scholarly journals NEW SOLUTION TO THE DROPLET KERNEL MODEL

Globus ◽  
2021 ◽  
Vol 7 (2(59)) ◽  
pp. 42-58
Author(s):  
Evgeniy Georgievich Yakubovski
Keyword(s):  
Incompressible Fluid ◽  
Imaginary Part ◽  
Main Part ◽  
Bound State ◽  
Droplet Model ◽  
Special Means ◽  
Zero Radius ◽  
Hydrodynamic Potential ◽  
The Difference ◽  
Kernel Model

The droplet model of the nucleus is revived, for which an exact solution for an incompressible fluid is obtained using the hydrodynamic potential solution obtained from the Schrödinger equation. Moreover, for an incompressible fluid, there are formulas for the pressure or potential. There is the main part of the hydrodynamic potential, which is obtained by replacing the modulus of the inverse difference of vectors by the difference in moduli of the values of the vectors. The bulk of the potential is expressed in a finite formula with singularities. A formula is obtained for the integral containing the modulus of the difference between the exact values of the vectors minus the main part of the potential. This difference defines a continuous correction with the features taken into account. The main part of the potential at the boundary of the nucleus turned out to be infinitely large with an imaginary part, locking particles in the nucleus. In this case, the real part of the main potential decreases with decreasing radius, becomes negative, and determines the bound state. At half the radius of the nucleus, there is a linear term along the radius. At the zero radius, there is an infinite negative potential with an imaginary part. An expression for the quantum of the emitted energy is obtained. Note that the added mass was not used due to the rotational regime of the nucleus. An algorithm for calculating the spectrum of the kernel is proposed, and each state of the action of the kernel sn corresponds to n calculated frequencies, determined by n angles in the configuration space. The main space is n + 1 dimensional, and each dimension of space has its own energy. But without special means, the potential of the nucleus tends to infinity. It is necessary to introduce the imaginary degree of roughness of the corners, in expressions containing singularities, then the infinities disappear.

Probing of the Wave Function of Shallow Donors and Acceptors by EPR in SiC Crystals with Changed Isotopic Composition

2005 ◽  
Vol 483-485 ◽  
pp. 507-510
Author(s):  
Marina V. Muzafarova ◽  
Ivan V. Ilyin ◽  
E.N. Mokhov ◽  
P.G. Baranov ◽  
B.Ya. Ber ◽  
...  
Keyword(s):  
Wave Function ◽  
Band Structure ◽  
Isotopic Composition ◽  
Density Distribution ◽  
Spin Density ◽  
Main Part ◽  
Shallow Donor ◽  
Line Broadening ◽  
Electronic Wave Function ◽  
The Difference

The conclusion which is drawn from the EPR line broadening and narrowing of the N shallow donor in an isotope enriched and non-enriched 4H-SiC and 6H-SiC crystals along with previous ENDOR results shows that the spin-density distribution over the C and Si nuclei differs between the 4H-SiC and 6H-SiC polytypes. The main part of the spin density in 4H-SiC is located on the Si sublattice. In contrast, in 6H-SiC the main part of the spin density is located on the C sublattice. An explanation for the difference in the electronic wave function of the N donor in 4HSiC and 6H-SiC can be found in the large difference in the band structure of two polytypes and in the position of the minima in the Brillouin zone.

Gamma rays in the MeV region at balloon altitude

1968 ◽  
Vol 46 (10) ◽  
pp. S494-S497 ◽  
Author(s):  
K. Okudaira ◽  
Y. Hirasima
Keyword(s):  
Gamma Rays ◽  
Main Part ◽  
Counting Rate ◽  
Gamma Ray ◽  
Plastic Scintillator ◽  
Scintillation Counter ◽  
Lower Atmosphere ◽  
Upper Limit ◽  
Extraterrestrial Origin ◽  
The Difference

Gamma rays in the MeV region were observed from balloons at λ = 26 °N on September 29, 1966. A scintillation counter constructed with two NaI ⅓ in. × 2 in. [Formula: see text] crystals separated by 1 cm × 2 in. [Formula: see text] lead was used to measure the directional distribution of the gamma-ray flux. This counter was flown at an atmospheric depth of 14.2 g cm−2. As the response of each crystal of this counter depends on the direction of incidence of the gamma rays, an anisotropic distribution of gamma rays gives rise to a difference between the counting rates of two crystals. It was ascertained from the observation that albedo gamma rays from the lower atmosphere are predominant at this high altitude. The deviation from the calculated values of the difference in counting rate assuming only atmospheric gamma rays may be due to an extraterrestrial origin of part of the gamma-ray flux. For the measurement of the gamma-ray spectrum, a phoswich counter (1 in. × 1 in. [Formula: see text] NaI crystal surrounded by ¼-in.-thick plastic scintillator) was flown to 10 g cm−2. Though the main part of the gamma-ray flux is probably due to atmospheric gamma rays, an upper limit for the isotropic cosmic gamma-ray flux is deduced to be (1.25 ± 0.05) × 10−2 counts cm−2 s−1 sr−1 MeV−1 in the energy range 1.2–3.1 MeV.

Ab Initio Calculation of Shallow Defects: Results for P-Related Donors in SiC

2005 ◽  
Vol 483-485 ◽  
pp. 501-506 ◽  
Author(s):  
Uwe Gerstmann ◽  
E. Rauls ◽  
Harald Overhof ◽  
Thomas Frauenheim
Keyword(s):  
Wave Function ◽  
Band Structure ◽  
Density Distribution ◽  
Spin Density ◽  
Ab Initio Calculation ◽  
Main Part ◽  
Shallow Donor ◽  
Line Broadening ◽  
Electronic Wave Function ◽  
The Difference

The conclusion which is drawn from the EPR line broadening and narrowing of the N shallow donor in an isotope enriched and non-enriched 4H-SiC and 6H-SiC crystals along with previous ENDOR results shows that the spin-density distribution over the C and Si nuclei differs between the 4H-SiC and 6H-SiC polytypes. The main part of the spin density in 4H-SiC is located on the Si sublattice. In contrast, in 6H-SiC the main part of the spin density is located on the C sublattice. An explanation for the difference in the electronic wave function of the N donor in 4HSiC and 6H-SiC can be found in the large difference in the band structure of two polytypes and in the position of the minima in the Brillouin zone.

Quantum dissipation and friction attributed to plasmons

2021 ◽  
Author(s):  
Yang Wang ◽  
Yu Jia
Keyword(s):  
Imaginary Part ◽  
Frictional Force ◽  
Relative Velocity ◽  
Degrees Of Freedom ◽  
Vacuum Field ◽  
Quantum Dissipation ◽  
Metal Plates ◽  
Quantum Friction ◽  
Quantum Action ◽  
The Difference

In this paper, we computed quantum friction of two parallel metal plates separated by a small distance moving with constant relative velocity [Formula: see text]. The plasmons as the internal degrees of freedom living on the two plates are coupled to a vacuum field in the gap between the two plates. We got the in–out quantum action which contained all the dynamical information of the system. Furthermore, we associated the imaginary part of the in–out quantum action with dissipation and frictional force. For the case of dispersionless plasmons, the imaginary part of the in–out quantum action is strongly suppressed as [Formula: see text]. The frictional force exhibits the same feature as [Formula: see text]. The difference is that the frictional force increases as [Formula: see text] and decreases as [Formula: see text]. For the case of dispersive plasmons, there is a threshold for the imaginary part of the in–out quantum action and the frictional force, that is, there is no dissipation when the relative velocity [Formula: see text] is not big enough. We gave a classical argument of the existence of the threshold, and this argument matched the mathematical results.

SOME RESULTS ON COMPARING TWO INTEGRAL MEANS FOR ABSOLUTELY CONTINUOUS FUNCTIONS AND APPLICATIONS

2014 ◽  
Vol 90 (2) ◽  
pp. 264-274
Author(s):  
DAH-YAN HWANG ◽  
SILVESTRU SEVER DRAGOMIR
Keyword(s):  
Probability Density ◽  
Continuous Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
Absolutely Continuous Functions ◽  
Integral Means ◽  
Absolutely Continuous ◽  
Special Means ◽  
The Difference

AbstractSome better estimates for the difference between the integral mean of a function and its mean over a subinterval are established. Various applications for special means and probability density functions are also given.

scholarly journals A decomposition theorem on differential polynomials of theta functions

1984 ◽  
Vol 96 ◽  
pp. 113-126 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Entire Function ◽  
Imaginary Part ◽  
Theta Function ◽  
Theta Functions ◽  
Decomposition Theorem ◽  
Positive Definite ◽  
Complex Variables ◽  
Differential Polynomials ◽  
Symmetric Complex ◽  
The Difference

Let τ = (τij) be a symmetric complex g = g matrix with the positive definite imaginary part. A theta function of level n means an entire function f(z) in g complex variables z = (zl …, zg) satisfying the difference relations:

scholarly journals Возбуждение и ионизация частицы в одномерной потенциальной яме нулевого радиуса предельно коротким световым импульсом

2022 ◽  
Vol 130 (3) ◽  
pp. 414
Author(s):  
Р.М. Архипов ◽  
М.В. Архипов ◽  
А.В. Пахомов ◽  
Н.Н. Розанов
Keyword(s):  
Wave Function ◽  
Energy Level ◽  
Short Pulse ◽  
Bound State ◽  
Characteristic Scale ◽  
Potential Well ◽  
One Dimensional ◽  
Characteristic Period ◽  
Zero Radius ◽  
Perturbation Approximation

The Migdal sudden perturbation approximation is used to solve the problem of excitation and ionization particles in a one-dimensional potential of zero radius with an extremely short pulse. There is has only one energy level in such a one-dimensional the delta-shaped potential well. It is shown that for pulse durations shorter than the characteristic period of oscillations of the wave function of the particle in the bound state, the population of the level (and the probability of ionization) is determined by the ratio of the electric the area of ​​the pulse to the characteristic “scale” of the area inversely proportional to the area of ​​localization of the particle in a bound state.

scholarly journals Line profile modeling for non-LTE partially ionized plasmas based on average atom model with l–splitting

1993 ◽  
Vol 11 (1) ◽  
pp. 81-87 ◽  
Author(s):  
T. Nishikawa ◽  
H. Takabe ◽  
K. Mima
Keyword(s):  
Electronic State ◽  
Radiation Transport ◽  
Bound State ◽  
Electron Energy Level ◽  
Atom Model ◽  
Partially Ionized Plasmas ◽  
Partially Ionized ◽  
Charge States ◽  
The Difference ◽  
Average Atom Model

We have developed a new opacity modeling of partially ionized high-Z plasma to solve radiation transport in fluid codes. The average atom model is used to describe the electronic state of the plasma. The electronic state of the plasma is determined by solving the collisional radiative equilibrium model. We have taken into account the electron energy level splitting owing to the difference in the azimuthal quantum number. To model the line groups made of the same electronic transitions from ions indifferent charge states, we used a statistical method and calculated the distribution of the charge states from the averaged electron population in each bound state. By using the new opacity model, we can well reproduce the X-ray spectra from the plasmas. It is found that the Δn = 0 transition can explain the peaked spectra near hv = 300 eV and l–splitted emission of the n = 5–4 transition can explain the flat spectra in the region of hv = 400–800 eV seen in the experiments.

scholarly journals Waves in Two Coaxial Elastic Cubically Nonlinear Shells with Structural Damping and Viscous Fluid Between Them

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 335
Author(s):  
Lev Mogilevich ◽  
Sergey Ivanov
Keyword(s):  
Exact Solution ◽  
Incompressible Fluid ◽  
Difference Scheme ◽  
Viscous Incompressible Fluid ◽  
Initial Conditions ◽  
Numerical Study ◽  
Fluid Motion ◽  
Structural Damping ◽  
The Difference ◽  
The Mathematical Model

This article investigates longitudinal deformation waves in physically nonlinear coaxial elastic shells containing a viscous incompressible fluid between them. The presence of a viscous incompressible fluid between the shells, as well as the influence of the inertia of the fluid motion on the amplitude and velocity of the wave, are taken into account. The mathematical model phenomenon is constructed by means of the method of two-scale asymptotic expansion. Structural damping in the shells and surrounding elastic media did not allow discovery of the exact solution of the problem of the deformation waves propagation. This leads to the need for numerical methods. A numerical study of the model constructed in the course of this work is carried out by using a difference scheme for the equation similar to the Crank–Nicholson scheme for the heat equation. In the absence of the structural damping and surrounding media influences, and under the similar initial conditions for both shells, the velocity and amplitude of the wave do not change. The result of the numerical experiment coincides with the exact solution, which is found in the case of the absence of the structural damping and surrounding media influences; therefore, the difference scheme is adequate to the generalized modified Korteweg–de Vries equations system. There is energy is transferred in the presence of the fluid, between the shells. The presence of inertia of the fluid motion leads to a decrease in the velocity of the deformation wave.

scholarly journals A Comparative Study on Interactions of Antimicrobial Peptides L- and D-phenylseptin with 1,2-dimyristoyl-sn-glycero-3-phosphocholine

2019 ◽  
Vol 9 (13) ◽  
pp. 2601 ◽  
Author(s):  
Batsaikhan Mijiddorj ◽  
Yuta Matsuo ◽  
Hisako Sato ◽  
Kazuyoshi Ueda ◽  
Izuru Kawamura
Keyword(s):  
Circular Dichroism ◽  
Antimicrobial Peptides ◽  
Lipid Bilayers ◽  
Binding Constants ◽  
Bound State ◽  
Dynamics Simulation ◽  
Membrane Bound ◽  
The Difference ◽  
Α Helix ◽  
Circular Dichroïsm

L-phenylseptin (L-Phes) and D-phenylseptin (D-Phes) are amphibian antimicrobial peptides isolated from the skin secretion of Hypsiboas punctatus. In the N-termini, L-Phes and D-Phes contain three consecutive phenylalanine residues, l-Phe-l-Phe-l-Phe and l-Phe-d-Phe-l-Phe, respectively. They are known to exhibit antimicrobial activity against Staphylococcus aureus, Escherichia coli, Pseudomonas aeruginosa, and Xanthomonas axonopodis pv. Glycines. However, their mechanism of action and the role of the D-amino acid residue have not been elucidated yet. In this study, the interactions of both peptides with 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) were investigated by means of quartz crystal microbalance, circular dichroism, vibrational circular dichroism, 31P solid-state NMR, and molecular dynamics simulation. Both peptides have similar binding constants to the DMPC lipid bilayers, in the order of 106 M−1, and form an α-helix structure in the DMPC lipid bilayers. Both the peptides induce similar changes in the dynamics of DMPC lipids. Thus, in spite of the difference in the conformations caused by the chirality at the N-terminus, the peptides showed similar behavior in the membrane-bound state, experimentally and computationally.

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