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 ...

PURPOSE To determine whether face perception can be equalized across the visual field by scaling size and contrast simultaneously. METHODS Contrast sensitivities were measured for detection (N = 1) and identification (N = 2-8) of a target face as a function of size (0.4 degrees-10 degrees) across eccentricities (E = 0 degrees-10 degrees). RESULTS In all conditions contrast sensitivity first...

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski’s coagulation equation for the three simplest rate kernels K(x,y) = 2, x + y and xy. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak converg...

The numerical solutions of the non-linear evolution equation are shown to display the “geometric” scaling recently discovered in the experimental data. The phenomena hold both for proton and nucleus targets for all x below 10−2 and 0.25GeV2 ≤ Q2 ≤ 2.5 × 103 GeV2. The scaling is practically exact (few percent error) in the saturation region. In addition, an approximate scaling is found in the va...

When performing experimental work to study the recovery of NAPLs (non aqueous phase liquids) from porous media by water flood, scaling seems to be a critical step in the production of useful data that can be obtained from lab experiments. During many years, scaling was a very common technique in the petroleum industry. This technique was highly developed in the oil field in order to achieve gre...

Cocurrent spontaneous imbibition (COCSI) of an aqueous phase into matrix blocks arising from capillary forces is an important mechanism for petroleum recovery from fractured petroleum reservoirs. In this work, the modeling of countercurrent imbibition is used to develop the appropriate scaling equations. Considering the imbibition process and the water and oil movement respectively as the wet p...

The stochastic nonlinear partial differential equation known as the Kardar-Parisi-Zhang (KPZ) equation is a highly successful phenomenological mesoscopic model of surface and interface growth processes. Its suitability for analytical work, its explicit symmetries and its prediction of an exact dynamic scaling relation for a one-dimensional substratum led people to adopt it as a 'standard' model...

Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control problems, that have been proposed as approximate models for the study of these critically loaded controlled stochastic networks, can be regarded as formal scaling ...

The property of continuity of an arbitrary scaling function is known to be unstable with respect to the coeecients in the associated dilation equation. That is, if f is a continuous function which is a solution of the dilation equation f (x) = P N k=0 c k f (2x ? k) then a dilation equation with slightly perturbed coeecients f~ c 0 ; : : : ; ~ c N g need not have a continuous solution. The conv...

We study the scaling form for the cell boundary misorientation angle distribution of Hughes and co-workers. By formulating the problem in terms of random walks in rotation space, we are able to incorporate the new cell boundaries formed during cell refinement with increasing deformation ǫ. The simplest form for the corresponding diffusion equation yields a good fit to the experimental scaling c...