Papers by Sergey Kryuchkov
We consider the radiation field operators in a cavity with varying dielectric medium in terms of ... more We consider the radiation field operators in a cavity with varying dielectric medium in terms of solutions of Heisenberg's equations of motion for the most general one-dimensional quadratic Hamiltonian. Explicit solutions of these equations are obtained and applications to the radiation field quantization, including randomly varying media, are briefly discussed.
We critically analyze the concept of photon helicity and its connection with the Pauli-Lubanski v... more We critically analyze the concept of photon helicity and its connection with the Pauli-Lubanski vector from the viewpoint of the complex electromagnetic field, F=E+iH, sometimes attributed to Riemann but studied by Weber, Silberstein, and Minkowski. To this end, a complex form of Maxwell's equations is used.
We analyze basic relativistic wave equations for the classical fields, such as Dirac's equati... more We analyze basic relativistic wave equations for the classical fields, such as Dirac's equation, Weyl's two-component equation for massless neutrinos, and the Proca, Maxwell, and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir operators of the Poincare group. In general, in this group-theoretical approach, the above wave equations arise in certain overdetermined forms, which can be reduced to the conventional ones by a Gaussian elimination. A connection between the spin of a particle/field and consistency of the corresponding overdetermined system is emphasized in the massless case.
We find explicit solutions of the Heisenberg equations of motion for a general quadratic Hamilton... more We find explicit solutions of the Heisenberg equations of motion for a general quadratic Hamiltonian in a variable medium in the case of multi-parameter squeezed input photons. The corresponding photon statistics are also derived in the Schrödinger picture in an abstract Hilbert space operator settings. Their time evolution is given in terms of solutions of certain Ermakovtype system. The unitary transformation and an extension of the squeeze/evolution operator are introduced formally.
arXiv: Mathematical Physics, 2015
We analyze basic wave equations for the classical relativistic fields, such as Dirac's equati... more We analyze basic wave equations for the classical relativistic fields, such as Dirac's equation, Weyl's two-component equation for massless neutrinos, and the Proca and Maxwell equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir operators of the Poincare group. In general, in this group-theoretical approach, the above wave equations arise in certain overdetermined forms, which can be reduced to the conventional ones by a Gaussian elimination. A connection between the spin of a particle/field and consistency of the corresponding overdetermined system is established.
arXiv: Combinatorics, 2013
Connection of the Four Color Theorem (FCT) with some operations on trees is described. L.H. Kauff... more Connection of the Four Color Theorem (FCT) with some operations on trees is described. L.H. Kauffman's theorem about FCT and vector cross product is discussed. Operation of transplantation on trees linked with the move of brackets according to the associative law is used to formulate a conjecture. When map is represented as a tying of the trees this conjecture proposes the existence of special coloring of this map. This coloring makes possible successive transplantations such that one of these trees is transformed to another, and all the intermediate maps are colored properly. It means (in terms of L.H. Kauffman) that not only for two different positions of brackets in a product of n factors the associative law works (on special values of factors) but also there is a way of moving brackets that for all intermediate positioning of brackets the associative law is obeyed. Some classes of trees for which the conjecture is proved are presented.
In the past, measuring the NMR petrophysical properties of drill cuttings has been very difficult... more In the past, measuring the NMR petrophysical properties of drill cuttings has been very difficult for two reasons: first, small rock samples yield only a small NMR signal which corresponds to a small signal-to-noise ratio and, second, the procedures for sample preparation and processing did not allow fast enough turn-around time. The combination of these two factors prevented NMR measurement of drill cuttings from becoming a mud logging routine. We have developed technology to obtain the NMR petrophysical parameters both at the well site and in the laboratory. The instrument uses modern electronics to overcome the signal-tonoise problem and weighs only 25 kg, making it easily portable. Using our procedures on drill cuttings during mud logging allows us to determine: • Total and Effective porosity; • Absolute permeability; • Irreducible water saturation Swirr. Most other NMR petrophysical parameters (identifying pay zones, wettability condition etc.) can, in principle, also be derive...
We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or ... more We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the corresponding differential balance equations are given. Conservation laws and quantization of the electromagnetic field will be discussed in this covariant approach elsewhere.
Summary Numerical simulation studies are performed in two-dimensional porous media patterns. Two-... more Summary Numerical simulation studies are performed in two-dimensional porous media patterns. Two-phase flow is modeled by solving Navier-Stokes equations at the pore-level and using Volume of Fluid Method for interface capturing. A primary drainage process is simulated in which oil (non-wetting phase) displaces a 100% water (wetting phase) saturated media. The objective is to observe and discuss a predominant pore-scale instability, Haines jumps, which is responsible for drastic variations in pressure fields and fluids redistribution through the porous space. The presence of Haines jumps can lead to fluid re-distribution within pores during drainage of water by oil. This physical phenomenon is present in actual porous media, but it may be missed in more simple network based approaches to modeling flow in porous media.
Springer Proceedings in Mathematics & Statistics, 2017
We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or ... more We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the corresponding differential balance equations are given. Conservation laws and quantization of the electromagnetic field will be discussed in this covariant approach elsewhere.
Energy & Fuels
Solvent-based processes have shown technical advantages over thermal techniques for recovery of h... more Solvent-based processes have shown technical advantages over thermal techniques for recovery of heavy oil and bitumen. The success of these processes relies on accurate computation of molecular diffusion coefficient which determines how fast a solvent penetrates into oil. Concentration profile measurements of solvent in oil are used for the determination of the molecular diffusion coefficient. Although numerous experimental techniques have been proposed, the accurate estimation of this parameter is still a topic of debate in the literature. In this work, 1-D nuclear magnetic resonance imaging (MRI) is employed to obtain diffusivity data for a toluene–heavy oil system. Diffusion of toluene in heavy oil was monitored for 20 days at a controlled temperature of 35 °C and ambient pressure. Over time, toluene diffusion into oil leads to changes in spatial distribution of T1 and T2 that affect the received signal. This serves as the basis of the solvent and heavy oil concentration estimation. Consequently, conce...
Journal of Physics B: Atomic, Molecular and Optical Physics, 1994
ABSTRACT With the consideration of all the Feynman diagrams of the lowest order and electron spin... more ABSTRACT With the consideration of all the Feynman diagrams of the lowest order and electron spin correlation in the initial state, the one-photon decay rate of the Ps- ion in its ground state is found to be 3.9*10-2 s-1. Comparison is made with the previous calculations of other authors.
We find explicit solutions of the Heisenberg equations of motion for a quadratic Hamiltonian, des... more We find explicit solutions of the Heisenberg equations of motion for a quadratic Hamiltonian, describing a generic model of variable media, in the case of multi-parameter squeezed input photon configuration. The corresponding probability amplitudes and photon statistics are also derived in the Schroedinger picture in an abstract operator setting of the quantum electrodynamics (QED). Their time evolution is given in terms of solutions of certain Ermakov-type system. The unitary transformation and an extension of the squeeze/evolution operator are introduced formally.
The Canadian Journal of Chemical Engineering, 2016
Connection of the Four Color Theorem (FCT) with some operations on trees is described. L.H. Kauff... more Connection of the Four Color Theorem (FCT) with some operations on trees is described. L.H. Kauffman's theorem about FCT and vector cross product is discussed. Operation of transplantation on trees linked with the move of brackets according to the associative law is used to formulate a conjecture. When map is represented as a tying of the trees this conjecture proposes the existence of special coloring of this map. This coloring makes possible successive transplantations such that one of these trees is transformed to another, and all the intermediate maps are colored properly. It means (in terms of L.H. Kauffman) that not only for two different positions of brackets in a product of n factors the associative law works (on special values of factors) but also there is a way of moving brackets that for all intermediate positioning of brackets the associative law is obeyed. Some classes of trees for which the conjecture is proved are presented.
Journal of magnetic resonance (San Diego, Calif. : 1997), 2017
Multi-dimensional nuclear magnetic resonance (NMR) experiments are often used for study of molecu... more Multi-dimensional nuclear magnetic resonance (NMR) experiments are often used for study of molecular structure and dynamics of matter in core analysis and reservoir evaluation. Industrial applications of multi-dimensional NMR involve a high-dimensional measurement dataset with complicated correlation structure and require rapid and stable inversion algorithms from the time domain to the relaxation rate and/or diffusion domains. In practice, applying existing inverse algorithms with a large number of parameter values leads to an infinite number of solutions with a reasonable fit to the NMR data. The interpretation of such variability of multiple solutions and selection of the most appropriate solution could be a very complex problem. In most cases the characteristics of materials have sparse signatures, and investigators would like to distinguish the most significant relaxation and diffusion values of the materials. To produce an easy to interpret and unique NMR distribution with the...
Physica Scripta, 2015
We critically analyze the concept of photon helicity and its connection with the Pauli-Lubański v... more We critically analyze the concept of photon helicity and its connection with the Pauli-Lubański vector from the viewpoint of the complex electromagnetic field, E + iH, sometimes attributed to Riemann but studied by Weber, Silberstein and Minkowski. To this end, a complex covariant form of Maxwell's equations is used.
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Papers by Sergey Kryuchkov