Asphaltene instability is one of the major problems in gas injection projects throughout the world. Numerous models have been developed to predict asphaltene precipitation; The scaling equation is an attractive tool because of its simplicity and not involving complex properties of asphaltene. In this work, a new scaling model is presented to account  for asphaltene precipitation due to gas ...

We study G/G/n+GI queues in which customer patience times are independent, identically distributed following a general distribution. When a customer’s waiting time in queue exceeds his patience time, the customer abandons the system without service. For the performance of such a system, we focus on the abandonment process and the queue-length process. We prove that, under some conditions, a det...

We consider coupled models for particulate flows, where the disperse phase is made of particles subject to size variations. We are thus led to kinetic equations with coagulation and breakup operators, coupled to fluid mechanics equations. We discuss the existence and stability of stationary solutions. We also derive macroscopic models through asymptotic hydrodynamic regimes, once relevant scali...

In this paper we derive quantitative uniqueness estimates at infinity for solutions to an elliptic equation with unbounded drift in the plane. More precisely, let u be a real solution to ∆u + W · ∇u = 0 in R2, where W is real vector and ‖W‖Lp(R2) ≤ K for 2 ≤ p <∞. Assume that ‖u‖L∞(R2) ≤ C0 and satisfies certain a priori assumption at 0. Then u satisfies the following asymptotic estimates at R ...

The behavior of vector fields under translation, rotation and scaling differs withrespect to the underlying application. Moment invariants that are customized tothe specific problem can be constructed by means of normalization.In this paper, we calculate general TRS (translation, rotation, and scaling) mo-ment invariants for two-dimensional vector fields. As an example, we s...

The Tracy-Widom distribution that has been much studied in recent years can be thought of as an extreme value distribution. We discuss interpolation between the classical extreme value distribution exp(− exp(−x)), the Gumbel distribution, and the Tracy-Widom distribution. There is a family of determinantal processes whose edge behaviour interpolates between a Poisson process with density exp(−x...

In this paper, we find various analytic (1+3)D solutions to relativistic ideal hydrodynamic equations based on embedding of known low-dimensional scaling solutions. We first study a class of flows with 2D Hubble Embedding, for which a single ordinary differential equation for the remaining velocity field can be derived. Using this equation, all solutions with transverse 2D Hubble embedding and ...

We study scaling relations of compressible strongly magnetized turbulence. We find a good correspondence of our results with the Fleck (1996) model of compressible hydrodynamic turbulence. In particular, we find that the density-weighted velocity, i.e. u ≡ ρv, proposed in Kritsuk et al. (2007) obeys the Kolmogorov scaling, i.e. Eu(k) ∼ k −5/3 for the high Mach number turbulence. Similarly, we f...

We consider the Ginzburg-Landau energy for a type-I superconductor in the shape of an infinite three-dimensional slab, with two-dimensional periodicity, with an applied magnetic field which is uniform and perpendicular to the slab. We determine the optimal scaling law of the minimal energy in terms of the parameters of the problem, when the applied magnetic field is sufficiently small and the s...

Linear functions of many independent random variables lead to classical noises (white, Poisson, and their combinations) in the scaling limit. Some singular stochastic flows and some models of oriented percolation involve very nonlinear functions and lead to nonclassical noises. Two examples are examined, Warren’s ‘noise made by a Poisson snake’ and the author’s ‘Brownian web as a black noise’. ...