Extended Charge Distribution Research Articles

The Cornell black hole

The Cornell potential can be derived from a recently proposed non-local extension of Abelian electrodynamics. Non-locality can be alternatively described by an extended charge distributions in Maxwell electrodynamics. We state that in these models the energy momentum tensor necessarily requires the presence of the interaction term between the field and the charge itself. We show that this extended form of energy momentum tensor leads to an exact solution of the Einstein equations describing a charged AdS black hole. We refer to it as the “Cornell black hole”(CBH). Identifying the effective cosmological constant with the pressure of Van der Waals fluid, we study the gas-liquid phase transition and determine the critical parameters.

Estimation of Charge Transfer During Long Continuing Currents in Natural Downward Flashes Using Single‐Station E‐Field Measurements

AbstractThe amount of charge transferred to ground during long continuing currents in natural downward flashes can be obtained either through direct current measurements or using remote electromagnetic fields, if direct measurements are not feasible. In this study, measurements of a single‐station E‐field antenna were used to estimate charge transfer during continuing currents. With time‐synchronized high‐speed video recordings serving as ground‐truth data for continuing current occurrence, we estimate transferred charge during long continuing currents in 140 natural downward flashes from electric field changes, assuming a simple monopole charge model. We present average parameters for the duration, transferred charge, amplitude, and the average amplitude on five segments along the channel. Further, we perform a simulation to investigate the estimation performance of the monopole charge model, when the cloud charge is spatially extended. Using an extended charge distribution model, we generate single‐station remote field waveforms and infer the charge with the monopole model. Comparison of the known and inferred charge yields estimation errors depending on the leader orientation, its spatial extension, and the observation distance. A Monte Carlo approach is carried out to statistically evaluate parameter deviations. This novel estimation error analysis sheds light on the limitations of the applied simple techniques for charge transfer estimation of long continuing currents using single‐station electric field measurements.

Ab initio calculations of reactor antineutrino fluxes with exact lepton wave functions

New ab initio calculations of the isotopic reactor antineutrino fluxes are provided with exact numerical calculations of the lepton wave functions, assuming all the decay branches are allowed GT transitions. We illustrate that the analytical Fermi function and finite size effect each could have the largest spectral deviation of O(10%), whereas the effect of their combination could result in spectral deviations at the level of 5%—10%. Meanwhile, we also find that several forms of the extended charge distributions have negligible effects on the spectral variation. Using the state-of-the-art nuclear databases, compared to usual ab initio calculations using the analytical single beta decay spectrum, our new calculation shows sizable but opposite spectral deviations at the level of 2%—4% for the cumulative antineutrino and electron energy spectra which may partially contribute to the observed spectral excess in the high energy antineutrino range. Finally we observe that the bias of analytical beta decay spectrum approximation is rather universal for all the four fissionable isotopes.

Systematic Study of the Nuclear Structure for Some Exotic Nuclei Using Skyrme–Hartree–Fock Method

The ground state charge, neutron, proton and matter densities, the associated nuclear radii and the binding energy per nucleon of 8B, 17Ne, 23Al and 27P halo nuclei have been investigated using the Skyrme–Hartree–Fock (SHF) model with the new SKxs25 parameters. According to the calculated results, it is found that the SHF model with these Skyrme parameters provides a good description on the nuclear structure of above proton-rich halo nuclei. The elastic charge form factors of 8B and 17Ne halo nuclei and those of their stable isotopes 10B and 20Ne are calculated using plane-wave Born approximation with the charge density distributions obtained by SHF model to investigate the effect of the extended charge distributions of proton-rich nuclei on the elastic electron scattering. Calculations show that the major difference between the elastic charge form factors of halo nuclei and those of their stable isotopes is caused by the variation in the charge density distributions, especially the details of the outer parts.

Simulation study on the structural properties of colloidal particles with offset dipoles

A major research theme in materials science is determining how the self-assembly of new generations of colloidal particles of complex shape and surface charge is guided by their interparticle interactions. In this paper, we describe results from quasi-2D Monte Carlo simulations of systems of colloidal particles with offset transversely-oriented extended dipole-like charge distributions interacting via an intermediate-ranged Yukawa potential. The systems are cooled slowly through an annealing procedure during which the temperature is lowered in discrete steps, allowing the system to equilibrate. We perform ground state calculations for two, three and four particles at several shifts of the dipole vector from the particle center. We create state diagrams in the plane spanned by the temperature and the area fraction outlining the boundaries between fluid, string-fluid and percolated states at various values of the shift. Remarkably we find that the effective cooling rate in our simulations has an impact on the structures formed, with chains being more prevalent if the system is cooled quickly and cyclic structures more prevalent if the system is cooled slowly. As the dipole is further shifted from the center, there is an increased tendency to assemble into small cyclic structures at intermediate temperatures. These systems further self-assemble into open lattice-like arrangements at very low temperatures. The novel structures identified might be useful for photonic applications, new types of porous media for filtration and catalysis, and gel matrices with unusual properties.

Poisson-Boltzmann model of electrolytes containing uniformly charged spherical nanoparticles.

Like-charged macromolecules typically repel each other in aqueous solutions that contain small mobile ions. The interaction tends to turn attractive if mobile ions with spatially extended charge distributions are added. Such systems can be modeled within the mean-field Poisson-Boltzmann formalism by explicitly accounting for charge-charge correlations within the spatially extended ions. We consider an aqueous solution that contains a mixture of spherical nanoparticles with uniform surface charge density and small mobile salt ions, sandwiched between two like-charged planar surfaces. We perform the minimization of an appropriate free energy functional, which leads to a non-linear integral-differential equation for the electrostatic potential that we solve numerically and compare with predictions from Monte Carlo simulations. Nanoparticles with uniform surface charge density are contrasted with nanoparticles that have all their charges relocated at the center. Our mean-field model predicts that only the former (especially when large and highly charged particles) but not the latter are able to mediate attractive interactions between like-charged planar surfaces. We also demonstrate that at high salt concentration attractive interactions between like-charged planar surfaces turn into repulsion.

Radiation reaction: a case study

We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B0. This is a physically relevant, but difficult, dynamical problem, to which contributions range over more than 100 years. Specifically, we will study the Sommerfeld–Page approximation, which assumes an extended charge distribution at small velocities. The memory equation is then linear and many details become available. We discuss how the effective friction equation arises in the limit of ‘small’ B0 and contrast this result with the standard Taylor expansion resulting in a second-order equation for the velocity of the charge.

Analogy of the grounded conducting sphere image problem with mirror optics

We show that in the grounded conducting sphere image problem, all the necessary information about the image charge can be found from a mirror equation and a magnification formula. Then, we propose a method to solve the image problem for an extended charge distribution near a grounded conducting sphere.

One-component plasma of point charges and of charged rods

An approximate theory is developed to describe the properties of mobile particles with extended charge distributions in the presence of a neutralizing fixed background charge. Long-wavelength fluctuations of the electric potential are handled within a variational perturbation approximation, and the short-wavelength fluctuations are handled within a cumulant (fugacity) expansion. The distinct treatment of these two contributions to the free energy enables the theory to provide quantitative predictions for the properties of these systems from the weak- to the strong-coupling regimes. With this theory, we study three different variations in the classical one-component plasma model: a plasma of point charges, a plasma of particles consisting of 8 linearly bonded point charges (8-mer), and a plasma of line charges. The theory was found to agree well with the available computer simulation data for the electrostatic interaction energy of these systems for all values of the plasma coupling parameter examined ( Gamma=0 to 400). In addition, we find that both the 8-mer rod and the line charge systems form a strongly ordered nematic phase, which is entirely driven by electrostatic interactions. The nematic phase only exists within a finite range of lengths of the charged particles. If the particles are too short or too long, the nematic phase does not appear. Finally, we find that the nematic phase is stable over a broader range of conditions for the line charge system than for the 8-mer rod system; consequently, the phase behavior of the one-component plasma is sensitive to the manner in which the charge is distributed on the particles.

Rotational reorientation dynamics of Rhodamine 700 in different excited states

The rotational reorientation dynamics of rhodamine 700 (LD700) in the first (S 1) and the fifth (S 5) excited state in three aprotic polar solvents have been investigated using femtosecond time-resolved stimulated emission pumping fluorescence depletion (FS TR SEP TD) spectroscopy. In both excited states, the overall rotational relaxation of LD700 occurs on a time scale of 40–230 ps depending on the solvent, and a quantitative analysis of this time constant has been performed using the Stokes–Einstein–Debye (SED) hydrodynamic theory combined with the extended charge distribution model developed by Alavi and Waldeck. The experimentally measured reorientation times for LD700 in S 5 are smaller than those in S 1, which is in accord with the predictions by the SED theory. In addition, for LD700 in S 5, a rapid initial decrease on the time scale less than 0.5 ps has been found. According to our analysis, this fast component may account for the rapid internal conversion from S 5 to S 1, and the rate of internal conversion was found to be sensitive to the solvent polarity.

Rotational Reorientation Dynamics of Oxazine 750 in Polar Solvents

The rotational reorientation dynamics of oxazine 750 (OX750) in the first (with pump pulse at 660 nm) and a higher excited state (with pump pulse at 400 nm) in different polar solvents have been investigated using femtosecond time-resolved stimulated emission pumping fluorescence depletion (FS TR SEP FD) spectroscopy. In both excited states, three different anisotropy decay laws have been observed for OX750 in different solvents. Only in acetone and formamide could the anisotropy decays of OX750 be described by single-exponential functions, whereas the anisotropy decays have been found to exhibit biexponential behavior in other solvents. The slower anisotropy decay observed in all of the solvents has been assigned to the overall rotational relaxation of OX750 molecules, and a quantitative analysis of this time constant has been performed using the Stokes-Einstein-Debye hydrodynamic theory and the extended charge distribution model developed by Alavi and Waldeck. In both methanol and ethanol, a faster anisotropy decay on the order of picoseconds and a slower anisotropy decay on the hundreds of picoseconds time scale are observed. The most likely explanation for the faster anisotropy involves the rotation of the transition dipole moment in the excited state of OX750 resulting from the electron transfer (ET) reaction taking place from the alcoholic solvents to the OX750 chromophore. As a possible explanation, the wobbling-in-the-cone model has been used to analyze the biexponential anisotropy decays of OX750 in dimethylformamide (DMF) and dimethyl sulfoxide (DMSO). The observed faster anisotropy decays on the hundreds of femtoseconds time scale in DMF and DMSO are ascribed to the wobbling-in-the-cone motion of the ethyl group of OX750, which is sensitive to the strength of the hydrogen bond formed between the solvent and the protonation site of OX750.

Infrared spectra of SF6−∙(H2O)n (n=1–3): Incipient reaction and delayed onset of water network formation

We present data on the microsolvation of an extended charge distribution with SF(6)(-) as a model system. Infrared spectroscopy, aided by ab initio calculations, shows that the first two water molecules attach to the ion by a combination of single ionic H bonds, sharing one of the F atoms, and weak electrostatic interactions with other F atoms in the ion. No water-water bonds are formed at the dihydrate level, which is an unusual observation, given the strong propensity of water to form H-bonded networks. The onset of water networks occurs with the addition of the third water molecule. Moreover, the attachment of the first two water molecules considerably weakens the SF bond of the F atom involved in bonding to both ligands, indicating a possible mechanism for water-induced reactions.

Isotopic effects for the ground 1S1(L=) states in the light two-electron ions

The total energies and various bound state properties are determined to very high accuracy for the ground 1 (1)S(L=0) states in some light two-electron ions, including the Li(+), Be(2+), B(3+), and C(4+) ions. The corrections due to the finite nuclear masses and lowest order QED corrections ( approximately alpha(3)) are considered/computed for each of these ions. In particular, the specific mass shift is determined for each of the Li(+), Be(2+), B(3+), and C(4+) ions. We also discuss the field shift related to the extended nuclear charge distribution.

A variational field theory for solutions of charged, rigid particles

A general field theoretic formalism is developed for dealing with solutions of particles with rigid charge distributions. Combined with the mean-field approximation, the resulting theory extends the Poisson–Boltzmann equation to incorporate the presence of structured ions (e.g., uniformly charged rods or disks). When combined with a first-order variational approximation, the resulting theory, in the low density limit, is a generalization of the Debye–Hückel theory to extended charge distributions and reduces to the standard expressions when applied to point charges. A first-order variational theory is applied to solutions of uniformly charged disks and to solutions of uniformly charged disks with a neutralizing ring charge to examine the influence of electrostatic interactions on the isotropic-nematic transition.

A PHENOMENOLOGICAL DETERMINATION OF THE PION-NUCLEON SCATTERING LENGTHS FROM PIONIC HYDROGEN

A model independent expression for the electromagnetic corrections to a phenomenological hadronic pion-nucleon (πN) scattering length ah, extracted from pionic hydrogen, is obtained. In a non-relativistic approach and using an extended charge distribution, these corrections are derived up to terms of order α2 log α in the limit of a short-range hadronic interaction. We infer [Formula: see text] which gives for the πNN coupling through the GMO relation [Formula: see text].

Molecular Rotation as a Tool for Exploring Specific Solute–Solvent Interactions

Solute-solvent interactions play an important role in determining the physicochemical properties of liquids and solutions. As a consequence, understanding these interactions has been one of the long-standing problems in physical chemistry. This Minireview describes our approach towards attaining this goal, which is to investigate rotational relaxation of a pair of closely related, medium-sized nondipolar solutes in a set of appropriately chosen solvents. Our studies indicate that solute-solvent hydrogen bonding significantly hinders solute rotation. We have also examined the role of solvent size both in the absence and presence of specific interactions and it has been observed that the size of the solvent has a bearing on solute rotation especially in the absence of specific interactions. Our results point to the fact that only strong solute-solvent hydrogen bonds have the ability to impede the rotation of the solute molecule because, in such a scenario, hydrogen-bonding dynamics and rotational dynamics transpire on comparable time scales. This aspect has been substantiated by measuring the reorientation times of the chosen solutes in solvents such as ethanol and trifluoroethanol, which have distinct hydrogen-bond donating and accepting abilities, and correlating them with solute-solvent interaction strengths. As an alternative treatment, it has been shown that specific interactions between the solute and the solvent can be modeled as dielectric friction with the extended charge distribution model. This approach is not unrealistic considering the fact that specific as well as non-specific interactions are electrostatic by nature and the differences between them are subtle.

A phenomenological π−p scattering length from pionic hydrogen

We derive a closed, model independent, expression for the electromagnetic correction factor to a phenomenological hadronic scattering length ah extracted from a hydrogenic atom. It is obtained in a non-relativistic approach and in the limit of a short ranged hadronic interaction to terms of order α2logα using an extended charge distribution. A hadronic πN scattering length ahπ−p=0.0870(5)mπ−1 is deduced leading to a πNN coupling constant from the GMO relation gc2/(4π)=14.04(17).

Relationship between charge distribution and its image by electrostatic force microscopy

We shall demonstrate in this article that characterization of the charge distribution by electrostatic force microscopy is not straightforward: we will stress the important role played by the electrostatic images of the scanned charge distribution in the tip and by the operating mode in the formation of extra features in images obtained with this instrument. To illustrate this, we will describe two models that correspond to the scanning of small and extended charge distributions. These models will be compared with experimental images.

Rotational Diffusion of Coumarins in Electrolyte Solutions: The Role of Ion Pairs

In an attempt to explore how electrolyte ions influence the friction experienced by solutes with different functional groups, rotational diffusion of two structurally similar coumarins, coumarin 343 (C343) and coumarin 334 (C334), has been studied in dimethyl sulfoxide (DMSO) at several concentrations of LiNO3. The two coumarins are almost identical except for the different functional groups in the 3-position; C343 has −COOH whereas C334 has −COCH3. Because of the presence of the −COOH functional group, C343 exists as both anionic and neutral species in DMSO. Although both anionic and neutral forms of C343 exist in the ground state, C343 predominantly exists as neutral species in the excited state. The measured reorientation time of C343 in DMSO is slower by a factor of 2 compared to that of C334 due to the hydrogen bonding between the −COOH group of the probe and sulfoxide group of the solvent. However, the viscosity normalized reorientation times (τr/η) of C343 in LiNO3/DMSO solutions increase by 60% to 70% compared to that in pure DMSO. Addition of electrolyte ions shifts the equilibrium toward the anionic form of C343, which in turn forms ion pairs with Li+, and the large increase in τr/η values is due to the association of DMSO solvent molecules with these ion pairs. On the other hand, τr/η values of the neutral solute, C334, remain invariant in the entire range of the electrolyte concentration. The C343-Li+ ion pairs have been characterized using ab initio molecular orbital methods. Two approaches have been employed to model the friction experienced by the C343-Li+ ion pairs. In the first approach, the complex formed between C343-Li+ and the solvent molecules is treated as a rigid entity and the increase in the viscosity normalized reorientation time has been accounted for solely as an enhancement in the mechanical friction. Alternatively, the solvent association with the C343-Li+ ion pairs has been modeled as dielectric friction using the extended charge distribution theory.

Rotational dynamics of nondipolar probes in associative solvents: Modeling of hydrogen bonding interactions using the extended charge distribution theory of dielectric friction

As an exercise in our ongoing efforts to understand the solute–solvent frictional coupling, hydrogen bonding interactions between the probe 1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole and associative solvents such as n-alcohols, formamide and N-methylformamide are modeled as dielectric friction using Alavi–Waldeck (AW) extended charge distribution theory. The mechanical friction experienced by the probe is calculated using Stokes–Einstein–Debye hydrodynamic theory with slip boundary condition and also from the measured reorientation times of another structurally similar, but nonhydrogen bonding solute molecule, 2,5-dimethyl-1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole. When the size of the solvent domains is used as an adjustable parameter in the AW analysis, a good agreement between the experimentally measured reorientation times and the calculated ones is obtained. The limitations of the applicability of the AW model to associative solvents are discussed.