Search results for "Exponent"
showing 10 items of 896 documents
Experimental Evidence of Leaks in Elastic Pipes
2016
Several studies have been carried out in recent decades to establish a relationship between total head and leaks. In literature, the leakage governing equations have been analysed in light of pipe materials, water head, leak dimension or shape. Most of these contributions questioned the classical Torricelli equation, demonstrating through experimental evidence that the classical orifice law can give unsatisfactory results. Nevertheless, starting from the Torricelli equation, other exponential or linear governing equations have been proposed as mathematical models able to reproduce the leakages in water distribution systems (WDSs). To investigate the validity of the proposed governing equati…
Stochastic approach to highway traffic
2004
We analyze the characteristic features of jam formation on a circular one-lane road. We have applied an optimal velocity model including stochastic noise, where cars are treated as moving and interacting particles. The motion of N cars is described by the system of 2 N stochastic differential equations with multiplicative white noise. Our system of cars behaves in qualitatively different ways depending on the values of control parameters c (dimensionless density), b (sensitivity parameter characterising the fastness of relaxation), and α (dimensionless noise intensity). In analogy to the gas-liquid phase transition in supersaturated vapour at low enough temperatures, we observe three differ…
Nodal Solutions for Supercritical Laplace Equations
2015
In this paper we study radial solutions for the following equation $$\Delta u(x)+f (u(x), |x|) = 0,$$ where $${x \in {\mathbb{R}^{n}}}$$ , n > 2, f is subcritical for r small and u large and supercritical for r large and u small, with respect to the Sobolev critical exponent $${2^{*} = \frac{2n}{n-2}}$$ . The solutions are classified and characterized by their asymptotic behaviour and nodal properties. In an appropriate super-linear setting, we give an asymptotic condition sufficient to guarantee the existence of at least one ground state with fast decay with exactly j zeroes for any j ≥ 0. Under the same assumptions, we also find uncountably many ground states with slow decay, singular gro…
Anomalous tracer diffusion in film forming colloidal dispersions
2000
Film forming colloidal dispersions can be conceived as a material composed of interpenetrating hydrophobic (polymer) and hydrophilic (partially broken interfaces) phases where the transport properties of one phase are influenced by the geometric confinement effect imposed by the other. We studied the transport properties of film forming colloidal dispersions by introducing hydrophobic dye molecules into the colloidal particles and determining their motion with forced Rayleigh Scattering as a function of length scale (grating distance A) and water content. At water contents between 18 and 3 weight percent we find signatures of anomalous tracer diffusion, namely stretched exponential decay cu…
Two-Length-Scale Structure in Some Computer-Generated Aggregates Grown by Diffusion-Limited Aggregation
1994
AbstractThe properties of some aggregates “grown” on a computer by diffusion-limited aggregation have been investigated. Calculations showed that the intensity of the small-angle x-ray and neutron scattering from the aggregates was proportional to q−D for qL ≫ 1, where D > 0, L is a length that characterizes the large-scale structure of the aggregate, q = 4πλ−1 sin(θ/2), γ is the wavelength, and θ is the scattering angle. The magnitude of the exponent D was appreciably smaller than the fractal dimensions that many simulations have shown to be typical of the mass fractal aggregates grown by diffusion-limited aggregation. The calculations suggest that the aggregates have structure on two d…
Surface effects on spinodal decomposition in binary mixtures and the interplay with wetting phenomena.
1994
The phase separation of binary mixtures in a semi-infinite geometry is investigated both by a phenomenological theory and by numerical calculations using a discrete equivalent of the descriptive equations. In the framework of ``model B'' (which describes solid binary mixtures), attention is paid to a proper treatment of the boundary conditions at the free surfaces. We confine ourselves to short-range surface forces and consider parameter values that correspond to both nonwet and wet surfaces in thermal equilibrium. During the initial stages of spinodal decomposition, after a quench from considering an initial condition that corresponds to a completely random concentration distribution, one …
Do crossover functions depend on the shape of the interaction profile?
1999
We examine the crossover from classical to non-classical critical behaviour in two-dimensional systems with a one-component order parameter. Since the degree of universality of the corresponding crossover functions is still subject to debate, we try to induce non-universal effects by adding interactions with a second length scale. Although the crossover functions clearly depend on the range of the interactions, they turn out to be remarkably robust against further variation of the interaction profile. In particular, we find that the earlier observed non-monotonic crossover of the effective susceptibility exponent occurs for several qualitatively different shapes of this profile.
Dependence of two-proton radioactivity on nuclear pairing models
2017
Sensitivity of two-proton emitting decay to nuclear pairing correlation is discussed within a time-dependent three-body model. We focus on the $^6$Be nucleus assuming $\alpha + p + p$ configuration, and its decay process is described as a time-evolution of the three-body resonance state. For a proton-proton subsystem, a schematic density-dependent contact (SDDC) pairing model is employed. From the time-dependent calculation, we observed the exponential decay rule of a two-proton emission. It is shown that the density dependence does not play a major role in determining the decay width, which can be controlled only by the asymptotic strength of the pairing interaction. This asymptotic pairin…
2-D mapping of skin chromophores in the spectral range 500 - 700 nm
2009
The multi-spectral imaging technique has been used for distant mapping of in-vivo skin chromophores by analyzing spectral data at each reflected image pixel and constructing 2-D maps of the relative concentrations of oxy-/deoxy-haemoglobin and melanin. Instead of using a broad visible-NIR spectral range, this study focuses on narrowed spectral band 500–700 nm, speeding-up the signal processing procedure. Regression analysis confirmed that superposition of three Gaussians is optimal analytic approximation for the oxy-haemoglobin absorption tabular spectrum in this spectral band, while superposition of two Gaussians fits well for deoxy-haemoglobin absorption and exponential function – for mel…
Iterative approach to the exponential representation of the time–displacement operator
2005
An iterative method due to Voslamber is reconsidered. It provides successive approximations for the logarithm of the time–displacement operator in quantum mechanics. The procedure may be interpreted, a posteriori, as an infinite re-summation of terms in the so-called Magnus expansion. A recursive generator for higher terms is obtained. From two illustrative examples, a detailed comparative study is carried out between the results of the iterative method and those of the Magnus expansion.