We developed a simple analytical model for describing subvisible cirrus clouds qualitatively. Using theory of dynamical systems we found two different states for the long-term behaviour of subvisible cirrus clouds, i.e. an attractor case (stable equilibrium point) and a limit cycle scenario. The transition between the states constitutes a Hopf bifurcation and is determined by environmental conditions such as vertical updraughts and temperature.

The accuracy of the assimilation results crucially relies on the estimate accuracy of forecast error covariance matrix in data assimilation. Ensemble Kalman filter estimates the forecast error covariance matrix as the sampling covariance matrix of the ensemble forecast states, which need to be further inflated. The experiment results on the Lorenz-96 model show that the analysis error is reduced and the analysis sensitivity to observations is improved using the proposed inflation technique.

We concentrate on the stick-slip-like movement occurring under rate-independent friction due to the eigenoscillation of the fault faces and the associated wave propagation. Also, a simple mechanism of unusually high shear fracture or sliding zone propagation is considered. This is the P sonic propagation of sliding area over a fault based on the fact that the accumulation of elastic energy in the sliding plates can produce oscillations in the velocity of sliding (friction is constant).

The best reconstructions of the past ocean state involve the statistical combination of numerical models and observations; however, the computationally efficient method that produces physically interpretable fields is thought to not be applicable to chaotic dynamical systems, such as ocean models with eddies. Here we use a model of the chaotic, forced pendulum to show that the most popular existing method is successful so long as there are enough uncertain boundary conditions through time.

Lagrangian coherent structures have supported the description of transport processes in fluid dynamics. In this work we use the M function to provide new insights into the 3-D Lagrangian structure of the southern stratosphere. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied to describe the vertical extension of the stratospheric polar vortex and its evolution.

If climate is viewed as a chaotic dynamical system, its trajectories yield on an object called an attractor. Being perturbed by an external forcing, this attractor could be modified. With Wasserstein distance, we estimate on a derived Lorenz model the impact of a forcing similar to climate change. Our approach appears to work with small data sizes. We have obtained a methodology quantifying the deformation of well-known attractors, coherent with the size of data available.

The effects of the Sun upon the Earth's atmosphere occur in several ways. Significant electrodynamic coupling processes transfer particles and energy from the solar wind into the Earth's environment. Applied to the dynamical characteristics of high-intensity, long-duration, continuous auroral activity (HILDCAA) and non-HILDCAA events, nonlinear analysis tools like RQA aid to unravel peculiarities related to two concurrent space mechanisms known as magnetic reconnection and viscous interaction.

A spring-block model is used to determine an upper limit of slow-earthquake zones through study of self-oscillatory behavior with the Hopf bifurcation mechanism. What is the role of fluids in the mechanism of energy dissipation? Are the variations in oscillatory behavior (in the transition zone) due to external forces? What are the limits of parameters for this to occur? The proposed limit makes a difference to oscillatory behavior. Oscillation frequency, L, and fluids are related to results.

The article aids the understanding of the propagation of vibration through complex media (e.g., soil). It presents various techniques to better interpret signals (recorded vibrations). The mathematical work done in the article can be utilized for various engineering applications such as oil or mineral exploration, designing materials for shock protection or energy-trapping. The conclusion of the article also mentions some of the ongoing as well as future work related to the research.

The process of wave propagation in the discrete chain of bilinear oscillators subjected to several types of external harmonic excitation has been analysed. The phenomenon of sign inversion of the displacement is observed for tension–compression excitation. The solution for wave propagation in a continuous 1-D bimodular rod is developed and the numerical results are compared showing good agreement.

In order to assess energy loss during wave propagation in fragmented media, an impact model is proposed. The proposed model can be expressed by or used together with other linear damping models, which is important for the determination of mechanical characteristics of such media and mineral exploration.

In this paper, I study the frictional and viscous effects on multistable slip of earthquakes based on a one-degree-of-freedom model through numerical simulations. Results show three regimes of stable, intermittent, and unstable slip, depending on the values of model parameters.

This work arose from a desire to understand the nature of particle motions in turbulence. We sought a simple conceptual model that could describe such motions, then realized that this model could be applicable to an array of other problems. The basic idea is to create a string of random numbers, called a stochastic process, that mimics the properties of particle trajectories. This model could be useful in making best use of data from freely drifting instruments tracking the ocean currents.

We develop data assimilation techniques for numerical models using moving mesh methods. Moving meshes are valuable for explicitly tracking interfaces and boundaries in evolving systems. The application of the techniques is demonstrated on a one-dimensional model of an ice sheet. It is shown, using various types of observations, that the techniques predict the evolution of the edges of the ice sheet and its height accurately and efficiently.

The paper bridges cloud/aerosol modelling with bifurcation analysis. It identifies two nonlinear peculiarities in the differential equations describing formation of atmospheric clouds through vapour condensation on a population of aerosol particles. A key finding of the paper is an analytic estimate for the timescale of the process. The study emerged from discussions on the causes of hysteretic behaviour of the system that we observed in the results of numerical simulations.

A new method of analysing pressure wave dependences is presented and tested against the published experimental data. Upon the results of examination of more than 90 rock samples, it was found that a significant portion of rocks (~ 45 %) exhibit negative Poisson ratios at lower pressures. Such a significant number of naturally auxetic rocks suggests that the occurrence of negative Poisson ratios is not as exotic as assumed previously.

This is the first study assimilating the satellite-based leaf area index observations every 4 days into a numerical model simulating the growth and death of individual plants. The newly developed data assimilation system successfully reduced the uncertainties of the model parameters related to phenology and carbon dynamics. It also provides better estimates of the present vegetation structure which can be used as the initial states for the simulation of the future vegetation change.

We examine rainfall-induced change in soil microroughness of bare soil surfaces in agricultural landscapes with initial microroughness length scales on the order of 2 mm (smooth surfaces). Past studies have focused on scales of 5–50 mm and have reported a decrease in miccroroughness. Findings in this study show a consistent increase in microroughness under rainfall action for initial length scales of 2 mm. Thus, rainfall–surface interactions can be different for smooth and rough surfaces.