Higher Multipole Moments Research Articles

Hidden quasiconservation laws in fracton hydrodynamics.

We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden quasiconservation laws, in which certain higher multipole moments can only decay due to dangerously irrelevant corrections to hydrodynamics. We present two simple examples of this phenomenon. First, an isotropic dipole-conserving fluid in the infinite plane conserves an infinite number of harmonic multipole charges within linear response; we calculate the decay or growth of these charges due to dangerously irrelevant nonlinearities. Second, we consider a model with xy and x^{2}-y^{2} quadrupole conservation, in addition to dipole conservation, which is described by isotropic fourth-order subdiffusion, yet has dangerously irrelevant sixth-order corrections necessary to relax the harmonic multipole charges. We confirm our predictions for the anomalously slow decay of the harmonic conserved charges in each setting by using numerical simulations, both of the nonlinear hydrodynamic differential equations, and in quantum automaton circuits on a square lattice.

Observation of a polarized stochastic gravitational-wave background in pulsar-timing-array experiments

We study the observation of polarized stochastic gravitational-wave background (SGWB) in pulsar-timing-array experiments. The time residual for an observed pulsar is formulated as a line-of-sight integral that incorporates the effects of the pulsar term, from which we construct the correlation function of the time residual between a pair of pulsars in terms of the overlap reduction functions (ORFs) for the SGWB intensity and polarization anisotropies. Our formulation provides a numerical scheme for computing the ORFs for high multipole moments and the lowest-moment ORFs for the SGWB linear polarization are worked out for the first time.

Generalized theory of clustering of extended galaxies with core halos

We discuss the clustering of core halo-galaxies of radius predicted by gravitational lensing. We appeal to a blend of recent (1) mathematical results and (2) statistical mechanics techniques. The exact configurational integrals of extended galaxies is evaluated together with the pertinent partition functions, the corresponding thermodynamics, and the distribution function. We are motivated by data regarding observational deflections and measured Einstein radius in gravitational microlensing and macrolensing. The halo size comparable with that of the Einstein radius or the Schwarzschild one, is taken as the lower limit of the configurational integral. The work may provide new insight with regards to gravitational lensing. Giant arcs produced by gravitational lensing, as observed from clusters of galaxies, seem to require the inclusion of substantial quadruple and higher multipole moments in the cluster potential. This opens a possibility of ”modified gravities” , in clustering studies that compare data associated to gravitational lensing.

Dynamics of a droplet driven by an internal active device

A liquid droplet, immersed into a Newtonian fluid, can be propelled solely by internal flow. In a simple model, this flow is generated by a collection of point forces, which represent externally actuated devices or model autonomous swimmers. We work out the general framework to compute the self-propulsion of the droplet as a function of the actuating forces and their positions within the droplet. A single point force, F with general orientation and position, r_0, gives rise to both, translational and rotational motion of the droplet. We show that the translational mobility is anisotropic and the rotational mobility can be nonmonotonic as a function of | r_0|, depending on the viscosity contrast. Due to the linearity of the Stokes equation, superposition can be used to discuss more complex arrays of point forces. We analyse force dipoles, such as a stresslet, a simple model of a biflagellate swimmer and a rotlet, representing a helical swimmer, driven by an external magnetic field. For a general force distribution with arbitrary high multipole moments the propulsion properties of the droplet depend only on a few low order multipoles: up to the quadrupole for translational and up to a special octopole for rotational motion. The coupled motion of droplet and device is discussed for a few exemplary cases. We show in particular that a biflagellate swimmer, modeled as a stresslet, achieves a steady comoving state, where the position of the device relative to the droplet remains fixed. In fact there are two fixpoints, symmetric with respect to the center of the droplet. A tiny external force selects one of them and allows to switch between forward and backward motion.

Multipolar electrostatics for hairpin and pseudoknots in RNA: Improving the accuracy of force field potential energy function.

Molecular dynamics (MD) simulations that rely on force field methods has been widely used to explore the structure and function of RNAs. However, the current commonly used force fields are limited by the electrostatic description offered by atomic charge, dipole and at most quadrupole moments, failing to capture the anisotropic picture of electronic features. Actually, the distribution of electrons around atomic nuclei is not spherically symmetric but is geometry dependent. A multipolar electrostatic model based on high rank multipole moments is described in this work, which allows us to combine polarizability and anisotropy of electron density. RNA secondary structure was taken as a research system, and its substructures including stem, loops (hairpin loop, bulge loop, internal loop, and multi-branch loop), and pseudoknots (H-type and K-type) were investigated, respectively, as well as the hairpin. First, the atom-atom electrostatic properties derived from one chain of a duplex RNA 2MVY in our previous work (Ref. 58) were measured by the pilot RNA systems of hairpin, hairpin loop, stem, and H-type pseudoknot, respectively. The prediction results were not satisfactory. Consequently, to obtain a general set of electrostatic parameters for RNA force fields, the convergence behavior of the atom-atom electrostatic interactions in the pilot RNA systems was explored using high rank atomic multipole moments. The pilot RNA systems were cut into four types of different-sized molecular fragments, and the single nucleotide fragment and nucleotide-paired fragment proved to be the most reasonable systems for base-unpairing regions and base-pairing regions to investigate the convergence behavior of all types of atom-atom electrostatic interactions, respectively. Transferability of the electrostatic properties drawn from the pilot RNA systems to the corresponding test systems was also investigated. Furthermore, the convergence behavior of atomic electrostatic interactions in other substructures including bulge loop, internal loop, multi-branch loop, and K-type pseudoknot was expected to be modeled via the hairpin.

Electric field of a charge in the vicinity of a higher dimensional black hole

We find the electric field of a point charge in the presence of a higher-dimensional black hole. As the charge is lowered to the horizon, all higher multipole moments go to zero, and only the Coulomb field remains.

Irreducible Cartesian multipole decomposition of scattered light with explicit contribution of high order toroidal moments

Multipole decomposition is a powerful tool for analysis of electromagnetic systems. This work considers high order irreducible Cartesian multipole moments in approximation of electric 32-pole and magnetic 16-pole. The explicit contributions to scattering of high order toroidal moments up to toroidal electric octupole and toroidal magnetic quadrupole are demonstrated for a dielectric high refractive index scatterer.

Bondi mass with a cosmological constant

The mass loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant $\Lambda\in\R$ was recently worked out, using the Newman-Penrose-Unti approach. In that same article, an expression for the Bondi mass of the isolated system, $M_\Lambda$, for the $\Lambda>0$ case was proposed. The stipulated mass $M_\Lambda$ would ensure that in the absence of any incoming gravitational radiation from elsewhere, the emitted gravitational waves must carry away a positive-definite energy. That suggested quantity however, introduced a $\Lambda$-correction term to the Bondi mass $M_B$ (where $M_B$ is the usual Bondi mass for asymptotically flat spacetimes) which would involve not just information on the state of the system at that moment, but ostensibly also its past history. In this paper, we derive the identical mass-loss equation using an integral formula on a hypersurface formulated by Frauendiener based on the Nester-Witten identity, and argue that one may adopt a generalisation of the Bondi mass with $\Lambda\in\R$ \emph{without any correction}, viz. $M_\Lambda=M_B$ for any $\Lambda\in\R$. Furthermore with $M_\Lambda=M_B$, we show that for \emph{purely quadrupole gravitational waves} given off by the isolated system (i.e. when the "Bondi news" $\sigma^o$ comprises only the $l=2$ components of the "spherical harmonics with spin-weight 2"), the energy carried away is \emph{manifestly positive-definite} for the $\Lambda>0$ case. For a general $\sigma^o$ having higher multipole moments, this perspicuous property in the $\Lambda>0$ case still holds if those $l>2$ contributions are weak --- more precisely, if they satisfy any of the inequalities given in this paper.

Multipole Moments of Lipid Headgroups

As implied by their names, polar lipids have non-uniform distribution of electric charge. In particular, the dipole moment of phosphatidylcholine is on the order of 5 eA. Dipole-dipole interactions, therefore, play a significant role in the overall lipid interactions at the lipid-water interface. In addition, given the proximity of neighboring lipid headgroups, higher multipole moments can also be relevant. Treating the lipid head group as a collection of partial charges, we investigated correlations between dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole moments for lipid head groups obtained from all atom membrane simulations. We discuss the effects of near-neighbor interactions as well as correlations at larger length scales. Lipid headgroup interactions and correlations as described here are relevant to lipid phase transitions as well as to interactions with membrane insertions such as ion channels and transmembrane protein domains in general.

Effects of cosmic strings with delayed scaling on CMB anisotropy

The network of cosmic strings generated in a phase transition during inflation enters the scaling regime later than that of usual strings. If it occurs after the recombination, temperature anisotropies of the cosmic microwave background (CMB) at high multipole moments are significantly reduced. In this paper, we study such effects qualitatively and show that the constraint on the cosmic string tension from the CMB temperature anisotropies and B-mode polarizations can be relaxed. It is shown to be difficult to explain the recent BICEP2 and POLARBEAR results in terms of signals induced by cosmic strings alone even if we take into account the delayed scaling. However, the inflationary tensor-to-scalar ratio required to explain the observed B-mode signals can be slightly reduced to be consistent with the Planck constraint.

Relativistic effects in the tidal interaction between a white dwarf and a massive black hole in Fermi normal coordinates

We consider tidal encounters between a white dwarf and an intermediate mass black hole. Both weak encounters and those at the threshold of disruption are modeled. The numerical code combines mesh-based hydrodynamics, a spectral method solution of the self-gravity, and a general relativistic Fermi normal coordinate system that follows the star and debris. Fermi normal coordinates provide an expansion of the black hole tidal field that includes quadrupole and higher multipole moments and relativistic corrections. We compute the mass loss from the white dwarf that occurs in weak tidal encounters. Secondly, we compute carefully the energy deposition onto the star, examining the effects of nonradial and radial mode excitation, surface layer heating, mass loss, and relativistic orbital motion. We find evidence of a slight relativistic suppression in tidal energy transfer. Tidal energy deposition is compared to orbital energy loss due to gravitational bremsstrahlung and the combined losses are used to estimate tidal capture orbits. Heating and partial mass stripping will lead to an expansion of the white dwarf, making it easier for the star to be tidally disrupted on the next passage. Finally, we examine angular momentum deposition. By including the octupole tide, we are able for the first time to calculate deflection of the center of mass of the star and debris. With this observed deflection, and taking into account orbital relativistic effects, we compute directly the change in orbital angular momentum and show its balance with computed spin angular momentum deposition.

Effect of Solvation on the Vertical Ionization Energy of Thymine: From Microhydration to Bulk

The effect of hydration on the vertical ionization energy (VIE) of thymine was characterized using equation-of-motion ionization potential coupled-cluster (EOM-IP-CCSD) and effective fragment potential (EFP) methods. We considered several microsolvated clusters as well as thymine solvated in bulk water. The VIE in bulk water was computed by averaging over solvent-solute configurations obtained from equilibrium molecular dynamics trajectories at 300 K. The effect of microsolvation was analyzed and contrasted against the combined effect of the first solvation shell in bulk water. Microsolvation reduces the ionization energy (IE) by about 0.1 eV per water molecule, while the first solvation shell increases the IE by 0.1 eV. The subsequent solvation lowers the IE, and the bulk value of the solvent-induced shift of thymine's VIE is approximately -0.9 eV. The combined effect of the first solvation shell was explained in terms of specific solute-solvent interactions, which were investigated using model structures. The convergence of IE to the bulk value requires the hydration sphere of approximately 13.5 Å radius. The performance of the EOM-IP-CCSD/EFP scheme was benchmarked against full EOM-IP-CCSD using microhydrated structures. The errors were found to be less than 0.01-0.02 eV. The relative importance of the polarization and higher multipole moments in EFP model was also investigated.

A new method for computing quasi-local spin and other invariants on marginally trapped surfaces

We accurately compute the scalar 2-curvature, Weyl scalars, associated quasi-local spin, mass and higher multipole moments on marginally trapped surfaces in numerical 3+1 simulations. To determine the quasi-local quantities, we introduce a new method which requires a set of invariant surface integrals, allowing for surface grids of a few hundred points only. The new technique circumvents solving the Killing equation and is also an alternative to approximate Killing vector fields. We apply the method to a perturbed non-axisymmetric black hole ringing down to Kerr and compare the quasi-local spin with other methods that use Killing vector fields, coordinate vector fields, quasi-normal ringing and properties of the Kerr metric on the surface. Interesting is the agreement with the spin of approximate Killing vector fields during the phase of perturbed axisymmetry. Additionally, we introduce a new coordinate transformation, adapting spherical coordinates to any two points on the sphere such as the two minima of the scalar 2-curvature on axisymmetric trapped surfaces.

A general formula for the rate of resonant transfer of energy between two electric multipole moments of arbitrary order using molecular quantum electrodynamics

A general expression is derived for the matrix element for the resonant transfer of energy between an initially excited donor species and an acceptor moiety in the ground state, with each entity possessing an electric multipole moment of arbitrary order. In the quantum electrodynamical framework employed, the coupling between the pair is mediated by the exchange of a single virtual photon. The probability amplitude found from second-order perturbation theory is a product of the electric moments located at each center and the resonant multipole-multipole interaction tensor. Using the Fermi golden rule, a general formula for the rate of energy transfer is obtained. As an illustration of the efficacy of the theory developed, rates of excitation energy exchange are calculated for systems interacting through dipole-quadrupole, dipole-octupole, quadrupole-quadrupole, and the familiar dipole-dipole coupling. For each of the cases examined, the near- and far-zone limits of the migration rate are calculated from the result valid for all donor-acceptor separations beyond wave function overlap. Expression of the octupole contribution to the transfer rate in terms of its irreducible components of weights 1 and 3 leads to new features. The octupole weight-1 term is found to contribute only when the interaction is retarded, while the dipole-octupole weight-1 contribution appears as a higher-order correction term to the dipole-dipole rate. Order of magnitude estimates are given for the contributions of dipole-quadrupole and dipole-octupole terms relative to the leading dipole-dipole rate for near-, intermediate-, and far-zone separations to further understand the role played by higher multipole moments in the transfer of excitation and the mechanism dominating the process.

Cumulative coordinate technique for approximation of high atomic multipole moments of aluminophosphate sieves on the basis of electron densities calculated with DFT methods

AbstractAtomic multipole moments (AMMs) for aluminophosphate sieves (ALPOs) were evaluated considering the electron density (ED) computed with the CRYSTAL98 code at various periodic Density Functional Theory (PDFT) levels as well as basis sets. Using the EDs calculated with B3LYP, Perdew‐Wang (PW91), and Perdew‐Burke‐Ernzerhof (PBE) functionals, “Mulliken” AMMs were computed within the scheme developed by Saunders et al. and approximated using a cumulative coordinate (CC) scheme similar to the one developed earlier for AMMs calculated from Hartree‐Fock EDs. The convergence of the AMMs with the basis set is discussed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

The elusive atomic rationale for DNA base pair stability.

A systematic analysis of the electrostatic interaction between 27 natural DNA base pairs was carried out, based on ab initio correlated wave functions and the topology of the electron density. Using high rank multipole moments we show that the atomic partitioning of the interaction energy contains many substantial contributions between distant atoms. Profiles of cumulative energy versus internuclear distance show large fluctuations and provide an electrostatic fingerprint of the partitioning of interaction energy in a complex. A quantified comparison between each pair of energy profiles, one for each base pair, makes clear that there is no correlation between the total base pair interaction energy and the shape of the profile. In other words, base pairs with similar interaction energy are not stable for the same reasons in terms of atomic partitioning. In summary, simple rules to rationalize the pattern of energetic stability of naturally occurring base pairs in terms of subsets of atoms are elusive. Our work cautions against inappropriate use of Jorgensen's secondary interaction hypothesis.

The theory of particle diffusion in a strong random magnetic field with an allowance for higher multipole moments of the distribution function

The kinetic equation including a small-scale collisional integral for the particles propagating in a strong random and regular magnetic field [29] is solved by expanding the distribution function into series in spherical harmonics of the particle momentum angles. Using methods of the quantum theory of the angular moment [41], the equations for higher multipole moments of the distribution function in the space of momentum angles are derived and solved in the stationary case for the galactic cosmic rays in interplanetary space. The observed amplitudes and phases of the diurnal variation harmonics can be explained using the results of measurements of the interplanetary magnetic field performed on board the Ulysses spacecraft [12–14] and other satellites [45, 46] with an allowance for redistribution of the interplanetary and interstellar magnetic field lines. The spatial structure of the convection and diffusion fluxes of the galactic cosmic rays is refined. Formulas taking into account a change in the Earth’s axis tilt relative to the direction toward the Sun are derived, which allow the annual changes in contributions to the diurnal variation harmonics to be determined. The equation of diffusion taking into account the 2nd harmonic is obtained, and the contribution of this effect to the relative particle density in the cosmic rays in a spherically symmetric case is analyzed.

Effects of the Quadrupole Moment of Rapidly Rotating Neutron Stars on the Motion of the Accretion Disks

We investigate the effects of the quadrupole moment of rapidly rotating neutron stars (NSs) on the motion of the accretion disks. The geometry outside rapidly rotating NSs does not agree with that of Kerr black holes, so that we must correctly take into account the quadrupole moment (and the higher multipole moments) of NS, which depends on their equation of state. We show that the magnitude of the quadrupole dependent term appearing in several orbital frequencies is comparable to that of the spin-orbit (SO) coupling term for orbits near the surface of rapidly rotating NSs, and effects of the quadrupole moment largely suppress the SO coupling effect. Observations of the low-mass X-ray binaries (LMXBs) with the Rossi X-ray

Time-dependent multipoles and their application for radiation from volume source distributions

The radiation from a pulsed source distribution is expressed directly in the time-domain using a sum of time-dependent spherical (multipole) wave functions. Two alternative expressions for the time-dependent multipole moments (the excitation pulses) are derived. It is shown how they are related to the time-dependent plane-wave spectrum of the source (obtained via a Radon transform of the source distribution in the four space-time coordinates). Furthermore, the time-dependent multipole moments, and thereby the total time-dependent field outside the source region, are completely determined by the time-dependent radiation pattern. The series convergence is addressed by showing that the high order multipole moments tend to the quasistatic extension of the static multipole moments. This also puts an upper limit on the spatial resolution that can be achieved by a source distribution with specified size and pulse length.

Development of Molecules for All‐Optical Switching Devices

AbstractThe prospects for developing efficient molecular devices for all‐optical switching are discussed on the basis of measurements of the second molecular hyperpolarizability coefficient, γ, responsible for third harmonic generation. More than twenty structurally different organic compounds comprising organic metal complexes, polyenes, cyanines, and derivatives of triarylmethyl cations have been examined. The dependence of γon the number of π‐electrons in the nonlinear chromophore leads to a classification of the data in four categories; (i) the polyene ‐ like, (ii) the cyanine‐like, (iii) the bis‐1,2‐dithiole metal complexes, and (iv) a new category comprising molecules with significant ligand‐to‐metal or other “periphery‐to‐center” charge transfer transitions. Values of γ as high as 3 × 10−32 esu are reported in this new category. The importance of changes in higher multipole moments such as quadrupole and octupole moments upon electronic excitation is addressed. Strategies for improved molecular and materials design are discussed.