Deposition of Heavy Particles from a Spherical Cloud on the Earth′s Surface. Analytical solution

2015 ◽  
Vol 88 (2) ◽  
pp. 342-350
Author(s):  
K. O. Sabdenov ◽  
G. T. Zholdybaeva
Keyword(s):  
Analytical Solution ◽  
Heavy Particles ◽  
The Earth ◽  
Spherical Cloud

AN ANALYTICAL SOLUTION OF THE COSMIC RAYS TRANSPORT EQUATION IN THE PRESENCE OF THE GEOMAGNETIC FIELD

2002 ◽  
Vol 17 (12n13) ◽  
pp. 1645-1653
Author(s):  
MARINA GIBILISCO
Keyword(s):  
Magnetic Field ◽  
Cosmic Rays ◽  
Analytical Solution ◽  
Transport Equation ◽  
Geomagnetic Field ◽  
The Earth ◽  
Factorization Technique ◽  
Diffusion Motion ◽  
Geomagnetic Fields ◽  
The Magnetic Field

In this work, I study the propagation of cosmic rays inside the magnetic field of the Earth, at distances d ≤ 500 Km from its surface; at these distances, the geomagnetic field deeply influences the diffusion motion of the particles. I compare the different effects of the interplanetary and of the geomagnetic fields, by also discussing their role inside the cosmic rays transport equation; finally, I present an analytical method to solve such an equation through a factorization technique.

The Analytical Solution of Single Pipe Piles under Axially and Laterally Free Loads

2011 ◽  
Vol 383-390 ◽  
pp. 1701-1707
Author(s):  
Zhe Wang ◽  
Si Fa Xu ◽  
Guo Cai Wang ◽  
Yong Zhang
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Lateral Deformation ◽  
Lateral Loads ◽  
Axial Loads ◽  
Influence Curves ◽  
The Earth ◽  
Inclined Loads ◽  
Single Pipe ◽  
Foundation Type

The analytical solution of a single pipe piles under axially and laterally loads is presented, when the laterally loads is optional free load. As piles foundations are becoming a preferred foundation type, piles usually work under simultaneous axial and lateral loads in engineering. To analyze the function of free loads to pipe piles under inclined loads conditions, in the basis of ‘m’ method, deformation differential equation of elastic piles under inclined loads is established first in the paper with analytical method. Differential equation has two parts in according to the piles in the earth or in the air, and lateral deformation, obliquity, moment; shearing force of the piles can be gotten respectively by soluting equations. In the end of the paper, influences of several parameters is analyzed of the top axial loads, the top lateral loads and the free loads, and their influence curves are given.

scholarly journals ON ONE NUMERICAL METHOD FOR THE COMPUTING OF SEDIMENTATION OF THE SURFACE OF THE SOIL MASSIVE CAUSED BY THE CONSTRUCTION OF THE SHELL LINING OF THE TUNNEL

2018 ◽  
Vol 14 (1) ◽  
pp. 78-91
Author(s):  
Sergey B. Kosytsyn ◽  
Vladimir Y. Akulich
Keyword(s):  
Analytical Solution ◽  
Numerical Method ◽  
Strain State ◽  
Soil Mass ◽  
Stress Strain ◽  
Stress Strain State ◽  
The Earth ◽  
Surrounding Soil

The distinctive work is aimed at the geotechnical forecast of the influence of the construction of the tunnel on the change in the stress-strain state of the surrounding soil mass, namely, the precipitations that arise on the surface of the earth. The work assumes both a numerical and an analytical solution with subsequent com-parative analysis

scholarly journals Occurrence of “precursors” of PKP-waves in the layered radial-symmetric Earth

2019 ◽  
Vol 489 (1) ◽  
pp. 84-88
Author(s):  
A. G. Fatyanov ◽  
V. Yu. Burmin
Keyword(s):  
Analytical Solution ◽  
Wave Field ◽  
Travel Time ◽  
High Frequency ◽  
Spherical Model ◽  
Outer Core ◽  
Small Scale ◽  
Longitudinal Waves ◽  
High Frequency Oscillations ◽  
The Earth

It is generally accepted that PKP‑waves precursors, which are observed on a real data ahead of PKP‑waves, are explained by scattering on small-scale inhomogeneities in the lower mantle. In this paper, a stable analytical solution (without interference) was obtained for the wave field of longitudinal waves in a layered (discrete) ball of planetary size. The calculations of the total wave field, rays and travel-time curves of longitudinal waves for the spherical model of the Earth AK135 with a carrier frequency of 1 hertz are presented. The analytical solution showed that at angles smaller than 145 degrees ahead of the PKP‑waves, low-amplitude waves appear, with a higher frequency of about 1,3 hertz. Indeed, these high-frequency oscillations have the form characteristic for waves scattered at a certain object. The ray pattern and the travel-time graph show that these high-frequency oscillations are due to exclusively to the spherical geometry of the Earth. This could be explained by the interference of refracted and reflected longitudinal waves in the bottom of a discrete outer core. This field propagates even further towards smaller angles due to the interference of diffraction waves.

scholarly journals Bjerknes Compensation in a Coupled Global Box Model

2021 ◽  
Author(s):  
Jiaqi Shi ◽  
Haijun Yang
Keyword(s):  
Analytical Solution ◽  
Thermohaline Circulation ◽  
Climate System ◽  
Box Model ◽  
Climate Feedback ◽  
Local Climate ◽  
The Earth ◽  
Set Up ◽  
The One ◽  
Heat And Moisture

Abstract The Earth climate system has an intrinsic mechanism to maintain its energy conservation by impelling opposite changes in meridional ocean and atmosphere heat transports, in response to climate change or variability. This mechanism is briefed as the Bjerknes compensation (BJC). We set up a global coupled two-hemisphere box model in this study, and obtain an analytical solution to the BJC of this system. In the two-hemisphere model, the thermohaline circulation is interhemispheric and parameterized by the density difference between two polar boxes. The symmetric poleward atmosphere heat and moisture transports are considered and parameterized by the temperature gradient between tropical and polar boxes. Different from the BJC in the one-hemisphere box model that depends only on the local climate feedback, the BJC here is determined by both local climate feedback and temperature change. The asymmetric thermohaline circulation leads to a better BJC in the Northern Hemisphere than in the Southern Hemisphere. Furthermore, an analytical solution to the probability of a valid BJC (i.e., negative BJC) is derived, which is determined only by the local climate feedback. The probability of a valid BJC is usually very high under reasonable climate feedback, which is also found to be robust in the real world based on observational data, implying that the Earth climate system maintains it energy balance very well during the past one hundred years.

scholarly journals Nature and Properties of the Chandler Motion and Mechanism of its Damping and Excitation

2000 ◽  
Vol 178 ◽  
pp. 447-453 ◽  
Author(s):  
J.M. Ferrándiz ◽  
Yu. V. Barkin
Keyword(s):  
Analytical Solution ◽  
Polar Motion ◽  
The Body ◽  
Lower Envelope ◽  
Meridian Plane ◽  
The Earth ◽  
Deformable Bodies ◽  
Characteristic Behaviour ◽  
Special Approach ◽  
Chandler Period

AbstractThe analytical studies of the Chandler motion of the Earth’s pole on the basis of the special approach to the problem, using the canonical and noncanonical equations in the Andoyer elastic variables (Barkin, et al. 1995; Barkin, 1996; in press) have been fulfilled. The Earth is considered as an isolated celestial body with the anelastic (in general case) external envelope (the mantle) and an invariant central part (the core).The interpretation of the Chandler motion of the body, deformed by its own rotation, was given in the case of an elastic envelope. It was shown that the body rotates as a fictitious rigid body with different moments of inertia. The analytical solution of the problem let us explain the next properties of the motion of the deformable bodies: 1) observed period of the Earth’s polar motion; 2) ellipticity of the pole trajectory and difference of the eccentricities of the Chandler and Euler motions; 3) nonuniform velocity of the counter-clockwise polar motion along the Chandler ellipse; 4) orientation of this ellipse (its minor axis is located in the meridian plane, at 14.5 W degrees).The influence of the dissipation on the damping of the Chandler polar motion was studied. The analytical solution of the problem was obtained for the simplest treatment of the delay of the tides caused by the Earth’s rotation (Getino & Ferrándiz 1991; Kubo, 1991). This model explains the characteristic behaviour of the amplitude of the Chandler motion in the periods 1905–1920, 1943–1960 (Vondrák, & Cyril, 1966). The excitation of the Chandler motion can be explained by the upper and lower envelope displacements (Barkin, 1999) with Moon-Sun forced attraction with a period of 412 days, close to the Chandler period.

scholarly journals Anomalies of geomagnetic field due to a vertical prolate rotational ellipsoid

2010 ◽  
Vol 40 (3) ◽  
pp. 185-205 ◽  
Author(s):  
Milan Hvoždara ◽  
Ján Vozár
Keyword(s):  
Analytical Solution ◽  
Geomagnetic Field ◽  
Exact Analytical Solution ◽  
Aeromagnetic Survey ◽  
Prolate Ellipsoid ◽  
Gaussian Curve ◽  
The Earth ◽  
Theoretical Results

Anomalies of geomagnetic field due to a vertical prolate rotational ellipsoid We present an exact analytical solution of the forward magnetometric problem for the perturbing body having the shape of the rotational prolate ellipsoid with the longer axis oriented vertically to the surface of the earth. The anomaly of ΔZ and ΔT is calculated for the network of points in the plane z = const above the ellipsoid, as well as for the points on the surfaces of the volcanic hill: i) the cut cone, ii) the smooth shape given by the rotation of the Gaussian curve. Theoretical results can be useful for the interpretation of land or aeromagnetic survey in the volcanic areas.

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