Search results for "scaling"
showing 10 items of 754 documents
Local-porosity theory for flow in porous media
1992
A recently introduced geometric characterization of porous media based on local-porosity distributions and local-percolation probabilities is used to calculate dc permeabilities for porous media. The disorder in porous media is found to be intimately related to the percolation concept. The geometric characterization is shown to open a possibility for understanding experimentally observed scaling relations between permeability, formation factor, specific internal surface, and porosity. In particular, Kozeny's equation k\ensuremath{\propto}\ensuremath{\varphi}\ifmmode\bar\else\textasciimacron\fi{} $^{\mathit{b}}$ between effective permeability and bulk porosity and the relation k\ensuremath{\…
Absence of hyperscaling violations for phase transitions with positive specific heat exponent
1994
Finite size scaling theory and hyperscaling are analyzed in the ensemble limit which differs from the finite size scaling limit. Different scaling limits are discussed. Hyperscaling relations are related to the identification of thermodynamics as the infinite volume limit of statistical mechanics. This identification combined with finite ensemble scaling leads to the conclusion that hyperscaling relations cannot be violated for phase transitions with strictly positive specific heat exponent. The ensemble limit allows to derive analytical expressions for the universal part of the finite size scaling functions at the critical point. The analytical expressions are given in terms of generalH-fu…
Tricritical universality in a two-dimensional spin fluid
1995
Monte Carlo simulations are used to investigate the tricritical point properties of a 2d spin fluid. Measurements of the scaling operator distributions are employed in conjunction with a finite-size scaling analysis to locate the tricritical point and determine the directions of the relevant scaling fields and their associated tricritical exponents. The scaling operator distributions and exponents are shown to match quantitatively those of the 2d Blume-Capel model, confirming that both models belong to the same universality class. Mean-field calculations of the tricritical point properties are also compared with the simulation measurements.
Engineering the Success of Quantum Walk Search Using Weighted Graphs
2016
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.
Dynamical Processes in Open Quantum Systems from a TDDFT Perspective: Resonances and Electron Photoemission
2015
We present a review of different computational methods to describe time-dependent phenomena in open quantum systems and their extension to a density-functional framework. We focus the discussion on electron emission processes in atoms and molecules addressing excited-state lifetimes and dissipative processes. Initially we analyze the concept of an electronic resonance, a central concept in spectroscopy associated with a metastable state from which an electron eventually escapes (electronic lifetime). Resonances play a fundamental role in many time-dependent molecular phenomena but can be rationalized from a time-independent context in terms of scattering states. We introduce the method of c…
Finite-size scaling approach for critical wetting: rationalization in terms of a bulk transition with an order parameter exponent equal to zero.
2012
Clarification of critical wetting with short-range forces by simulations has been hampered by the lack of accurate methods to locate where the transition occurs. We solve this problem by developing an anisotropic finite-size scaling approach and show that then the wetting transition is a ``bulk'' critical phenomenon with order parameter exponent equal to zero. For the Ising model in two dimensions, known exact results are straightforwardly reproduced. In three dimensions, it is shown that previous estimates for the location of the transition need revision, but the conclusions about a slow crossover away from mean-field behavior remain unaltered.
Scaling the abruptly autofocusing beams in the direct-space
2017
International audience; We propose a simple technique to scale the abruptly autofocusing beams in the direct space by introducing a scaling factor in the phase. Analytical formulas are deduced based on optical caustics, explicitly revealing how the scaling factor controls location, peak intensity, and size of the focal spot. We demonstrate that the multiplication of a scaling factor on the phase is equivalent to the axial-scaling transformation under the paraxial approximation. Further numerical and experimental results confirm theoretical predictions. In addition, amplitude modulation using phase-only holograms is used to maintain the peak intensity level of the focal spots.
Nonsymmetric Fourier transforming with an anamorphic system
1984
The idea of obtaining a nonsymmetric Fourier transform with crossed cylindrical lenses of different focal lengths is presented. The anamorphic rotation-variant system produces a scaled Fourier transform F(u,mv) of an object f(x,y), where m is a scaling constant. The system performs controlled angular magnification of an object spectrum. It is shown that the super resolution in one direction is gained by reducing the number of degrees of freedom of the optical message in the other. Experimental results are shown where the scaling constant m of up to 10 has been obtained.
The effect of the slope of irregularly distributed roughness elements on turbulent wall-bounded flows
2008
Wall roughness produces a downward shift of the mean streamwise velocity profile in the log region, known as the roughness function. The dependence of the roughness function on the height and arrangement of roughness elements has been confirmed in several studies where regular rough walls were analysed; less attention has been paid to non-regular rough walls. Here, a numerical analysis of turbulent flows over irregularly shaped rough walls is performed, clearly identifying the importance of a parameter, called the effective slope (ES) of the wall corrugations, in characterizing the geometry of non-smooth irregular walls. The effective slope proves to be one of the fundamental geometric para…
New Development of Monte Carlo Techniques for Studying Bottle-brush Polymers
2011
Due to the complex characteristics of bottle-brush polymers, it became a challenge to develop an efficient algorithm for studying such macromolecules under various solvent conditions or some constraints in the space by using computer simulations. In the limit of a bottle-brush polymer with a rather stiff backbone (straight rigid backbone), we generalize the variant of the biased chain growth algorithm, the pruned-enriched Rosenbluth method, for simulating polymers with complex architecture, from star polymers to bottle-brush polymers, on the simple cubic lattice. With the high statistics of our Monte Carlo results, we check the theoretical predictions of side chain behavior and radial monom…