Homogeneous deformation of a continuous medium

1997 ◽  
Vol 38 (3) ◽  
pp. 445-452
Author(s):  
A. F. Revuzhenko
Keyword(s):  
Continuous Medium ◽  
Homogeneous Deformation

Instabilities in a continuous medium model for the retina

1980 ◽  
Vol 39 (1) ◽  
pp. 11-14 ◽  
Author(s):  
Hendrik J. Van Ouwerkerk ◽  
Jan H. Tulp ◽  
Hans A. L. Piceni ◽  
Jacques A. J. Roufs ◽  
Frans J. J. Blommaert
Keyword(s):  
Continuous Medium ◽  
Medium Model

scholarly journals Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 395-409 ◽  
Author(s):  
Mayeul Arminjon
Keyword(s):  
Gravitational Field ◽  
Lorentz Force ◽  
Maxwell Equations ◽  
Gravitational Force ◽  
Continuous Medium ◽  
Pressure Force ◽  
Local Charge ◽  
Theory Of Gravitation ◽  
External Forces ◽  
Continuum Dynamics

AbstractAn alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes’ thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton’s second law. This implies Einstein’s geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell’s equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a “free” photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field.

General theory of small elastic deformations superposed on finite elastic deformations

1952 ◽  
Vol 211 (1104) ◽  
pp. 128-154 ◽  
Keyword(s):  
General Theory ◽  
Elastic Material ◽  
Finite Deformation ◽  
Plane Surface ◽  
Thin Sheet ◽  
Potential Functions ◽  
Homogeneous Deformation ◽  
Infinitesimal Deformation ◽  
Elastic Deformations ◽  
Isotropic Elastic Material

Using tensor notations a general theory is developed for small elastic deformations, of either a compressible or incompressible isotropic elastic body, superposed on a known finite deformation, without assuming special forms for the strain-energy function. The theory is specialized to the case when the finite deformation is pure homogeneous. When two of the principal extension ratios are equal the changes in displacement and stress due to the small superposed deformation are expressed in terms of two potential functions in a manner which is analogous to that used in the infinitesimal deformation of hexagonally aeolotropic materials. The potential functions are used to solve the problem of the infinitesimally small indentation, by a spherical punch, of the plane surface of a semi-infinite body of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation symmetrical about the normal to the force-free plane surface. The general theory is also applied to the infinitesimal deformation of a thin sheet of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation by forces in its plane. A differential equation is obtained for the small deflexion of the sheet due to small forces acting normally to its face. This equation is solved completely in the case of a clamped circular sheet subjected to a pure homogeneous deformation having equal extension ratios in the plane of the sheet, the small bending force being uniformly distributed over a face of the sheet. Finally, equations are obtained for the homogeneously deformed sheet subjected to infinitesimal generalized plane stress, and a method of solution by complex variable technique is indicated.

scholarly journals Variational theory for (2+1)-dimensional fractional dispersive long wave equations

2021 ◽  
pp. 23-23
Author(s):  
Xiao-Qun Cao ◽  
Cheng-Zhuo Zhang ◽  
Shi-Cheng Hou ◽  
Ya-Nan Guo ◽  
Ke-Cheng Peng
Keyword(s):  
Porous Media ◽  
Nonlinear Waves ◽  
Inverse Method ◽  
Wave Equations ◽  
Continuous Medium ◽  
Variational Principles ◽  
Variational Theory ◽  
Long Wave ◽  
Potential Applications ◽  
Fractional System

This paper extends the (2+1)-dimensional Eckhaus-type dispersive long wave equations in continuous medium to their fractional partner, which is a model of nonlinear waves in fractal porous media. The derivation is shown briefly using He?s fractional derivative. Using the semi-inverse method, the variational principles are established for the fractional system, which up to now are not discovered. The obtained fractal variational principles are proved correct by minimizing the functionals with the calculus of variations, and might find potential applications in numerical modelling.

scholarly journals NMR Analysis Method of Gas Flow Pattern in the Process of Shale Gas Depletion Development

Geofluids ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-7
Author(s):  
Rui Shen ◽  
Zhiming Hu ◽  
Xianggang Duan ◽  
Wei Sun ◽  
Wei Xiong ◽  
...  
Keyword(s):  
Flow Pattern ◽  
Pore Pressure ◽  
Shale Gas ◽  
Gas Flow ◽  
Continuous Medium ◽  
Slip Flow ◽  
Flow Patterns ◽  
Transitional Flow ◽  
Analysis Method ◽  
Adsorbed Gas

Shale gas reservoirs have pores of various sizes, in which gas flows in different patterns. The coexistence of multiple gas flow patterns is common. In order to quantitatively characterize the flow pattern in the process of shale gas depletion development, a physical simulation experiment of shale gas depletion development was designed, and a high-pressure on-line NMR analysis method of gas flow pattern in this process was proposed. The signal amplitudes of methane in pores of various sizes at different pressure levels were calculated according to the conversion relationship between the NMR T 2 relaxation time and pore radius, and then, the flow patterns of methane in pores of various sizes under different pore pressure conditions were analyzed as per the flow pattern determination criteria. It is found that there are three flow patterns in the process of shale gas depletion development, i.e., continuous medium flow, slip flow, and transitional flow, which account for 73.5%, 25.8%, and 0.7% of total gas flow, respectively. When the pore pressure is high, the continuous medium flow is dominant. With the gas production in shale reservoir, the pore pressure decreases, the Knudsen number increases, and the pore size range of slip flow zone and transitional flow zone expands. When the reservoir pressure is higher than the critical desorption pressure, the adsorbed gas is not desorbed intensively, and the produced gas is mainly free gas. When the reservoir pressure is lower than the critical desorption pressure, the adsorbed gas is gradually desorbed, and the proportion of desorbed gas in the produced gas gradually increases.

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