The interaction of flexural-gravity waves with periodic geometries

A periodic structure of finite extent is embedded within an otherwise uniform two-dimensional system consisting of finite-depth fluid covered by a thin elastic plate. An incident harmonic flexural-gravity wave is scattered by the structure. By using an approximation to the corresponding linearised boundary value problem that is based on a slowly varying structure in conjunction with a transfer matrix formulation, a method is developed that generates the whole solution from that for just one cycle of the structure, providing both computational savings and insight into the scattering process. Numerical results show that variations in the plate produce strong resonances about the ‘Bragg frequencies’ for relatively few periods. We find that certain geometrical variations in the plate generate these resonances above the Bragg value, whereas other geometries produce the resonance below the Bragg value. The familiar resonances due to periodic bed undulations tend to be damped by the plate.

Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

Ensemble clustering in deterministic ensemble Kalman filters

Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M−1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF.

Using the significant dust deposition event on the glaciers of Mt. Elbrus, Caucasus Mountains, Russia on 5 May 2009 to develop a method for dating and "provenancing" of desert dust events recorded in snow pack

A significant desert dust deposition event occurred on Mt. Elbrus, Caucasus Mountains, Russia on 5 May 2009, where the deposited dust later appeared as a brown layer in the snow pack. An examination of dust transportation history and analysis of chemical and physical properties of the deposited dust were used to develop a new approach for high-resolution “provenancing” of dust deposition events recorded in snow pack using multiple independent techniques. A combination of SEVIRI red-green-blue composite imagery, MODIS atmospheric optical depth fields derived using the Deep Blue algorithm, air mass trajectories derived with HYSPLIT model and analysis of meteorological data enabled identification of dust source regions with high temporal (hours) and spatial (ca. 100 km) resolution. Dust, deposited on 5 May 2009, originated in the foothills of the Djebel Akhdar in eastern Libya where dust sources were activated by the intrusion of cold air from the Mediterranean Sea and Saharan low pressure system and transported to the Caucasus along the eastern Mediterranean coast, Syria and Turkey. Particles with an average diameter below 8 μm accounted for 90% of the measured particles in the sample with a mean of 3.58 μm, median 2.48 μm. The chemical signature of this long-travelled dust was significantly different from the locally-produced dust and close to that of soils collected in a palaeolake in the source region, in concentrations of hematite. Potential addition of dust from a secondary source in northern Mesopotamia introduced uncertainty in the “provenancing” of dust from this event. Nevertheless, the approach adopted here enables other dust horizons in the snowpack to be linked to specific dust transport events recorded in remote sensing and meteorological data archives.

Using the significant dust deposition event on the glaciers of Mt. Elbrus, Caucasus Mountains, Russia on 5 May 2009 to develop a method for dating and provenancing of desert dust events recorded in snow pack.

A significant desert dust deposition event occurred on Mt. Elbrus, Caucasus Mountains, Russia on 5 May 2009, where the deposited dust later appeared as a brown layer in the snow pack. An examination of dust transportation history and analysis of chemical and physical properties of the deposited dust were used to develop a new approach for high-resolution provenancing of dust deposition events recorded in snow pack using multiple independent techniques. A combination of SEVIRI red-green-blue composite imagery, MODIS atmospheric optical depth fields derived using the Deep Blue algorithm, air mass trajectories derived with HYSPLIT model and analysis of meteorological data enabled identification of dust source regions with high temporal (hours) and spatial (ca. 100 km) resolution. Dust, deposited on 5 May 2009, originated in the foothills of the Djebel Akhdar in eastern Libya where dust sources were activated by the intrusion of cold air from the Mediterranean Sea and Saharan low pressure system and transported to the Caucasus along the eastern Mediterranean coast, Syria and Turkey. Particles with an average diameter below 8 μm accounted for 90% of the measured particles in the sample with a mean of 3.58 μm, median 2.48 μm and the dominant mode of 0.60 μm. The chemical signature of this long-travelled dust was significantly different from the locally-produced dust and close to that of soils collected in a palaeolake in the source region, in concentrations of hematite and oxides of aluminium, manganese, and magnesium. Potential addition of dust from a secondary source in northern Mesopotamia introduced uncertainty in the provenancing of dust from this event. Nevertheless, the approach adopted here enables other dust horizons in the snowpack to be linked to specific dust transport events recorded in remote sensing and meteorological data archives.

A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

Reduced-order dynamics of the Martian atmospheric dynamics

In this paper we explore the possibility of deriving low-dimensional models of the dynamics of the Martian atmosphere. The analysis consists of a Proper Orthogonal Decomposition (POD) of the atmospheric streamfunction after first decomposing the vertical structure with a set of eigenmodes. The vertical modes were obtained from the quasi-geostrophic vertical structure equation. The empirical orthogonal functions (EOFs) were optimized to represent the atmospheric total energy. The total energy was used as the criterion to retain those modes with large energy content and discard the rest. The principal components (PCs) were analysed by means of Fourier analysis, so that the dominant frequencies could be identified. It was possible to observe the strong influence of the diurnal cycle and to identify the motion and vacillation of baroclinic waves.

Coalescence of particles by differential sedimentation

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.

Gaussian processes autoencoder for dimensionality reduction

Learning low dimensional manifold from highly nonlinear data of high dimensionality has become increasingly important for discovering intrinsic representation that can be utilized for data visualization and preprocessing. The autoencoder is a powerful dimensionality reduction technique based on minimizing reconstruction error, and it has regained popularity because it has been efficiently used for greedy pretraining of deep neural networks. Compared to Neural Network (NN), the superiority of Gaussian Process (GP) has been shown in model inference, optimization and performance. GP has been successfully applied in nonlinear Dimensionality Reduction (DR) algorithms, such as Gaussian Process Latent Variable Model (GPLVM). In this paper we propose the Gaussian Processes Autoencoder Model (GPAM) for dimensionality reduction by extending the classic NN based autoencoder to GP based autoencoder. More interestingly, the novel model can also be viewed as back constrained GPLVM (BC-GPLVM) where the back constraint smooth function is represented by a GP. Experiments verify the performance of the newly proposed model.

Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

Shubnikov de Haas oscillations in double wells with opposite signs of the electronic g-factor

We report on the measurements of the Shubnikov de Haas oscillations (SdH) in symmetrically doped AlxGa1-xAs double wells with different Al compositions in wells, which lead to the opposite signs of the electronic g-factor in each layer. Surprisingly, the spin splitting appears and collapses several times with increase in the magnetic field, We attribute such behaviour to the oscillations of the exchange-correlation term with Landau filling factor. (C) 2007 Elsevier B.V. All rights reserved.

Magnetoresistance oscillations in triple quantum wells under microwave irradiation

The interference of magneto-intersubband oscillations and microwave-induced resistance oscillations is studied in high-density triple quantum wells. We give an introduction into magnetotransport in trilayer systems and focus on photoresistance measurements. The power and frequency dependence of the observed magnetoresistance oscillations can be described by the inelastic mechanism of photoresistance, generalized to the three-subband case. (C) 2009 Elsevier B.V. All rights reserved.

Microwave induced magnetoresistance oscillations and inelastic scattering time in double quantum wells

The interference of microwave-induced resistance oscillations and magneto-intersubband oscillations in double quantum wells exposed to a continuous microwave irradiation is under study. By comparing experimental and theoretical magnetoresistance traces at different temperatures, we confirm that the inelastic mechanism of photoresistance explains our observations up to T similar or equal to 4 K. For higher temperatures, our results suggest a deviation of the inelastic scattering time tau(in) from the predicted T(-2) dependence. (C) 2009 Elsevier B.V. All rights reserved.

Magneto-intersubband oscillations in triple quantum wells

We present magnetotransport studies of high-density triple quantum well samples with different barrier widths. Because of electron transitions between three occupied 2D subbands, the magneto-resistance shows magneto-intersubband oscillations whose periodicity is determined by the subband separation energies. Temperature-dependent measurements allow us to extract quantum lifetime of electrons. A theoretical consideration of the observed phenomenon is also presented. (C) 2009 Elsevier B.V. All rights reserved.

Spectroscopic evidence of extended states in quantized Hall phase of weakly coupled GaAs/AlGaAs multi-layers

The influence of the interlayer coupling on formation of the quantized Hall conductor phase at the filling factor v = 2 was studied in the multi-layer GaAs/AlGaAs heterostructures. The disorder broadened Gaussian photoluminescence line due to the localized electrons was found in the quantized Hall phase of the isolated multi-quantum well structure. On the other hand, the quantized Hall phase of the weakly coupled multi-layers emitted an unexpected asymmetrical line similar to that one observed in the metallic electron systems. We demonstrated that the observed asymmetry is caused by a partial population of the extended electron states formed in the quantized Hall conductor phase due to the interlayer percolation. A sharp decrease of the single-particle scattering time associated with these extended states was observed at the filling factor v = 2. (c) 2007 Elsevier B.V. All rights reserved.