. In addition, a backward Euler sine pseudospectral method is presented for computing the ground states and a time-splitting sine pseudospectral method is proposed for computing the dynamics of dipolar BECs. Due to the adoption of new mathematical formulation, our new numerical methods avoid evaluating integrals with high singularity and thus they are more efficient and accurate than those numerical methods currently used in the literatures for solving the problem. Extensive numerical examples in 3D are reported to demonstrate the efficiency and accuracy of our new numerical methods for computing the ground states and dynamics of dipolar BECs.     

Dipolar contrast for dense tissues imaging

A new type of contrast called dipolar contrast is obtained by a decrease in the dipolar line broadening of protons. This contrast is usable for dense tissue NMR imaging and more generally for the study of dipolar linked protons in biological tissues. The sequence used is based on a variant of the Magic Sandwich Echoes (MSE) technique. In vitro experiments on a tendon sample are used to reinforce the image intensity of regions where the direct proton dipolar interaction exists.     

Effective dipolar couplings determined by dipolar dephasing of double-quantum coherences

It is shown how homonuclear distances and homonuclear dipolar lattice sums between spin-1/2 nuclei can be measured by a pulsed solid-state NMR experiment under magic-angle spinning conditions. The presented technique is based on double-quantum coherence filtering. Instead of measuring a build-up of double-quantum coherence the pulse sequence is designed to dephase double-quantum coherence. This is achieved by exciting double-quantum coherence either with the help of the through-space dipolar coupling or the through-bond dipolar coupling while the dephasing relies on the through-space dipolar coupling as selected by a gamma-encoded pulse sequence from the C/R symmetry class. Since dephasing curves can be normalized on zero dephasing, it is possible to analyze the initial dephasing regime and hence determine dipolar lattice sums (effective dipolar couplings) in multiple-spin systems. A formula for the effective dipolar coupling is derived theoretically and validated by numerical calculations and experiments on crystalline model compounds for (13)C and (31)P spin systems. The double-quantum dephasing experiment can be combined with constant-time data sampling to compensate for relaxation effects, consequently only two experimental data points are necessary for a single distance measurement. The phase cycling overhead for the constant-time experiment is minimal because a short cogwheel phase cycle exists. A 2D implementation is demonstrated on [(13)C(3)]alanine.     

Variation of molecular alignment as a means of resolving orientational ambiguities in protein structures from dipolar couplings

Residual dipolar couplings for pairs of proximate magnetic nuclei in macromolecules can easily be measured using high-resolution NMR methods when the molecules are dissolved in dilute liquid crystalline media. The resulting couplings can in principle be used to constrain the relative orientation of molecular fragments in macromolecular systems to build a complete structure. However, determination of relative fragment orientations based on a single set of residual dipolar couplings is inherently hindered by the multi-valued nature of the angular dependence of the dipolar interaction. Even with unlimited dipolar data, this gives rise to a fourfold degeneracy in fragment orientations. In this Communication, we demonstrate a procedure based on an order tensor analysis that completely removes this degeneracy by combining residual dipolar coupling measurements from two alignment media. Application is demonstrated on (15)N-(1)H residual dipolar coupling data acquired on the protein zinc rubredoxin from Clostridium pasteurianum dissolved in two different bicelle media.     

Geometry of multiple-spin systems as reflected in 13C-{1H} dipolar spectra measured at Lee-Goldburg cross-polarization

Theoretical calculation and analysis of (13)C-{(1)H} dipolar spectra of small-size spin clusters is presented. Dipolar spectra simulated using the time-independent average Hamiltonian are compared with the dipolar profiles obtained by 2D and 3D (1)H-(13)C correlation experiments employing Lee-Goldburg off-resonance cross-polarization (LG-CP). It is demonstrated that the structural parameters such as interatomic distances as well as mutual orientation of internuclear vectors can be derived from the dipolar profiles of simple spin clusters. Simplified analysis of the dipolar spectra based on isolated-like spin-pair approach can be used only if interacting spin cluster is reduced to the three-spin system in which the angle between both internuclear vectors ranges from 45 degrees to 135 degrees . For other local arrangements of spin systems the produced dipolar spectra must be analyzed with high caution. Contributions of all interacting spins to dipolar evolution of (13)C magnetization are mutually mixed and cannot be easily separated. However, simplification of the dipolar spectra is achieved by selective excitation. Enhanced selectivity of LG-CP transfer due to the initial (1)H chemical-shift-evolution period makes it possible to construct the dipolar spectra from (1)H-(13)C cross-peak intensities for every detected (1)H-(13)C spin-pair. Consequently, isolated-like spin pair evolution of the detected (1)H-(13)C coherence dominates to the resulting dipolar profile, while the influence of other interacting spins is suppressed. However, this suppression is not quite complete and analysis of the selective dipolar spectra based on isolated-like spin-pair approach cannot be used generally. Especially evolution of long-range (1)H-(13)C coherence is still significantly affected by spin states of other coupled hydrogen atoms.     

Rotary resonance echo double resonance for measuring heteronuclear dipolar coupling under MAS

A rotary resonance echo double resonance (R-REDOR) experiment is described for measuring heteronuclear dipolar coupling under magic-angle spinning. Rotary resonance reintroduces both dipolar coupling and chemical shift anisotropy with an rf field matching the spinning frequency. The resonance effect from chemical shift anisotropy can be refocused with a rotary resonance echo. The R-REDOR experiment thus measures the dephasing of the rotary resonance echo from the heteronuclear dipolar coupling to determine the dipolar coupling constant. The rotary resonance experiment is suitable for measuring dipolar coupling with quadrupolar nuclei because it applies the recoupling rf only to the observed spin-1/2. The rotary resonance scheme has the advantages of a long T2' and susceptible to spinning frequency fluctuation.     

Transverse instability of straight vortex lines in dipolar Bose-Einstein condensates

The physics of vortex lines in dipolar condensates is studied. Because of the nonlocality of the dipolar interaction, the 3D character of the vortex plays a more important role in dipolar gases than in typical short-range interacting ones. In particular, the dipolar interaction significantly affects the stability of the transverse modes of the vortex line. Remarkably, in the presence of a periodic potential along the vortexline, the spectrum of transverse modes shows a rotonlike minimum, which eventually destabilizes the straight vortex when the BEC as a whole is still stable, opening the possibility for new scenarios for vortex-line configurations in dipolar gases.     

NMR determination of the torsion angle psi in alpha-helical peptides and proteins: the HCCN dipolar correlation experiment

Several existing methods permit measurement of the torsion angles phi, psi and chi in peptides and proteins with solid-state MAS NMR experiments. Currently, however, there is not an approach that is applicable to measurement of psi in the angular range -20 degree to -70 degree, commonly found in alpha-helical structures. Accordingly, we have developed a HCCN dipolar correlation MAS experiment that is sensitive and accurate in this regime. An initial REDOR driven (13)C'--(15)N dipolar evolution period is followed by the C' to C(alpha) polarization transfer and by Lee--Goldburg cross polarization recoupling of the (13)C(alpha)(1)H dipolar interaction. The difference between the effective (13)C(1)H and (13)C(15)N dipolar interaction strengths is balanced out by incrementing the (13)C--(15)N dipolar evolution period in steps that are a factor of R(R approximately omega(CH)/omega(CN)) larger than the (13)C--(1)H steps. The resulting dephasing curves are sensitive to variations in psi in the angular region associated with alpha-helical secondary structure. To demonstrate the validity of the technique, we apply it to N-formyl-[U-(13)C,(15)N] Met-Leu-Phe-OH (MLF). The value of psi extracted is consistent with the previous NMR measurements and close to that reported in diffraction studies for the methyl ester of MLF, N-formyl-[U-(13)C,(15)N]Met-Leu-Phe-OMe.     

Cluster structure and the first-order phase transition in dipolar systems

The European Physical Journal E - The Monte Carlo technique is used to simulate a 3D dipolar hard-sphere system. The spatial and magnetic structure of clusters formed by magnetic dipolar...     

Atomic refinement with correlated solid-state NMR restraints

The orientation data provided by solid-state NMR can provide a great deal of structural information about membrane proteins. The quality of the information provided is, however, somewhat degraded by sign degeneracies in measurements of the dipolar coupling tensor. This is reflected in the dipolar coupling penalty function used in atomic refinement, which is less capable of properly restraining atoms when dipolar sign degeneracies are present. In this report we generate simulated solid-state NMR data using a variety of procedures, including back-calculation from crystal structures of alpha-helical and beta-sheet membrane proteins. We demonstrate that a large fraction of the dipolar sign degeneracies are resolved if anisotropic dipolar coupling measurements are correlated with anisotropic chemical shift measurements, and that all sign degeneracies can be resolved if three data types are correlated. The advantages of correlating data are demonstrated with atomic refinement of two test membrane proteins. When refinement is performed using correlated dipolar couplings and chemical shifts, perturbed structures converge to conformations with a larger fraction of correct dipolar signs than when data are uncorrelated. In addition, the final structures are closer to the original unperturbed structures when correlated data are used in the refinement. Thus, refinement with correlated data leads to improved atomic structures. The software used to correlate dipolar coupling and chemical shift data and to set up energy functions and their derivatives for refinement, CNS-SS02, is available at our web site.     

Molecular rotation in liquid crystals selective deuterium spin-lattice relaxation times in the nematic mesophase of 4-cyano-4′-d17-n-octylbiphenyl

The Gibbs ensemble is used to simulate the liquid–liquid equilibria of binary mixtures containing dipolar and non-polar components.The interactions of the dipolar fluid are calculated using the Keesom intermolecular potential. The liquid–liquid coexistence properties are reported for different pressures and different combinations of dipolar/non-polar molecules. The critical properties of the mixtures are estimated. The ability of a dipole to induce phase separation is influenced by the dispersion energy of the molecule. Phase separation is enhanced if the dipolar molecule is also the component with the greatest dispersion energy.