Complex Heterogeneous Systems Research Articles

Prediction of reservoir quality in carbonates via porosity spectrum from image logs

The Majiagou Formation is an important gas-bearing stratigraphic unit in the Ordos basin of west China. The highly complex lithology and heterogeneous pore systems make it difficult to predict the reservoir quality via petrophysical and image logs. This study investigates the lithology, pore systems and well log responses of the Majiagou Formation Member 5 (Ma 5) carbonate reservoirs using a comprehensive analysis of cores, thin sections, routine core analysis, conventional and porosity spectrum derived from image logs. The results show that the lithologies of the Ma 5 are dominantly of mud-sized to silt-sized crystalline dolomite, and there are some dolomites containing gypsums mudstones and limestone. The pore systems include vugs, intercrystalline pores, dissolution pores and microfractures. The vuggy dolomites and the fractured dolomites are the best quality reservoir rocks, and the mud-sized to silt-sized crystalline dolomites containing intercrystalline pores are good quality reservoirs with high porosity and permeability.Open fractured zones are recognized as dark sinusoidal waves, and the vuggy dolomites can be recognized by the dark spots on the image logs. However, the fractured and vuggy dolomites are only occasionally detected, and most of the dolomite reservoirs in Ma 5 contain only intercrystalline pores, which are difficult to be recognized by image logs. In addition, good quality reservoirs have very similar log responses (low natural gamma-ray (GR), low-moderate bulk density (DEN), and moderate-high resistivity) with the poor reservoir quality intervals. By applying the Archie's formula to the flushed zone, a total of 150 porosity curves can be obtained from the XRMI image logs. Then the porosity spectrum is derived from the histogram of porosity distribution for a certain interpretation interval. The best quality reservoir rocks (fractured or vuggy dolomites) have very broad porosity spectrums with long tails due to the presence of vugs and fractures. The abundance of intercrystalline pores containing in the mud-sized to silt-sized crystalline dolomites also result in the broad porosity spectrums without any tails. In contrast, the very narrow porosity spectrums correspond to the poor reservoir quality intervals. The interpretation results are verified by core observations and thin section analysis. By using the porosity spectrum analysis derived from the image logs, the reservoir quality can be predicted. The results can help improve the understanding and prediction of the reservoir quality in carbonates using well logs.

Broadband Coherent Raman Scattering Microscopy

AbstractSpontaneous Raman (SR) microscopy allows label‐free chemically specific imaging based on the vibrational response of molecules; however, due to the low Raman scattering cross section, it is intrinsically slow. Coherent Raman scattering (CRS) techniques, by coherently exciting vibrational oscillators in the focal volume, increase signal levels by several orders of magnitude under appropriate conditions. In its single‐frequency version, CRS microscopy has reached very high imaging speeds, up to the video rate; however, it provides information which is not sufficient to distinguish spectrally overlapped chemical species within complex heterogeneous systems, such as cells and tissues. Broadband CRS combines the acquisition speed of CRS with the information content of SR, but it is technically very demanding. In this Review, the current state of the art in broadband CRS microscopy, both in the coherent anti‐Stokes Raman scattering (CARS) and the stimulated Raman scattering (SRS) versions are reviewed. Different technical solutions for broadband CARS and SRS, working both in the frequency and in the time domains, are compared and their merits and drawbacks assessed.

Optimal energy dispatch in a smart micro-grid system using economic model predictive control

The problem of energy dispatch in heterogeneous complex systems such as smart grids cannot be efficiently addressed using classical control or ad hoc methods. This article discusses the application of economic model predictive control to the management of a smart micro-grid system connected to an electrical power grid. The considered system is composed of several subsystems, namely, some photovoltaic panels, a wind generator, a hydroelectric generator, a diesel generator, and some storage devices (batteries). The batteries are charged with the energy from the photovoltaic panels, wind and hydroelectric generators, and they are discharged whenever the generators produce less energy than needed. The subsystems are interconnected via a DC Bus, from which load demands are satisfied. Modeling smart grids components is based on the generalized flow-based networked systems paradigm, and assuming energy generators to be stable, load demands and energy prices are known. This study shows that economic model predictive control is economically superior to a two-layer hierarchical model predictive control.

STUDYING THE PROPERTIES OF GRAPE POMACE AS OF AN OBJECT OF DRYING

Grape pomace contains a complex of valuable and biologically active compounds. Drying is one of the main ways of microbiological stabilisation and preservation of the nutritional value of this secondary raw material. Kinetic parameters of dehydration of grape pomace from different industrially cultivated and processed varieties have been studied, namely, of the red grape varieties Cabernet and Shiraz, and of the white varieties Chardonnay and Riesling. Dependences of the moisture content in the process of convective drying at different drying agent rates have been obtained at a regulated temperature of 80 °C. The components of such an important technological parameter as the drying time have been determined. These components include the duration of the constant drying rate period Φ2 and the time of the decreasing drying rate period Φ1 of the two zones of the second drying period. The coefficients of the dehydration process have been calculated depending on the type of grape pomace processing. It has been shown that the discrepancy between the calculated and experimental results does not exceed ±3.9%. The specific features of the moisture yield of the pomace have been revealed, the pomace being viewed as a complex heterogeneous system with colloidal and capillary-porous properties. There are different types of its technological preparation: it can be fresh, frozen, fermented, and this makes for the fact that the drying time and drying rate may differ by 1.32–1.46 times. High preservation of valuable properties of grape pomace has been shown. Thus, the concentration of biologically active substances (BAS) in the total polyphenolic compounds is up to 69% of their initial concentration in the grape pomace samples, and the microbial contamination of the samples after drying is reduced by 51–82% of their initial contamination.

Statistical description of depth-dependent turbulent velocity measured in Taihu Lake, China

Quantitative description of turbulence using simple physical/mathematical models remains a challenge in classical physics and hydrologic dynamics. This study monitored the turbulence velocity field at the surface and bottom of Taihu Lake, in China, a large shallow lake with a heterogeneous complex system, and conducted a statistical analysis of the data for the local turbulent structure. Results show that the measured turbulent flows with finite Reynolds numbers exhibit properties of non-Gaussian distribution. Compared with the normal distribution, the Lévy distribution with meaningful parameters can better characterize the tailing behavior of the measured turbulence. Exit-distance statistics and multiscaling extended self-similarity (ESS) were used to interpret turbulence dynamics with different scale structures. Results show that the probability density function of the reverse structure distance and the multiscaling ESS can effectively capture the turbulent flow dynamics varying with water depth. These results provide an approach for quantitatively analyzing multiscale turbulence in large natural lakes.

Experience from Introducing Systems Engineering in an Academic Environment Using an Industry Training Course

Training and educating Systems Engineers is a key activity for any organization developing complex heterogeneous systems. Ideally, the regional/national academic community will provide courses and education programs facilitating for the needs of industry and society. However, Systems Engineering is not a traditional academic subject and despite the growing academic interest in the subject there are many regions with no dedicated academic courses and programs in the subject. This paper presents experience from introducing Systems Engineering via a capstone project course in a mechatronics master's program at the Royal Institute of Technology (KTH) in Sweden. System engineers from industry give an industry-developed Systems Engineering course, as part of a capstone course. We believe that the approach is novel and can serve as a mechanism for introducing Systems Engineering to both students and lecturers in the academic world, who have no previous exposure to the subject. Moreover, student feedback indicate that having lecturers with industrial experience was highly appreciated, making the activity a worthwhile branding investment for industry as well.

Deviations from universality in the fluctuation behavior of a heterogeneous complex system reveal intrinsic properties of components: The case of the international currency market

Identifying behavior that is relatively invariant under different conditions is a challenging task in far-from-equilibrium complex systems. As an example of how the existence of a semi-invariant signature can be masked by the heterogeneity in the properties of the components comprising such systems, we consider the exchange rate dynamics in the international currency market. We show that the exponents characterizing the heavy tails of fluctuation distributions for different currencies systematically diverge from a putative universal form associated with the median value (≃2) of the exponents. We relate the degree of deviation of a particular currency from such an “inverse square law” to fundamental macroscopic properties of the corresponding economy, viz., measures of per capita production output and diversity of export products. We also show that in contrast to uncorrelated random walks exhibited by the exchange rate dynamics for currencies belonging to developed economies, those of the less developed economies show characteristics of sub-diffusive processes which we relate to the anti-correlated nature of the corresponding fluctuations. Approaches similar to that presented here may help in identifying invariant features obscured by the heterogeneous nature of components in other complex systems.

ПОЛНОПОТОЧНАЯ КОМБИНИРОВАННАЯ ФИЛЬТРОВАНИЕМ И ЦЕНТРИФУГИРОВАНИЕМ ТОНКАЯ ОЧИСТКА МОТОРНОГО МАСЛА В СУДОВЫХ ДИЗЕЛЯХ

The article gives analysis of the advantages and disadvantages of cleaning engine oil in internal combustion engines by filtration and centrifugation. The principles of increasing the efficiency of fine oil purification by combining these methods are formulated. The scheme of a perspective system for fine cleaning of engine oil is presented, which most fully realizes the advantages of full-flow filtration and centrifugation for a two-circuit lubrication system of forced internal combustion engines. The operating conditions of diesel engines are shown, under which the advantages of filtration and centrifugation can be realized to the full. The indices for the specific productivity index and capacity of the centrifugal cleaner are calculated, contributing to the attainment of the minimum wear rate of the engine parts and the maximum service life of the filter elements. Prospects for the application of a full-flow fine engine oil purification system in forced engines with a sequential connection of purification units with different principles of separation of complex heterogeneous polydisperse systems, which include the products of contamination of lubrication systems, are outlined. Particularly effective is the use of the developed combined fine-cleaning system in marine diesel engines with increased rotational speed, operating on screw characteristics. The results of motor tests in the ship's trunk boosted diesels of the new combined lubrication oil fine cleaning system are reported. The results of operational tests in the marine diesel engine ДД108 (8ЧСПН 18/22) of a combined engine oil purification system have been analyzed, which combine the advantages of a full-flow filter and a centrifuge with a discharge head connected in series. The parameters of efficient regular and experienced combined engine oil cleaning system are compared with the effect on aging, wear and varnish and lacquer formation of a diesel engine.

Computer modeling of water cleaning in wetland taking into account of suffosion ang colmatation

The mathematical model of filtering with regard to colmatation and suffusion in the system bioplato-filter 2. This saturated porous medium is considered in terms of a complex heterogeneous system fill-concentration of pollutants in porous liquid-concentration of colmatating particles. Vzaemovplivi system parameters are taken into account through: 1) the dynamic change of the porosity of the backfill in the process of filtering; 2) nonlinear dependence coefficient filter porosity of backfill; 3) dependence of velocity of filtration coefficient of filtering and gradient heads, and hence – and porosity. Taking into account the following interplays allowed to increase the adequacy of mathematical models for the study of physical processes, however, led to the necessity of the study of nonlinear boundary value problems for systems of differential equations in partial derivatives. Nonlinearity of the boundary value problem does not allow to speak about her analytical solutions. Numerical solutions of the problems found by the method of finite elements with a software implementation of the relevant algorithms in FreeFem ++. Computer modeling showed that when taking into account nonlinear dependence coefficient of filtration from the concentration of colmatating particles and dynamic changes of porosity in the process of filtering, predictive performance bioplato for six months reduced by 25 % . Therefore, it is necessary to develop engineering solutions for reducing the influence of the colmatation-suffusion processes on the processes of filtering. The forecasting work bioplato relevant conduct on the design stage in order to implement predictive calculations. It is done by means of mathematical and computer modeling

Removal of persistent organic pollutants from water using a newly developed atmospheric plasma reactor

A new bench‐top reactor employing a streamer discharge in air was developed and tested for potential use in an advanced oxidation stage in water treatment processes. The complex heterogeneous system and the ensuing chemical processes were characterized using an integrated approach to map the morphology of the plasma/gas/liquid interface, identify the plasma short‐lived excited species, determine the oxidants in solution and monitor the organic pollutants degradation. Three model pollutants were used in these experiments, rhodamine B, phenol and metolachlor. The first two are common standards used to evaluate the performance of advanced oxidation processes. Metolachlor is a widely used herbicide listed among the most important recalcitrant emerging organic pollutants. Energy efficiency, kinetics and products of our tests show a good performance of the reactor. Specifically, mineralization appears feasible also in the case of metolachlor.

On approximate predictability of metric systems

In this paper we introduce and characterize the notion of approximate predictability for the general class of metric systems, which are a powerful modeling framework to deal with complex heterogeneous systems such as hybrid systems. Approximate predictability corresponds to the possibility of predicting the occurrence of specific states belonging to a particular subset of interest, in advance with respect to their occurrence, on the basis of observations corrupted by measurement errors. We establish a relation between approximate predictability of a given metric system and approximate predictability of a metric system that approximately simulates the given one. This relation allows checking approximate predictability of a system with an infinite number of states, provided that one is able to construct a metric system with a finite number of states and inputs, approximating the original one in the sense of approximate simulation. The analysis of approximate predictability of Piecewise Affine (PWA) systems is carried out as an application of the proposed approach.

Macroscale multimodal imaging reveals ancient painting production technology and the vogue in Greco-Roman Egypt

Macroscale multimodal chemical imaging combining hyperspectral diffuse reflectance (400–2500 nm), luminescence (400–1000 nm), and X-ray fluorescence (XRF, 2 to 25 keV) data, is uniquely equipped for noninvasive characterization of heterogeneous complex systems such as paintings. Here we present the first application of multimodal chemical imaging to analyze the production technology of an 1,800-year-old painting and one of the oldest surviving encaustic (“burned in”) paintings in the world. Co-registration of the data cubes from these three hyperspectral imaging modalities enabled the comparison of reflectance, luminescence, and XRF spectra at each pixel in the image for the entire painting. By comparing the molecular and elemental spectral signatures at each pixel, this fusion of the data allowed for a more thorough identification and mapping of the painting’s constituent organic and inorganic materials, revealing key information on the selection of raw materials, production sequence and the fashion aesthetics and chemical arts practiced in Egypt in the second century AD.

A lattice Boltzmann model for interphase conjugate heat transfer

ABSTRACTA lattice Boltzmann model is proposed with a newly modified equilibrium distribution function for solving the conservation form of the energy equation to treat the interphase conjugate heat transfer problems under both steady state and unsteady state. The temperature and heat flux continuity conditions at the interface can be inherently satisfied without needing any additional treatments, such as iterative computation, correcting procedure for the incoming distribution function, and the complicated calculation procedure for the source term, to account for the interphase conjugate heat transfer. The implementation of the present LB model, therefore, is more straightforward and more efficient than those in most previous models, especially for problems with complex interfaces. The applicability and accuracy of the proposed LB model were evaluated by some benchmark problems including both simple flat interface and complex interface geometry. The results show excellent agreements with analytical solutions or finite volume results, demonstrating that the present model can serve as a promising numerical technique for dealing with fluid flow and heat transfer in complex heterogeneous systems.

Robust Optimization based Energy Dispatch in Smart Grids Considering Simultaneously Multiple Uncertainties: Load Demands and Energy Prices

Solving the problem of energy dispatch in a heterogeneous complex system is not a trivial task. The problem becomes even more complex considering uncertainties in demands and energy prices. This paper discusses the development of several Economic Model Predictive Control (EMPC) based strategies for solving an energy dispatch problem in a smart micro-grid. The smart grid components are described using control-oriented model approach. Considering uncertainty of load demands and energy prices simultaneously, and using an economic objective function, leads to a non-linear non-convex problem. The technique of using an affine dependent controller is used to convexify the problem. The goal of this research is the development of a controller based on EMPC strategies that tackles both endogenous and exogenous uncertainties, in order to minimize economic costs and guarantee service reliability of the system. The developed strategies have been applied to a hybrid system comprising some photovoltaic (PV) panels, a wind generator, a hydroelectric generator, a diesel generator, and some storage devices interconnected via a DC Bus. Additionally, a comparison between the standard EMPC, and its combination with MPC tracking in single-layer and two-layer approaches was also carried out based on the daily cost of energy production.

Retrieval of solvent injected during heavy-oil recovery: Pore scale micromodel experiments at variable temperature conditions

Solvent injection has been given attention to enhance oil recovery by sole use or in combination with a thermal method to develop light, medium, and heavy-oil fields. To make this process efficient, retrieval of expensive solvent efficiently is required. This can be achieved by alternative injection of water (WAG) if the reservoir is homogeneous. In case of heterogeneous reservoirs (fractured carbonates or sands with wormholes), one needs to develop techniques other than viscous displacement to retrieve the solvent diffused into less permeable matrix portion. A method of injecting steam/hot water to heat the solvent to vaporize and retrieve it was introduced recently (steam-over-solvent injection in fractured reservoirs) and tested through core experiments. Although these tests provide valuable data to design the optimal temperature of injected water to make the process viable, the mechanics of the nucleation of the solvent vapor and its entrapment in the pores at the micro scale requires further research.A series of experiments using a 2-D etched glass micromodel (sandstone replica with a fracture) were carried out to investigate the mechanics of solvent retrieval and entrapment at variable temperature conditions. The micromodel was saturated with dyed processed oils and different solvents were injected through fracture. After the solvent was diffused into matrix completely to recover the oil, the model was heated mimicking a thermal method to reach the boiling point of the solvent and retrieve it. The wettability of the micromodel was also altered to achieve water-wet and oil-wet conditions as wettability dictates the phase distribution in the pores. Following the heating phase, water was injected to retrieve the remaining solvent in the liquid or vapor phase.Visual observations of solvent diffusion/dispersion into matrix and its retrieval from the matrix clarified the miscibility process in the presence of an immiscible phase, interaction between different phases in a complex heterogeneous system, and phase distributions as a function of temperature. This information can be used to determine the efficiency of solvent retrieval process and optimal application conditions for EOR applications in heterogeneous sands and carbonates.

Numerical investigation of arches in brick-masonry bridges

A significant number of old masonry bridges are still in use and need to be assessed considering current traffic loading and safety requirements. Masonry bridges are complex heterogeneous systems, where masonry arches represent the main components. Thus, a realistic modelling of arches is vital for accurate assessment of masonry bridges. The authors have previously proposed and validated a detailed mesoscale description for masonry arches allowing for the actual masonry bond and the specific arch geometry including the case of skew arches. In this paper, the proposed mesoscale modelling strategy is used in a comprehensive numerical study to investigate the effects of various parameters, including masonry bond and defects in the brickwork, abutment stiffness and movements at the supports, which are usually disregarded in practical assessment of masonry arches and bridges. The results achieved show how these parameters affect the ultimate load capacity, failure mechanisms and initial stiffness of square and skew arches, where the use of detailed 3D mesoscale modelling is critical in providing accurate response predictions under a variety of loading conditions for which reduced models might provide incorrect results.

Kinetic Modeling of the Extraction–Oxidation Coupling Process for the Removal of Dibenzothiophene

Extraction–oxidation desulfurization (EODS) technology would be a potential industrial application for achieving ultralow-sulfur fuel oils. A combined extraction–oxidation system for dibenzothiophene removal from model fuel with H2O2 as an oxidant, acetonitrile as an extractant, and Mo/γ-Al2O3 as a catalyst was performed in a batch reactor. To study this complex heterogeneous system, the chemical reaction and mass transfer on each phase were individually assessed. Kinetics of the EODS system for dibenzothiophene in model fuel was developed, comprising the chemical kinetic mechanism and mass transfer effects. The kinetic parameters of the kinetic model, such as the kinetic constants and apparent activation energy, were determined. The EODS system in the experimental condition is determined by both the extraction process and catalytic oxidation reaction, because the terms involving the intrinsic resistance of the chemical reaction are no more important than mass transfer resistance.

An integrated workflow to assess the remaining potential of mature hydrocarbon basins: a case study from Northwest Germany (Upper Jurassic/Lower Cretaceous, Lower Saxony Basin)

Mature hydrocarbon provinces require a high level of geological understanding in order to extend the lives of producing fields, to replace reserves through smaller targets and to reduce the risks of exploring for more and more subtle hydrocarbon traps. Despite a large number of existing wells in the area studied in this paper, the depositional environments and the stratigraphic architecture were still poorly known. In order to improve the geological understanding, we propose a workflow to assess the remaining reservoir potential of mature hydrocarbon areas, integrating cores, cuttings, well-logs, biostratigraphy and seismic data. This workflow was developed for and is exemplified with the northwest of the Lower Saxony Basin (LSB), a mature hydrocarbon province in northwest Germany, but can be applied in a similar fashion to other areas. Systematic integration of lithofacies analysis, chrono- and sequence stratigraphy, combined with electrofacies analysis and modern digital methods like neural network-based lithology determination and 3D facies modelling provides a high-resolution understanding of the spatial facies and reservoir architecture in the study area. Despite widely correlatable litho-units in the Upper Jurassic and Lower Cretaceous in the LSB, complex heterogeneous sedimentary systems can be found in the basin’s marginal parts. Two new play types were determined in the study area, showing a remaining potential for stratigraphic hydrocarbon traps. The results of this exploration scale study also provide the basis for re-evaluations on a field development scale. On a basin scale, this study may encourage further data acquisition and re-evaluations to discover previously unknown reservoirs.

A Novel Concept for Intermetallic Anodes: Electrochemistry and Thermodynamic Modeling

Secondary lithium ion cells are now universally accepted as a viable key component for electrical energy storage in portable, entertainment, computing and telecommunication equipment required by todays information-rich, mobile society. Predominantly, the lack of suitable reversible negative electrode materials hinders the generation of new lithium ion batteries with distinctly higher charge densities and cycling stabilities. Until now, a variety of (semi-)metal anodes have been tested, promising unrivalled capacities as well as safety due to more positive potentials against Li/Li+ compared to graphite. Sn-based intermetallic anodes are expected to deliver significant capacity increases (960 mAh/g) compared to graphite (372 mAh/g) although they suffer from large volume changes during lithiation/de-lithiation (L/D) which lead to electrode degradation and poor cycling stability. A significant improvement of cyclability can be achieved by using intermetallic alloys, e.g. Cu-Sn or Sb-Sn as anode materials [2015Nit]. The aim of the current project is to combine key experimental data (thermodynamic properties, phase diagram information, crystallographic data) with electrochemically derived data from prototype cells, an approach which was recently validated by Huggins in “Advanced batteries” [2008Hug]. Consistent thermodynamic descriptions of corresponding material systems are developed using the CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) method [2007Luk] which is up to now the most advanced method for thermodynamic modeling and simulation of complex heterogeneous systems. This is also a key component of the new ICME (Integrated Computational Materials Engineering) method [2008Com], in which the use of computational thermodynamics helps bridge materials processing and materials structure to be able to predict materials properties. Our thermodynamic descriptions are critical for the design of new electrode materials with optimally tailored properties and allow the evaluation and even the prediction of internal cell reactions and open circuit voltages (OCV). The preparation of phase-pure Li-Sn and Cu-Li-Sn alloys was done by metallurgical techniques adopting special pre-heat treatments and annealing routines. Subsequent characterization was performed by powder X-ray diffraction (XRD), ICP-OES and BSED imaging. The heat capacity (Cp) of selected phase-pure alloys was determined by differential scanning calorimetry (DSC) using a Tian-Calvet type arrangement. Due to the high reactivity of Li, both the synthesis and heat capacity measurements of the respective compounds required the use of tantalum crucibles as well as the manipulation inside an inert gas (Ar) glove box. The derived heat capacity data are implemented into the thermodynamic dataset which enables the temperature-dependent modeling of Gibbs energies and a reliable prediction of electrochemical data at various battery operation temperatures. To verify our calculations, respective phase-pure alloys were used as active materials in battery test cells. Particularly, galvanostatic coulometry and cycling voltammetry were performed in suitable coin cell arrangements against Li/Li+. To facilitate the production of compact electrode materials, active materials were dispersed in N-Methyl-2-pyrrolidone (NMC) together with carbon black to improve conductivity and Polyvinylidene fluoride (PVDF) was added as a binder. Relevant lithiation steps at constant electrochemical potentials were investigated by ex-situ XRD and BSED imaging. For the first time, already lithiated multicomponent intermetallic alloys were used as anode materials so that in the initial cycling step Li was removed from the active Sn-based material. Corresponding effects on cell performance from this new approach will be discussed in detail. [2015Nit] N. Nitta, F. Wu, J.T. Lee, G. Yushin. Materials Today 18 (2015): 252-264 [2008Hug] R.A. Huggins. Advanced Batteries. Materials Science Aspects (2008), New York: Springer [2007Luk] H.L. Lukas, S.G. Fries, B. Sundman. Computational Thermodynamics: The Calphad Method (2007), Cambridge University Press, United Kingdom [2008Com] Committee on ICME. National Research Council (2008), Washington: National Academies

Introduction to Focus Issue: Complex Dynamics in Networks, Multilayered Structures and Systems.

In the last years, network scientists have directed their interest to the multi-layer character of real-world systems, and explicitly considered the structural and dynamical organization of graphs made of diverse layers between its constituents. Most complex systems include multiple subsystems and layers of connectivity and, in many cases, the interdependent components of systems interact through many different channels. Such a new perspective is indeed found to be the adequate representation for a wealth of features exhibited by networked systems in the real world. The contributions presented in this Focus Issue cover, from different points of view, the many achievements and still open questions in the field of multi-layer networks, such as: new frameworks and structures to represent and analyze heterogeneous complex systems, different aspects related to synchronization and centrality of complex networks, interplay between layers, and applications to logistic, biological, social, and technological fields.