Delbruck scattering and the g-factor of a bound electron

The leading contribution of the light-by-light scattering effects to g-factor of a bound electron is derived. The corresponding amplitude is expressed in terms of low-energy Delbruck scattering of a virtual photon. The result reads Delta g = (7/216) alpha (Z alpha)^5

Dynamics of monolayer physisorption in homogeneous mesoporous media

This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes.A model for monolayer physisorption of a one-component gas on the pore surface of a homogeneous macroporous or mesoporous porous medium is presented. It originates from an averaging over many pores of a macroporous medium filled with a one-component fluid. The resulting model does not assume anything about pore shape, but assumes that the pores are so large that capillary condensation does not occur. Mathematically, the model gives coverage as the solution of an ordinary, first-order, differential equation, where the time derivative of coverage is proportional to the difference between the chemical potential of the adsorbate and the chemical potential of the ambient gas. Coverage is determined by the ambient gas density, with temperature, adsorbate critical temperature, and the Henry adsorption constant as parameters. The rest of this abstract describes what is deduced from the equations of the model. Adsorbate phase transitions are built into the model by the use of van der Waals equations of state. Equilibrium isotherms are derived from the equality of the chemical potentials. The differential equation for coverage makes it possible to determine the mathematical stability of the equilibrium isotherms, and a number of properties of the isotherms are derived, the most important being as follows: (i) an adsorbate phase transition is always accompanied by a well-defined hysteresis loop, although “loop” is somewhat misleading as its vertical boundaries do not consist of equilibrium states; (ii) the vertical boundaries are exactly located; (iii) the upper and lower boundaries consist of states that are mathematically stable, while being either physically stable or metastable, and if physical metastability is the case, then the actual state of the adsorbate (mono- or bi-phasic) will not be visible on the equilibrium isotherm. The shapes of the equilibrium isotherms are largely determined by the value of the Henry constant, whether the isotherms are subcritical or supercritical. Expressions for the location of an equilibrium isotherm’s region of fastest variation and for the locations of the vertical boundaries of its hysteresis loop are found that also show the importance of Henry’s constant. Dynamical, that is, time-dependent isotherms are presented for the case describing the variation of coverage resulting from forcing the ambient gas to undergo a compression–decompression loop. Two subcases are considered: the subcritical and the supercritical adsorbate. It is shown that coverage in terms of ambient pressure exhibits closed loops, even in supercritical isotherms. However, supercritical loops shrink when the cycle time increases, reminiscent of rate-dependent hysteresis observed in piezoelectricity. The model is used to interpret two experiments on the sorption of CO2 and CH4 on coal that showed hysteresis loops in isotherms of supercritical adsorbates and that were originally interpreted as leading to different Henry constants for adsorption and for desorption. The interpretation set forth here uses the inherent dynamics of the model and looks at the loop as just one isotherm evolving in time, thus leading to a unique Henry constant.publishedVersio

Lattice Boltzmann simulations of contact line motion in a liquid-gas system

We use a lattice Boltzmann algorithm for liquid-gas coexistence to investigate the steady state interface profile of a droplet held between two shearing walls. The algorithm solves the hydrodynamic equations of motion for the system. Partial wetting at the walls is implemented to agree with Cahn theory. This allows us to investigate the processes which lead to the motion of the three-phase contact line. We confirm that the profiles are a function of the capillary number and a finite size analysis shows the emergence of a dynamic contact angle, which can be defined in a region where the interfacial curvature tends to zero.Comment: 13 pages, 5 figures, to appear in Phil. Trans. Roy. Soc. A (Proceedings of the Xth International Conference on Discrete Simulation of Fluid Dynamics.

Porous Flow with Diffuse Interfaces

This chapter presents a model developed by the author, in publications dated from 2002 to 2016, on flow in porous media assuming diffuse interfaces. It contains five sections. Section 1 is an Introduction, tracing the origin of the diffuse interface formalism. Section 1 also presents the traditional compositional model, pointing out its emphasis on phases and questioning the concept of relative permeabilities. Section 2 presents the mass, momentum, and energy balance equations, for a multicomponent continuous fluid, in their most general form, at the pore level. The existence of constitutive equations with phase-inducing terms is mentioned, but the equations are not introduced at this level, and phases are not an explicit concern. Section 3 is about the averaging of the pore level equations inside a region containing many pores. There is no explicit mention of phases and therefore not of relative permeabilities. Section 4 is the technical basis from which the constitutive equations of the model arise, and it is shown that many models can exist. Section 5 introduces constitutive equations and presents a minimal model for multicomponent, multiphase, and thermal flow in neutrally wetting porous media, i.e., a model with a minimal amount of phenomenological parameters

Coulomb corrections to the Delbrueck scattering amplitude at low energies

In this article, we study the Coulomb corrections to the Delbrueck scattering amplitude. We consider the limit when the energy of the photon is much less than the electron mass. The calculations are carried out in the coordinate representation using the exact relativistic Green function of an electron in a Coulomb field. The resulting relative corrections are of the order of a few percent for scattering on for a large charge of the nucleus. We compare the corrections with the corresponding ones calculated through the dispersion integral of the pair production cross section and also with the magnetic loop contribution to the g-factor of a bound electron. The last one is in a good agreement with our results but the corrections calculated through the dispersion relation are not.Comment: 8 pages, 6 figure

The Helmholtz free energy of pure fluid substances and fluid mixtures

Paper presented at the 8th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Mauritius, 11-13 July, 2011.The Helmholtz free energy is essential to the modelling of multiphase flow with the diffuse interface formalism. In models where it is a good approximation to let the temperature be constant and uniform, a simplified calculation of the Helmholtz free energy is performed, that leaves a number of functions of temperature unspecified (one per chemical component, in case of mixtures). If the model is to include the energy balance equation, i.e., account for flow with variable temperature, then the Helmholtz free energy must include these temperature dependent terms. This paper is an exposition of the determination of such terms, where three types of molecules are considered: (i) single conformation, (ii) multiple conformation, and (iii) polar. A specific example for each case is included: methane, n-pentane, and water. The Helmholtz free energy of fluid mixtures is also considered.mp201

Laser-dressed vacuum polarization in a Coulomb field

We investigate quantum electrodynamic effects under the influence of an external, time-dependent electromagnetic field, which mediates dynamic modifications of the radiative corrections. Specifically, we consider the quantum electrodynamic vacuum-polarization tensor under the influence of two external background fields: a strong laser field and a nuclear Coulomb field. We calculate the charge and current densities induced by a nuclear Coulomb field in the presence of a laser field. We find the corresponding induced scalar and vector potentials. The induced potential, in first-order perturbation theory, leads to a correction to atomic energy levels. The external laser field breaks the rotational symmetry of the system. Consequently, the induced charge density is not spherically symmetric, and the energy correction therefore leads to a "polarized Lamb shift." In particular, the laser generates an additional potential with a quadrupole moment. The corresponding laser-dressed vacuum-polarization potential behaves like 1/r**3 at large distances, unlike the Uehling potential that vanishes exponentially for large r. Our investigation might be useful for other situations where quantum field theoretic phenomena are subjected to external fields of a rather involved structure.Comment: 13 pages, RevTe

Photon-Photon Scattering at the Photon Linear Collider

Photon-photon scattering at the Photon Linear Collider is considered. Explicit formulas for helicity amplitudes due to $W$ boson loops are presented. It is shown that photon-photon scattering should be easily observable at PLC and separation of the $W$ loop contribution (which dominates at high energies) will be possible at $e^+e^-$ c.m. energy of 500~GeV or higher.Comment: Standard LaTeX. 8 pages+5 figures (available by regular mail). IHEP 93-8

Delbr\"uck scattering in combined Coulomb and laser fields

We study Delbr\"uck scattering in a Coulomb field in the presence of a laser field. The amplitudes are calculated in the Born approximation with respect to the Coulomb field and exactly in the parameters of the laser field having arbitrary strength, spectral content and polarization. The case of high energy initial photon energy is investigated in detail for a monochromatic circularly polarized laser field. It is shown that the angular distribution of the process substantially differs from that for Delbr\"uck scattering in a pure Coulomb field. The value of the cross section under discussion may exceed the latter at realistic laser parameters that essentially simplify the possibility of the experimental observation of the phenomenon. The effect of high order terms in the quantum intensity parameter $\chi$ of the laser field is found to be very important already at relatively small $\chi$.Comment: 21 pages, 4 figure

Relativistic Oscillator Model and Delbr\"uck scattering

Elastic scattering of photons in a Lorentz-scalar potential via virtual spin-zero particle-antiparticle pairs (`` Delbr\"uck scattering") is considered. An analytic expression for the Delbr\"uck amplitude is found exactly in case of an oscillator potential. General properties of the amplitude and its asymptotics are discussed.Comment: 8 pages, LATEX, BINP 94-6