Dipole-quadrupole force ratios determine the ability of potential models to describe the phase diagram of water

We show that, in order to yield an acceptable phase diagram for water, the key ingredient is the relative strength of the dipolar and quadrupolar forces. We also demonstrate that for three-point-charge water models the relative strength of the dipolar to quadrupolar forces is determined by the position of the negative charge. This provides a theoretical background--supported by the experiment--to our knowledge of the water interactions which at present is essentially dominated by empirical models. In addition, it can be quite useful in the development of improved water models with a more physical basis.     

Finite size effect of ions and dipoles close to charged interfaces

The modified dipolar Poisson-Boltzmann(MDPB) equation,where the electrostatics of the dipolar interactions of solvent molecules and also the finite size effects of ions and dipolar solvent molecules are explicitly taken into account on a mean-field level,is studied numerically for a two-plate system with oppositely charged surfaces.The MDPB equation is solved numerically,using the nonlinear Multigrid method,for one-dimensional finite volume meshes.For a high enough surface charge density,numerical results of the MDPB equation reveal that the effective dielectric constant decreases with the increase of the surface charge density.Furthermore,increasing the salt concentration leads to the decrease of the effective dielectric constant close to the charged surfaces.This decrease of the effective dielectric constant with the surface charge density is opposite to the trend from the dipolar Poisson-Boltzmann(DPB) equation.This seemingly inconsistent result is due to the fact that the mean-field approach breaks down in such highly charged systems where the counterions and dipoles are strongly attracted to the charged surfaces and form a quasi two-dimensional layer.In the weak-coupling regime with the electrostatic coupling parameter(the ratio of Bjerrum length to Gouy-Chapman length) Ξ 1,where the MDPB equation works,the effective dielectric constant is independent of the distance from the charged surfaces and there is no accumulation of dipoles near the charged surfaces.Therefore,there are no physical and computational advantages for the MDPB equation over the modified Poisson-Boltzmann(MPB) equation where the effect of dipolar interactions of solvent dipoles is implicitly taken into account in the renormalised dielectric constant.     

Dipolar Poisson-Boltzmann equation: ions and dipoles close to charge interfaces

We present an extension to the Poisson-Boltzmann model where the dipolar features of solvent molecules are taken explicitly into account. The formulation is derived at mean-field level and can be extended to any order in a systematic expansion. It is applied to a two-plate system with oppositely charged surfaces. The ion distribution and profiles in the dipolar order parameter are calculated and can result in a large correction to the interplate pressure.     

Colloidal inclusions in smectic films with spontaneous bend

Inclusions in free-standing smectic films are simple model systems for two-dimensional anisotropic dispersions. From theory and experiment, different topologies of elastic distortions of the embedding liquid crystal are known. Quadrupolar and different dipolar defect configurations in the vicinity of the inclusion are possible, and these configurations determine the type of interactions between the inclusions. The quadrupolar configuration is often energetically preferred. We show, however, that dipolar director configurations around inclusions can be energetically favourable over quadrupolar arrangements in chiral smectics, as a consequence of a spontaneous-bend term in the elastic-energy formulation. As the inclusion size influences the selection of the deformation types, the corresponding spontaneous-bend constant can be estimated for the strong anchoring limit if the c -director fields around inclusions of different diameters are taken into account.     

Effects of pH and molecular charge on dipolar coupling interactions of solutes in skeletal muscle observed by DQF, 1H NMR spectroscopy

In this study we tested the effect of molecular charge and chirality as well as tissue pH on dipolar coupling interaction in skeletal muscle. These results were demonstrated by double quantum filtered, DQF, 1H NMR spectra acquired on permeable skeletal muscle samples dialyzed against buffered solutions containing three classes of solutes-electrolytes (lactate and Tris), zwitterions (alanine and glycine), and non-electrolytes (dioxane and ethanol)-as a function of pH ranging from 5.0 to 8.5. The results show that charge density on the protein filaments strongly influences dipolar coupling of solutes in muscle whereas charge on the solutes themselves has only a small effect. The frequency splitting of the dipolar coupled peaks for all the molecules tested was strongly affected by muscle pH. Higher pH increased negative charge density on the filaments and resulted in weaker dipolar coupling for anions and zwitterions but stronger coupling for the cation TRIS. Molecular charge per se or chirality did not affect the frequency splitting of the dipolar coupled peaks. The molecules, lactate, ethanol, and alanine, have scalar coupled spins and consequently a double quantum signal in solution. However, spectra acquired from these molecules in muscle showed an additional frequency splitting due to additional dipolar coupling interactions. Due to lack of scalar coupling, spectra from Tris, glycine, and dioxane showed no double quantum signal in solution but did when in muscle. All these observations can be explained by the fact that the net charge on protein filaments dominates the mechanism of dipolar coupling interactions in the highly anisotropic structures in muscle.     

Dielectric properties of multiband electron systems II. Collective modes

Starting from the tight-binding dielectric matrix in the random phase approximation we examine the collective modes and electron-hole excitations in a two-band electronic system. For long wavelengths (q → 0), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tight-binding states. In insulators there are only inter-band charge oscillations. If atomic dipolar transitions are allowed, the corresponding collectivemodes reduce in the asymptotic limit of vanishing bandwidths to Frenkel excitons for an atomic insulator with weak on-site interactions. The finite bandwidths renormalize the dispersion of these modes and introduce a continuum of incoherent inter-band electron-hole excitations. The possible Landau damping of collective modes due to the presence of this continuum is discussed in detail. In conductors the intra-band charge fluctuations give rise to plasmons. If the atomic dipolar transitions are forbidden, the coupling of inter-band collective modes and plasmons tends to zero as q → 0. On the contrary, in dipolar conductors this coupling is strong and nonperturbative, due to the long range monopole-dipole interactions between intra-band and inter-band charge fluctuations. The resulting collective modes are hybrids of intra-band plasmons and inter-band dipolar oscillations. It is shown that the frequency of the lower hybridized longitudinal mode is proportional to the frequency of the transverse dipolar mode when the latter is small. The dielectric instability in a multi-band conductor is therefore characterized by the simultaneous softening of a transverse and a longitudinal mode, which is an important, directly measurable consequence of the present theory.     

Reduction of spin diffusion artifacts from 2D zfr-INADEQUATE MAS NMR spectra

The primary shortcoming of the z-filtered refocused INADEQUATE MAS NMR pulse sequence is the possibility of artifacts introduced during the z-filter due to spin diffusion where by extra peaks in the single-quantum dimension (from other sites in the molecule) appear correlated with a given double-quantum frequency. This is a problem when the spinning speeds are too slow (less than 15 kHz) to sufficiently average the proton-proton homonuclear dipolar couplings. This would be especially important when working with large volume rotors that are difficult to spin fast enough to completely average the homonuclear couplings. In our experiments we used the frequency-switched Lee-Goldberg (FSLG) method of homonuclear decoupling during the z-filter to remove the artifact peaks. This method has the advantage of being quite easy to setup and implement on most modern NMR spectrometers.     

Magnetostrictive and quadrupolar anisotropy in nuclear magnetic fcc systems

The spin hamiltonian for nuclear magnetic order in copper is investigated with respect to magnetoelastic couplings to the lattice. These arise due to the dipolar, Ruderman Kittel and the quadrupolar interaction. While the latter is quenched for the ideal fcc-lattice, it is found that for copper it will dominate the magnetoelastic terms of the nuclear spin hamiltonian. The absolute size of the quadrupole contribution is determined by the effective charge and (anti-) shielding effects. This interaction can give rise to an effective anisotropy in the fcc-system which can be quite large compared to the small stabilisation energies for nuclear order in copper. Consequences for the nuclear ordering in copper are briefly discussed and compared to the available experimental and theoretical data.     

Accretion onto a Kerr black hole in the presence of a dipole magnetic field

We analyze the accretion of charged matter onto a rotating black hole immersed in an aligned dipolar magnetic field. We specialize to motion in the equatorial plane and calculate the ‘Keplerian’ angular momentum distribution, the marginally stable and marginally bound orbits, and the efficiency of mass-to-energy conversion as functions of the angular momentum of the black hole and of the product of the dipole moment and the charge of the infalling matter. Although the detailed results are quite different from those previously obtained in the case of an uniform magnetic field, the astrophysically relevant results are very similar; when hydrodynamical accretion is considered, these effects of the magnetic field are always very small. But for test particles the efficiency can be significantly increased for limited ranges of the parameters.     

Mach Like Principle from Conserved Charges

We study models where the gauge coupling constants, masses and the gravitational constant are functions of some conserved charge in the universe, and furthermore a cosmological constant that depends on the total charge of the universe. We first consider the standard Dirac action, but where the mass and the electromagnetic coupling constant are a function of the charge in the universe and afterwards extend this to curved spacetime and consider gauge coupling constants, the gravitational constant and the mass as a function of the charge of the universe, which represent a sort of Mach principle for all the constants of nature. In the flat space formulation, the formalism is not manifestly Lorentz invariant, however Lorentz invariance can be restored by performing a phase transformation of the Dirac field. One interesting model of this type is one where the action is invariant under rescalings of the Dirac wave function. In the curved space time formulation, there is the additional feature that some of the equations of motion break the general coordinate invariance also, but in a way that can be understood as a coordinate choice only, so the equations are still of the General Relativity type, but with a certain natural coordinate choice, where there is no current of the charge. We have generalized what we have done and also constructed a cosmological constant which depends on the total charge of the universe. We discuss how these ideas work when the space where the charges live is finite. If we were to use some only approximately conserved charge for these constructions, like say baryon number (in the context of the standard model), this will lead to corresponding violations of Lorentz symmetry in the early universe for example. We also briefly discuss another non-local formulations where the coupling constants are functions of the Pontryagin index of some non-abelian gauge field configurations. The construction of charge dependent contributions can also be motivated from the structure of the “infra-red counter terms” needed to cancel infra red divergences for example in three dimensions.     

Limitations on the NMR determination of structural corrections for correlated deformation of partially oriented linear molecules

The dipolar couplings of partially oriented acetylene and biacetylene have been measured in various liquid crystal solvents. The results confirm the theoretical prediction that in linear molecules, due to the interdependence of the direct couplings, the information is drastically reduced and the structures corrected for the correlated deformation cannot be determined. Measured couplings corrected for harmonic vibration fulfill with excellent precision an additivity relation. This indicates that higher-order terms in the theory of correlated deformation can safely be neglected.     

A spin-one Ising model on the Bethe lattice

We study the statistical mechanics of spin-one Ising models on the Bethe lattice assuming that the spins interact by dipolar and quadrupolar interactions. An exact calculation of the properties of the system is performed on the basis of the general formulation of Morita. An exact expression for the Curie temperature is derived and the results are found to be in agreement with those of Obokata and Oguchi who utilized a generalized Bethe approximation to a spin-one Ising system. The nature of variation of the Curie temperature with respect to the change of quadrupolar exchange is discussed for various coordination numbers and the results agree qualitatively with the earlier works. The temperature variation of both dipolar and quadrupolar moments is studied.     

On the Constraints Defining BPS Monopoles

We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the Ercolani-Sinha constraints, and show that the Corrigan-Goddard conditions for constructing monopoles of arbitrary charge can be regarded as a special case of these. As an application, we study the spectral curve of the tetrahedrally symmetric 3-monopole, an example where the Corrigan-Goddard conditions need to be modified. A particular 1-cycle on the spectral curve plays an important rôle in our analysis.     

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.     

Does magnetic charge imply a massive photon?

In Abelian monopole theories the magnetic coupling is required to be enormous. Using the electric-magnetic duality of electromagnetism, it is argued that the existence of such a large, nonperturbative magnetic coupling should lead to a phase transition where magnetic charge is permanently confined and the photon becomes massive. The apparent masslessness of the photon could then be used as an argument against the existence of such a large, nonperturbative magnetic charge. Finally it is shown that even in the presence of this conjectured dynamical mass generation the Cabbibo-Ferrari (1962) formulation of magnetic charge gives a consistent theory.     

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.     

Theory of surface recombination of spin-polarized hydrogen

A theory is presented, based on the Faddeev equations, for direct two-body recombination of hydrogen atoms on a liquid helium surface. The equations developed are applicable to hydrogen or deuterium atoms in any spin state, but are applied in particular to dipolar recombination ofb state hydrogen atoms. The equations yield terms corresponding to one- and two-step processes. These terms are calculated for low temperatures (T-0.1 to 1.1 K) and high field strengths (B=4 to 14 T). The one-step term increases slowly withB, while the two-step term is rapidly decreasing. While the overall rate is quite small (5×10^–18 cm²/s) compared to recombination by two-body spin-relaxation, the results have important consequences in understanding the experimentally measured three-atom dipolar surface recombination rates. In three-atom recombination, where the role of spin-relaxation and the two-atom one-step processes are repressed, the role of the underlying two-atom, two-step process is enhanced. The field dependence of the process relevant to the three-atom system is calculated and found to be in fairly good agreement with the experimental three-atom data. The role of possible liquid excitations in enhancing the contribution of the two-step processes is also discussed.     

Considerations on a unified field theory

A geometrical formulation of gravitational and electromagnetic fields is presented for systems composed of point mass charged particles where the charge is small enough that electromagnetic radiation may be neglected. It is assumed that such charges produce a non-negligible contribution to the metric, and that their motion describes geodesics in the total metric which consists of that due to the charge itself and that due to the external environment of the charge. The above, together with several other assumptions yields the customary Einstein-Maxwell relations. It is demonstrated that this construction is not merely a re-statement of the Einstein-Maxwell theory in different terms.     

Dipolar Biexcitons in Lateral Traps in Si/SiGe/Si Heterostructures

Si/Si_1–xGe_x/Si heterostructures with large-scale (micrometer-size) lateral potential fluctuations at the upper SiGe/Si-cap heterointerface are grown. These potential fluctuations are caused by partial strain relaxation in the SiGe layer. Low-temperature photoluminescence (PL) spectra show that these fluctuations form lateral traps where photoexcited nonequilibrium charge carriers are accumulated and bind into dipolar excitons, which ultimately recombine. At temperatures below 6 K, a new narrow line with a width considerably less than that of the dipolar exciton PL line emerges in the spectra as the level of excitation increases. It is shown that this line is associated with the recombination of dipolar biexcitons in large-scale traps.     

Electrophoretic mobility without charge driven by polarisation of the nanoparticle–water interface

Polarisation of the interface, spontaneously occurring when water is in contact with hydrophobic solutes or air, couples with the uniform external field to produce a non-zero force acting on a suspended particle. This force exists even in the absence of a net particle charge, and its direction is affected by the first-order, dipolar and the second-order, qudrupolar orientational order parameters of the interfacial water. The quadrupolar polarisation gives rise to an effectively negative charge. The corresponding surface charge density is inversely proportional to the area of the shear surface. As a result, the overall contribution from the quadrupolar polarisation to the particle mobility becomes negligible compared to experimentally reported values for particles exceeding a few nanometres in size. In contrast, the contribution of the dipolar order of the interface to the effective surface charge scales inversely with the particle size and dominates the zero-charge mobility of submicron particles. The corresponding electrokinetic charge is determined by the preferential orientation of interfacial dipoles relative to the surface normal.