Numerical and Analytical Methods for the Analysis of Flow of Water Through Soils and Earth Structures

AbstractAt the probe approximation, we construct a holographic p-wave conductor/superconductor model in the five-dimensional Lifshitz black hole with the Weyl correction via both numerical and analytical methods, and study the effects of the Lifshitz parameter z as well as the Weyl parameter $$\gamma $$ γ on the superconductor model. As we take into account one of the two corrections separately, the increasing z ($$\gamma $$ γ ) inhibits(enhances) the superconductor phase transition. When the two corrections are considered comprehensively, they display the obviously competitive effects on both the critical temperature and the vector condensate. In particular, the promoting effects of the Weyl parameter $$\gamma $$ γ on the critical temperature are obviously suppressed by the increasing Lifshitz parameter. Meanwhile, in the case of $$z<2.35$$ z < 2.35 ($$z>2.35$$ z > 2.35 ), the condensate at lower temperature decreases(increases) with the increasing Weyl parameter $$\gamma $$ γ . What is more, the difference among the condensate with the fixed Weyl parameter($$\gamma =-\frac{6}{100},0,\frac{4}{100}$$ γ = - 6 100 , 0 , 4 100 ) decreases(increases) with the increasing Lifshitz parameter z in the region $$z<2.35$$ z < 2.35 ($$z>2.35$$ z > 2.35 ). Furthermore, the increasing z obviously suppresses the real part of conductivity for all value of the Weyl parameter $$\gamma $$ γ . In addition, the analytical results agree well with the ones from the numerical method.

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Gaussian beam diffraction in inhomogeneous and logarithmically saturable nonlinear media

Open Physics ◽

10.2478/s11534-012-0066-3 ◽

2012 ◽

Vol 10 (4) ◽

Cited By ~ 1

Author(s):

Pawel Berczynski

Keyword(s):

Gaussian Beam ◽

Wave Front ◽

Analytical Methods ◽

Cylindrical Symmetry ◽

Nonlinear Media ◽

First Order ◽

Self Focusing ◽

Complex Curvature ◽

Numerical And Analytical Methods ◽

Beam Diffraction

AbstractThe method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear saturable media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, PCGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous and nonlinear media as compared to the numerical and analytical methods of nonlinear optics. The power of PCGO method is presented on the example of Gaussian beam evolution in logarithmically saturable medium with either focusing and defocusing refractive profile. Besides, the influence of initial curvature of the wave front on GB evolution in nonlinear saturable medium is discussed in this paper.

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Temporal inactivation enhances robustness in an evolving system

Royal Society Open Science ◽

10.1098/rsos.181471 ◽

2019 ◽

Vol 6 (2) ◽

pp. 181471

Author(s):

Fumiko Ogushi ◽

János Kertész ◽

Kimmo Kaski ◽

Takashi Shimada

Keyword(s):

Phase Diagram ◽

Dynamic Model ◽

Analytical Methods ◽

The Other ◽

Entire System ◽

Dormant State ◽

Random Interactions ◽

Active Elements ◽

Evolving System ◽

Numerical And Analytical Methods

We study the robustness of an evolving system that is driven by successive inclusions of new elements or constituents with m random interactions to older ones. Each constitutive element in the model stays either active or is temporarily inactivated depending upon the influence of the other active elements. If the time spent by an element in the inactivated state reaches T W , it gets extinct. The phase diagram of this dynamic model as a function of m and T W is investigated by numerical and analytical methods and as a result both growing (robust) as well as non-growing (volatile) phases are identified. It is also found that larger time limit T W enhances the system’s robustness against the inclusion of new elements, mainly due to the system’s increased ability to reject ‘falling-together’ type attacks. Our results suggest that the ability of an element to survive in an unfavourable situation for a while, either as a minority or in a dormant state, could improve the robustness of the entire system.

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