scholarly journals Hydrodynamics and proper vibrations of quantum liquids with conformational degrees of freedom

2020 ◽  
Keyword(s):  
Dispersion Equation ◽  
Fermi Liquid ◽  
Degrees Of Freedom ◽  
Cooper Pair ◽  
Energy Functional ◽  
Mutual Orientation ◽  
Thermodynamic Quantities ◽  
Spherical Coordinate ◽  
Symmetry Properties ◽  
Conformational Degrees Of Freedom

The order parameters are constructed for a Fermi liquid with conformational degrees of freedom. Based on them, additional thermodynamic parameters were introduced: the spin unit vector dα (determining the anisotropy in the spin subspace), the unit spatial vectors mi and ni (determining the anisotropy in space), and also three scalar parameters determining the shape of the Cooper pair u, v, q ( first two items are half-axes of ellipsoid of Cooper pair and last item is mutual orientation in space of these half axes). The symmetry properties of the order parameter operator are considered. The equations of ideal hydrodynamics of a Fermi liquid are derived taking into account the influence of conformational degrees of freedom. By conformational degrees of freedom should be understood the parameters associated with the shape and size of the Cooper pair. Expressions are obtained for the flows of thermodynamic quantities of such a Fermi liquid in terms of the density of the energy functional. The energy functional depends both on the additive integrals of motion (classical fluid parameters) and on conformational parameters. The dispersion equation of such a liquid is obtained for a model representation of the energy functional (the work was performed as part of the Fermi-liquid approach). The dispersion equation includes spin modes, first, second, and third sounds. The dispersion equation for the spatial subsystem, including the first, second, and third sounds characteristic of superfluid systems, is analyzed. Particular solutions of the dispersion equation are simulated using the Maple software package (several 3D figures are given for the angular dependence of the speeds of 1 and 2 sounds in a spherical coordinate system). All of the above allows us to conclude that such a Fermi liquid can be considered as a superfluid liquid crystal of a nematic type. The presence of conformational parameters distinguishes the considered phase from the F phase of a superfluid Fermi liquid.

Relativistic Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
B. L. Gyorffy
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Schr6dinger Equation ◽  
Relativistic Effects ◽  
Relativistic Quantum Mechanics ◽  
Absolute Minimum ◽  
Crystalline Anisotropy ◽  
Symmetry Properties ◽  
Finite Set

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

scholarly journals Computational High-Throughput Screening of Polymeric Photocatalysts: Exploring the Effect of Composition, Sequence Isomerism and Conformational Degrees of Freedom

2018 ◽  
Author(s):  
isabelle Heath-Apostolopoulos ◽  
Liam Wilbraham ◽  
Martijn Zwijnenburg
Keyword(s):  
High Throughput ◽  
High Throughput Screening ◽  
Degrees Of Freedom ◽  
Chemical Space ◽  
Low Cost ◽  
Computational Screening ◽  
Computational Workflow ◽  
Conformational Degrees Of Freedom

We discuss a low-cost computational workflow for the high-throughput screening of polymeric photocatalysts and demonstrate its utility by applying it to a number of challenging problems that would be difficult to tackle otherwise. Specifically we show how having access to a low-cost method allows one to screen a vast chemical space, as well as to probe the effects of conformational degrees of freedom and sequence isomerism. Finally, we discuss both the opportunities of computational screening in the search for polymer photocatalysts, as well as the biggest challenges.

Small oscillations of systems with several degrees of freedom

2020 ◽  
pp. 29-40
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Free Oscillations ◽  
Small Oscillations ◽  
Symmetry Properties ◽  
Gyroscopic Forces ◽  
Simple Molecules ◽  
Simple Systems ◽  
Three Degrees Of Freedom

This chapter addresses the free and forced oscillations of simple systems (with two or three degrees of freedom), the free oscillations of systems with the degenerate frequencies, and the eigen-oscillations of the electromechanical systems. This chapter also studies the oscillations of more complex systems using orthogonality of eigenoscillations and the symmetry properties of the system, the free oscillations of an anisotropic charged oscillator moving in a uniform constant magnetic field, and the perturbation theory adapted for the small oscillations. Finally, the chapter addresses oscillations of systems in which gyroscopic forces act and the eigen-oscillations of the simple molecules.

scholarly journals Non-Specific Adsorption of Hydrocarbons on Microporous Surfaces: A Comprehensive Molecular-Statistical/Chromatographic Approach

1992 ◽  
Vol 9 (2) ◽  
pp. 54-71 ◽  
Author(s):  
E.V. Aksenenko ◽  
Yu. I. Tarasevich
Keyword(s):  
Statistical Methods ◽  
Computational Methods ◽  
Short Range ◽  
Statistical Approach ◽  
Adsorption Properties ◽  
Specific Adsorption ◽  
Thermodynamic Quantities ◽  
Good Correspondence ◽  
Symmetry Properties ◽  
Adsorption Systems

The results are presented of a series of investigations concerning the application of the molecular-statistical approach to the calculation of thermodynamic quantities for the adsorption of molecules in the Henry region on adsorbent surfaces possessing certain surface symmetry properties, and in particular for systems characterized by dispersion and polarization attraction and short-range atom-atom repulsion. Computational methods have been developed and the results for particular adsorption systems are presented with emphasis on the adsorption properties of layer silicates. Good correspondence between the calculated results and chromatographic data for a number of adsorbents strongly supports the view that the combination of chromatographic and molecular-statistical methods provides a powerful tool for the investigation of the structural and adsorption-selective characteristics of surface-porous adsorbents.

Numerical treatment for solving two-dimensional space-fractional advection–dispersion equation using meshless method

2018 ◽  
Vol 32 (06) ◽  
pp. 1850073 ◽  
Author(s):  
Rongjun Cheng ◽  
Fengxin Sun ◽  
Qi Wei ◽  
Jufeng Wang
Keyword(s):  
Dispersion Equation ◽  
Convergence Rates ◽  
Dimensional Space ◽  
Energy Functional ◽  
Least Square ◽  
Approximation Schemes ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Moving Least Square ◽  
Advection Dispersion

Space-fractional advection–dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann–Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

scholarly journals Decoupling of crystalline and conformational degrees of freedom in lipid monolayers

1989 ◽  
Vol 91 (3) ◽  
pp. 1855-1865 ◽  
Author(s):  
John Hjort Ipsen ◽  
Ole G. Mouritsen ◽  
Martin J. Zuckermann
Keyword(s):  
Degrees Of Freedom ◽  
Lipid Monolayers ◽  
Conformational Degrees Of Freedom

scholarly journals Criticality of Lamellar Surfaces by Conformational Degrees of Freedom

1995 ◽  
Vol 5 (9) ◽  
pp. 1161-1178
Author(s):  
B. Bassetti ◽  
G. Mazzoletti ◽  
P. Jona
Keyword(s):  
Degrees Of Freedom ◽  
Conformational Degrees Of Freedom

scholarly journals Quantum-Mechanical Substantiation of the Periodic System of Isotopes. Models of Nuclear Orbitals

2021 ◽  
pp. 1-26
Author(s):  
AS Magula ◽  
Keyword(s):  
Periodic System ◽  
Degrees Of Freedom ◽  
Nucleon Nucleon ◽  
Quantum Mechanical ◽  
Spherical Coordinate ◽  
Crystal Forms ◽  
Electromagnetic Interactions ◽  
Quantum Numbers ◽  
The Family ◽  
Fundamental Cause

The topic of this article lies in the field of problems: substantiating the periodic system of isotopes and the principle of multilevel periodicity using quantum mechanical calculations, combining strong and electromagnetic interactions, and searching for the fundamental cause of periodicity in general. This article is a theoretical section and a continuation of the article: "Periodic system of isotopes", in which the system was checked against 10 types of experimental data, the periodic change of properties at the level of nuclei and the vertical symmetry of subgroups of isotopes were found. Periodic system of isotopes was constructed with the help of a special algorithm, the principle of multilevel periodicity of the atom, from the electrons to the nucleus. As a description of the multilevel periodicity, this paper presents a unified system of quantum numbers, which is used to describe both electron and nucleon shells (binomial probabilistic interpretation). With the binomial interpretation the problem of a particle in a one-dimensional potential well has been solved; quantummechanical calculations for the probability functions of the orbitals and periods of both electrons and nucleons have been performed - characteristic equations have been obtained, the projections of electronic orbitals have been reproduced and the binomial interpretation has been shown to correspond to the family of spherical harmonics. For the electron orbitals the calculation and analysis of solutions of the Schrödinger equation for the binomial interpretation of quantum numbers have been performed. The spatial nature of quantum numbers, for this interpretation, in the form of degrees of freedom is shown. Based on the principle of multilevel periodicity, expressions are derived and planar projections of nucleon nucleon orbitals are constructed, and similarity of the forms with electron orbitals is analyzed and revealed. A critical analysis of the modern spherical coordinate system was made, possible errors in the construction of electron orbitals were shown and, taking into account the drawbacks, two alternative spherical coordinate systems were proposed, for which Lame coefficients were calculated and Laplace equations were derived. As a search for the fundamental cause of multilevel periodicity, a spatial model with changing degrees of freedom 0-n is presented, its manifestation in nature (crystal forms) is found; a number of experiments are proposed; the predictions about the applicability of the multilevel periodicity principle in quark theory are made

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