Fast numerical methods are used to solve the equations for periodically rotating spiral waves in excitable media, and the associated eigenvalue problem for the stability of these waves. Both equally and singly diffusi...
Fast numerical methods are used to solve the equations for periodically rotating spiral waves in excitable media, and the associated eigenvalue problem for the stability of these waves. Both equally and singly diffusive media are treated. Rotating-wave solutions are found to be discretely selected by the system and an isolated, complex-conjugate pair of eigenmodes is shown to cause instability of these waves. The instability arises at the point of zero curvature on the spiral interface and results in wavelike disturbances which propagate from this point along the interface.
作者：
Ahrens, Cory D.Colorado School of Mines
Department of Applied Mathematics and Statistics Program in Nuclear Science and Engineering Golden CO 80401-1887 United States
The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, deriv...
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ISBN:
(纸本)9781622763894
The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, derived using Lagrange interpolation and collocation, retains the classical Sn structure, with the main difference being how the scattering source is calculated. Because of the formal similarity with the classical S n equations, it should be possible to modify existing computer codes to take advantage of the new formulation. In addition, the new S n-like equations correctly capture delta function scattering. The second set of equations, derived using a Galerkin technique, does not retain the classical Sn structure because the streaming term is not diagonal. However, these equations can be cast into a form similar to existing methods developed to reduce ray effects. Numerical investigation of both sets of equations is under way.
A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form...
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A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form depends on the assumptions made concerning the intermittency.
Intermittency effects in turbulence are discussed from a dynamical point of view. A two-fluid model is developed to describe quantitatively the non-gaussian statistics of turbulence at small scales. With a self-simila...
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Intermittency effects in turbulence are discussed from a dynamical point of view. A two-fluid model is developed to describe quantitatively the non-gaussian statistics of turbulence at small scales. With a self-similarity argument, the model gives rise to the entire set of inertial range scaling exponents for normalized velocity structure functions. The results are in excellent agreement with experimental and numerical measurements. The model suggests a physical mechanism of intermittency, namely the self-interaction of turbulence structures.
Direct numerical simulations with up to 10242 resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian ...
Direct numerical simulations with up to 10242 resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian white-in-time noise. The energy spectra for the inverse energy cascade deviate strongly from the expected k−5/3 law and are close (somewhat flatter) to k−3. The reason for the deviation is traced to the emergence of strong vortices distributed over all scales. Statistical properties of the vortices are explored.
Polynomially large ground-state energy gaps are rare in many-body quantum systems, but useful in quantum information and an interesting feature of the one-dimensional quantum Ising model. We show analytically that the...
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Polynomially large ground-state energy gaps are rare in many-body quantum systems, but useful in quantum information and an interesting feature of the one-dimensional quantum Ising model. We show analytically that the gap is generically polynomially large not just for the quantum Ising model, but for one-, two-, and three-dimensional interaction lattices and Hamiltonians with certain random interactions. We extend the analysis to Hamiltonian evolutions and we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. These results also yield a new perspective on the one-dimensional cluster state.
We consider two-dimensional flow stirred by a small-scale, white-in-time random noise in the zero viscosity limit. Numerical simulations show that, after a transient state, an inertial-range energy spectrum E(k)∝k−x ...
We consider two-dimensional flow stirred by a small-scale, white-in-time random noise in the zero viscosity limit. Numerical simulations show that, after a transient state, an inertial-range energy spectrum E(k)∝k−x with x=5/3±0.05 is established by the inverse cascade process. This range grows in time until a Bose condensate is formed at the largest scales in the system (k≊1). Prior to condensate formation the statistics of velocity differences are extremely close to Gaussian, and only after Bose condensation strong deviations from Gaussian statistics are detected at small scales. The structures responsible for this effect are identified.
The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperatu...
The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperature and velocity spectra are ET≊k−7/5 and E≊k−11/5, respectively. At the smaller scales, in the dissipation range of the temperature fluctuations, the Kolmogorov range where most of the energy is dissipated is predicted. The new set of scaling exponents, which can be observed in the experiments in the small-aspect-ratio convection cells, is derived.
Heterogeneous flows are observed to result from variations in the geometry and topology of pore structures within stochastically generated three dimensional porous media. A stochastic procedure generates media compris...
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Heterogeneous flows are observed to result from variations in the geometry and topology of pore structures within stochastically generated three dimensional porous media. A stochastic procedure generates media comprising complex networks of connected pores. Inside each pore space, the Navier-Stokes equations are numerically integrated until steady state velocity and pressure fields are attained. The intricate pore structures exert spatially variable resistance on the fluid, and resulting velocity fields have a wide range of magnitudes and directions. Spatially nonuniform fluid fluxes are observed, resulting in principal pathways of flow through the media. In some realizations, up to 25% of the flux occurs in 5% of the pore space depending on porosity. The degree of heterogeneity in the flow is quantified over a range of porosities by tracking particle trajectories and calculating their attributes including tortuosity, length, and first passage time. A representative elementary volume is first computed so the dependence of particle based attributes on the size of the domain through which they are followed is minimal. High correlations between the dimensionless quantities of porosity and tortuosity are calculated and a logarithmic relationship is proposed. As the porosity of a medium increases the flow field becomes more uniform.
We propose the log-q-Gaussian distribution which is obtained as the distribution of a random variable whose logarithm is q-Gaussian. Various types of properties of the new distribution are given such as the moments, t...
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