Simple Periodic Model Research Articles

Particle saltation over rigid bumpy beds in viscous shearing flows

We investigate the steady motion of solid particles through successive jumps over a horizontal, rigid, bumpy bed driven by the shearing of a viscous fluid in the absence of turbulence, lubrication forces and collisions above the bed. We employ a discrete element method for the particles coupled to a mean field continuum model for the fluid to run quasi-two-dimensional simulations that we compare with the predictions of a simple model which assumes that all the particles follow identical periodic trajectories determined by the intensity of the shearing and compatible with previously suggested laws relating the particle velocities before and after the impact with the bed. We solve the periodic model both numerically and analytically, and identify the solutions that are linearly stable to small perturbations. We show that the stable solutions of the periodic model are in qualitative and quantitative agreement with the discrete simulations, as long as the number of moving particles in the system is not too large. The discrete simulations further reveal that there are two distinct families of particle trajectories, and that the simple periodic model is actually a good representation of the more energetic particles, that spend most of their time in the upper flow layers where they can gain momentum from the flow.

Demand forecast and allocation system of coalbed methane of different grades in mining area

ABSTRACT Coal mine drainage gas, also known as Coal-Bed Methane (CBM), is a type of clean energy. Different concentrations or grades of gas are extracted and used in the mining area, and the supply and demand of different concentrations of gas is complicated. To achieve optimal resource allocation and minimal environmental pollution, the utilization of different concentrations of CBM and the time characteristics of utilization are explored, and a method for forecasting the demand for different concentrations of gas is proposed based on the time series forecasting algorithm. With the model fitting parameters combined, the prediction models are evaluated by comparison of the predicted results with the actual data. The predicted results show that the simple periodic model can reasonably predict the demand for high-grade CBM in the mining area, while the Additive Holt-Winters (AHW) model can forecast the demand for low-grade CBM properly. And the fitting parameters of the prediction models indicate that the information is sufficiently extracted and the prediction results are satisfactory. Finally, the resource allocation system for different grades of CBM is proposed through the minimum element method and the analytic hierarchy process. The proposed allocation system can provide a reference for developing a better CBM allocation system in the mining area to reduce the waste of CBM.

Thickness-Modulated One-Dimensional Periodic Phononic Crystal

We have studied the dispersion curves of the thickness-modulated one-dimensional (1D) periodic phononic crystal. The dispersion curves of acoustic wave propagating perpendicular to the surfaces of the models are calculated based on the plane wave expansion (PWE) method. By compared the band gaps in thickness-modulated structure with the simple periodic structure, we have found that the band gaps in simple periodic model split into many sub-band gaps when the thickness of media layer is modulated periodically. This can be explained that the thickness-modulated structure can be considered to be made up of many periodic structures with different lattice spacing. It provides flexible choices for real engineering requirement.

Inertial capture in flow through porous media

We investigate through numerical calculation of non-Brownian particles transported by a fluid in a porous medium, the influence of geometry and inertial effects on the capture efficiency of the solid matrix. In the case of a periodic array of cylinders and under the action of gravity, our results reveal that δ ∼ St, where δ is the particle capture efficiency, and St is the Stokes number. In the absence of gravity, we observe a typical second order transition between non-trapping and trapping of particles that can be expressed as δ ∼ (St − Stc)α, with an exponent α ≈ 0.5, where Stc is the critical Stokes number. We also perform simulations for flow through a random porous structure and confirm that its capture behavior is consistent with the simple periodic model.

Antiferromagnetism and superconductivity in

The short-ranged antiferromagnetism recently seen in is proved incompatible with two-dimensional (2D) order parameter models that take the antiferromagnetism as a symmetry-breaking field. To adjust to the local moment direction, the order parameter twists over very long length scales as per the Imry-Ma argument. A variational solution to the Ginzburg-Landau equations is used to study the nature of the short-range superconducting order. Although there are still two transitions, the lower one is of first order - in contradiction to experiments. It is shown that the latent heat predicted by the 2D models at the lower transition is too large not to have been seen. A simple periodic model is numerically studied to show that the second transition cannot be a crossover either.

Statistical Predictability and Parametric Models of Daily Ambient Temperature and Solar Irradiance: An Analysis in the Italian Climate

Abstract Stochastic–dynamic models are discussed for both air temperature and solar irradiance daily time series in the Italian climate. Most of the methodologies discussed in this paper are well known and established for processes having a Gaussian distribution. However, a technique is presented that allows statistical inferences for non-Gaussian processes. Applying these models to 20-year time series, their predictability is analyzed for five meteorological stations of the Areonautica Militare Italiana. The following results were obtained: 1) the seasonalities in both the mean and the standard deviations of measured data are well fitted by simple periodic models; 2) the short range statistical fluctuations of the analyzed variables are well described by first order autoregressive processes whose parameters have constant values for all five stations. For the sake of brevity results are presented only for one station (Napoli).

Spin Waves and Long-Range Order in the Diluted Heisenberg Ferromagnet at Zero Temperature

The variational treatment of spin waves in the randomly diluted Heisenberg ferromagnet at zero temperature is studied. It is argued that a convenient variational principle for the excitation spectrum of an alloy is difficult to formulate rigorously. However, at extremely long wavelengths a simple variational calculatation probably has approximate validity providing localized excitations in isolated clusters of magnetic sites are excluded. Within the approximation which ignores this exclusion we obtain a second-order variational bound for the spin-wave energy which, unlike that found by Murray, is positive at all concentrations. Similar results for concentrations above the critical percolation concentration ${x}_{p}$ are obtained when the localized excitations are excluded in which case the restricted configuration averages can only be evaluated approximately. We point out that the critical concentration ${x}_{c}$ for the occurance of long-range order depends only on the properties of the infinite cluster. Thus the thermal stability of spin waves depends on the dimensionality of the infinite cluster. An argument is given to show that the infinite cluster is not one dimensional. The range of concentrations for which the infinite cluster is two dimensional is either nonexistent or small. We conclude, then, that ${x}_{c}$ is close, if not exactly equal, to ${x}_{p}$. The condition for a discontinuity in ${T}_{C}(x)$ for $x\ensuremath{\rightarrow}{x}_{c}$ is discussed in terms of a simple periodic model for dilution.

On Theoretical Limits of Predictability

The question of whether long-range deterministic predictions of the atmosphere are possible is examined directly in terms of growth of initial errors. Simple physical models are considered in which a unit mass moves at constant and variable speeds. It is concluded that the distant-future location of the mass is unpredictable in both cases. Estimated growth rates of temperature errors associated with a simple periodic model of the atmosphere are found to be appreciable. To generalize these results, it is suggested that deterministic predictions of meteorological variables are not feasible at long range, if only because of the growth of inevitable initial errors with time.