Water propagation in two-dimensional petroleum reservoirs

Najafi, M. N.; Ghaedi, Mojtaba; Moghimi-Araghi, S.

doi:10.1016/j.physa.2015.10.100

Cited by 28 publications

(56 citation statements)

References 28 publications

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“…This large class of natural systems inspired theoretical models with the aim of capturing the dominant internal dynamics that causes the avalanches.Here we find evidence for a novel non-equilibrium universality class, and propose a new type of outof-equilibrium phase transition between SOC models induced by the geometry of the underlying graph upon which the model is defined. It might be applicable to experiments with spatial flow patterns of transport in heterogeneous porous media [14], which involve the toppling of fluid [15]. Another example is the Barkhausen effect in magnetic systems [16], for which the avalanches have been shown to exhibit scaling behavior with an avalanche size exponent 1.27 ± 0.03 in amorphous ferromagnets (which constitutes a disordered medium) [17,18].…”

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confidence: 99%

Geometry-induced nonequilibrium phase transition in sandpiles

et al. 2020

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We study the sandpile model on three-dimensional spanning Ising clusters with the temperature T treated as the control parameter. By analyzing the three dimensional avalanches and their twodimensional projections (which show scale-invariant behavior for all temperatures), we uncover two universality classes with different exponents (an ordinary BTW class, and SOCT =∞), along with a tricritical point (at Tc, the critical temperature of the host) between them. The SOCT =∞ universality class is characterized by the exponent of the avalanche size distribution τ T =∞ = 1.27 ± 0.03, consistent with the exponent of the size distribution of the Barkhausen avalanches in amorphous ferromagnets (Phys. Rev. L 84, 4705 (2000)). The tricritical point is characterized by its own critical exponents and also some additional scaling behavior in its vicinity. In addition to the avalanche exponents, some other quantities like the average height, the spanning avalanche probability (SAP) and the average coordination number of the Ising clusters change significantly the behavior at this point, and also exhibit power-law behavior in terms of ≡ T −Tc Tc , defining further critical exponents. Importantly the finite size analysis for the activity (number of topplings) per site shows the scaling behavior with exponents β = 0.19 ± 0.02 and ν = 0.75 ± 0.05. A similar behavior is also seen for the SAP and the average avalanche height. The fractal dimension of the external perimeter of the two-dimensional projections of avalanches is shown to be robust against T with the numerical value D f = 1.25 ± 0.01.In the context of out-of-equilibrium critical phenomena, self-organized critical (SOC) systems have attracted much attention because of their role in a wide range of systems, from finance [1] and biological [2] to granular matter [3], the brain [4] and neural networks in general [5]. SOC systems are characterized by their avalanche dynamics resulting from slow driving of the system. Vortex avalanche dynamics in type II superconductors [6], earthquakes [7], solar flares [8], microfracturing processes [9], fluid flow in porous media [10], phase transition-like behavior of the magnetosphere [11], bursts in filters [12], phase transitions in jammed granular matter [3], and avalanches dynamics in the rat cortex [13] are some natural examples for SOC. This large class of natural systems inspired theoretical models with the aim of capturing the dominant internal dynamics that causes the avalanches.Here we find evidence for a novel non-equilibrium universality class, and propose a new type of outof-equilibrium phase transition between SOC models induced by the geometry of the underlying graph upon which the model is defined. It might be applicable to experiments with spatial flow patterns of transport in heterogeneous porous media [14], which involve the toppling of fluid [15]. Another example is the Barkhausen effect in magnetic systems [16], for which the avalanches have been shown to exhibit scaling behavior with an avalanche size exponent 1.27 ± 0....

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confidence: 99%

Geometry-induced nonequilibrium phase transition in sandpiles

et al. 2020

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“…We can imagine of this problem as the coupling of the driven interface problem with the random coulomb potential model, or the critical phenomena on the fractal systems [33]. This concept can be extended to dilute systems that are fractal in some limits [34][35][36][37][38]. Before describing the problem in this type of media, let us first briefly introduce our method of generating RCPs.…”

Section: Two-dimensional Random Coulomb Potential Noise; Our Modelmentioning

confidence: 99%

Edwards-Wilkinson Depinning Transition in the Background of Random Coulomb Potential

Valizadeh,

Samadpour,

Hamzehpour

et al. 2021

Preprint

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The Edwards-Wilkinson (EW) growth of 1 + 1 interface is considered in the background of the correlated random noise. We use random Coulomb potential as the background long-range correlated noise. A depinning transition is observed in a critical driving force Fc ≈ 0.37 in the vicinity of which the final velocity of the interface varies linearly with time. Our data collapse analysis for the velocity shows a crossover time t * at which the velocity is size independent. Based on a two-variable scaling analysis, we extract the exponents, which are different from all universality classes we are aware of. Especially noting that the dynamic and roughness exponents are zw = 1.55 ± 0.05, and αw = 1.05 ± 0.05 at the criticality, we conclude that the system is different from both EW and KPZ universality classes. Our analysis shows therefore that making the noise long-range-correlated, drives the system out of EW universality class. The simulations on the tilted lattice shows that the non-linearity term (λ term in the KPZ equations) goes to zero in the thermodynamic limit.

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“…The scaling behavior of the two point correlation function of the random field h was defined in Eq. (16). The measurement of local roughness exponent α l can be obtained by a linear fit C(r) with r in log − log scale.…”

Section: B Local and Global Roughness Exponentsmentioning

confidence: 99%

Scale-invariant puddles in graphene: Geometric properties of electron-hole distribution at the Dirac point

Najafi

Nezhadhaghighi

2017

Phys. Rev. E

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We characterize the carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity for zero gate voltage. We provide detailed analysis on the resulting spatially inhomogeneous electron gas taking into account the particleparticle interaction and the remote coulomb disorder on an equal footing within the Thomas-FermiDirac theory. We present some general features of the carrier density probability measure of the graphene sheet. We also show that, when viewed as a random surface, the resulting electron-hole puddles at zero chemical potential show peculiar self-similar statistical properties. Although the disorder potential is chosen to be Gaussian, we show that the charge field is non-Gaussian with unusual Kondev relations which can be regarded as a new class of two-dimensional (2D) randomfield surfaces.

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Water propagation in two-dimensional petroleum reservoirs

Cited by 28 publications

References 28 publications

Geometry-induced nonequilibrium phase transition in sandpiles

Geometry-induced nonequilibrium phase transition in sandpiles

Edwards-Wilkinson Depinning Transition in the Background of Random Coulomb Potential

Scale-invariant puddles in graphene: Geometric properties of electron-hole distribution at the Dirac point

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