Showing papers in "European Physical Journal B in 2015"

Evolutionary games on multilayer networks: a colloquium

Abstract: Networks form the backbone of many complex systems, ranging from the Internet to human societies. Accordingly, not only is the range of our interactions limited and thus best described and modeled by networks, it is also a fact that the networks that are an integral part of such models are often interdependent or even interconnected. Networks of networks or multilayer networks are therefore a more apt description of social systems. This colloquium is devoted to evolutionary games on multilayer networks, and in particular to the evolution of cooperation as one of the main pillars of modern human societies. We first give an overview of the most significant conceptual differences between single-layer and multilayer networks, and we provide basic definitions and a classification of the most commonly used terms. Subsequently, we review fascinating and counterintuitive evolutionary outcomes that emerge due to different types of interdependencies between otherwise independent populations. The focus is on coupling through the utilities of players, through the flow of information, as well as through the popularity of different strategies on different network layers. The colloquium highlights the importance of pattern formation and collective behavior for the promotion of cooperation under adverse conditions, as well as the synergies between network science and evolutionary game theory.

Modern temporal network theory: a colloquium

Abstract: The power of any kind of network approach lies in the ability to simplify a complex system so that one can better understand its function as a whole. Sometimes it is beneficial, however, to include more information than in a simple graph of only nodes and links. Adding information about times of interactions can make predictions and mechanistic understanding more accurate. The drawback, however, is that there are not so many methods available, partly because temporal networks is a relatively young field, partly because it is more difficult to develop such methods compared to for static networks. In this colloquium, we review the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years. This includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more. We also discuss future directions.

Towards real-world complexity: an introduction to multiplex networks

Abstract: Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven that the multiplexity has broad impact on the system’s structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the field are surveyed and some outstanding open challenges and future perspectives will be proposed.

From seconds to months: an overview of multi-scale dynamics of mobile telephone calls

Abstract: Big Data on electronic records of social interactions allow approaching human behaviour and sociality from a quantitative point of view with unforeseen statistical power. Mobile telephone Call Detail Records (CDRs), automatically collected by telecom operators for billing purposes, have proven especially fruitful for understanding one-to-one communication patterns as well as the dynamics of social networks that are reflected in such patterns. We present an overview of empirical results on the multi-scale dynamics of social dynamics and networks inferred from mobile telephone calls. We begin with the shortest timescales and fastest dynamics, such as burstiness of call sequences between individuals, and “zoom out” towards longer temporal and larger structural scales, from temporal motifs formed by correlated calls between multiple individuals to long-term dynamics of social groups. We conclude this overview with a future outlook.

Correlation between centrality metrics and their application to the opinion model

Abstract: In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a high-complexity centrality metric by a strongly correlated low-complexity metric, we first study the correlation between centrality metrics in terms of their Pearson correlation coefficient and their similarity in ranking of nodes. In addition to considering the widely used centrality metrics, we introduce a new centrality measure, the degree mass. The mth-order degree mass of a node is the sum of the weighted degree of the node and its neighbors no further than m hops away. We find that the betweenness, the closeness, and the components of the principal eigenvector of the adjacency matrix are strongly correlated with the degree, the 1st-order degree mass and the 2nd-order degree mass, respectively, in both network models and real-world networks. We then theoretically prove that the Pearson correlation coefficient between the principal eigenvector and the 2nd-order degree mass is larger than that between the principal eigenvector and a lower order degree mass. Finally, we investigate the effect of the inflexible contrarians selected based on different centrality metrics in helping one opinion to compete with another in the inflexible contrarian opinion (ICO) model. Interestingly, we find that selecting the inflexible contrarians based on the leverage, the betweenness, or the degree is more effective in opinion-competition than using other centrality metrics in all types of networks. This observation is supported by our previous observations, i.e., that there is a strong linear correlation between the degree and the betweenness, as well as a high centrality similarity between the leverage and the degree.

Generalized Blonder-Tinkham-Klapwijk theory and conductance spectra with particle-hole mixing interface potential

Abstract: We extend the Blonder-Tinkham-Klapwijk treatment including particle-hole mixing boundary conditions in the Bogoliubov-de Gennes scattering problem to describe anomalous conductance features often reported in normal-metal/superconductor junctions. We calculate the differential conductance spectra and show that conductance dips, not expected in the standard formulation, can be explained in terms of a phase π-shift between the bulk and the interface order parameter. A tight-binding model is also introduced to give a quantitative description of the phase-shift in terms of the transparency and polarization of the interface. We characterize the physics arising from particle-hole mixing boundary conditions at the interface and its effects on the conductance anomalies in superconductor-normal heterostructures.

Fermionic and Majorana bound states in hybrid nanowires with non-uniform spin-orbit interaction

Abstract: We study intragap bound states in the topological phase of a Rashba nanowire in the presence of a magnetic field and with non-uniform spin orbit interaction (SOI) and proximity-induced superconductivity gap. We show that fermionic bound states (FBS) can emerge inside the proximity gap. They are localized at the junction between two wire sections characterized by different directions of the SOI vectors, and they coexist with Majorana bound states (MBS) localized at the nanowire ends. The energy of the FBS is determined by the angle between the SOI vectors and the lengthscale over which the SOI changes compared to the Fermi wavelength and the localization length. We also consider double-junctions and show that the two emerging FBSs can hybridize and form a double quantum dot-like structure inside the gap. We find explicit analytical solutions of the bound states and their energies for certain parameter regimes such as weak and strong SOI. The analytical results are confirmed and complemented by an independent numerical tight-binding model approach. Such FBS can act as quasiparticle traps and thus can have implications for topological quantum computing schemes based on braiding MBSs.

From calls to communities: a model for time-varying social networks

Abstract: Social interactions vary in time and appear to be driven by intrinsic mechanisms that shape the emergent structure of social networks. Large-scale empirical observations of social interaction structure have become possible only recently, and modelling their dynamics is an actual challenge. Here we propose a temporal network model which builds on the framework of activity-driven time-varying networks with memory. The model integrates key mechanisms that drive the formation of social ties – social reinforcement, focal closure and cyclic closure, which have been shown to give rise to community structure and small-world connectedness in social networks. We compare the proposed model with a real-world time-varying network of mobile phone communication, and show that they share several characteristics from heterogeneous degrees and weights to rich community structure. Further, the strong and weak ties that emerge from the model follow similar weight-topology correlations as real-world social networks, including the role of weak ties.

Contrasting effects of strong ties on SIR and SIS processes in temporal networks

Abstract: Most real networks are characterized by connectivity patterns that evolve in time following complex, non-Markovian, dynamics. Here we investigate the impact of this ubiquitous feature by studying the Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Susceptible (SIS) epidemic models on activity driven networks with and without memory (i.e., Markovian and non-Markovian). We find that memory inhibits the spreading process in SIR models by shifting the epidemic threshold to larger values and reducing the final fraction of recovered nodes. On the contrary, in SIS processes memory reduces the epidemic threshold and, for a wide range of disease parameters, increases the fraction of nodes affected by the disease in the endemic state. The heterogeneity in tie strengths, and the frequent repetition of strong ties it entails, allows in fact less virulent SIS-like diseases to survive in tightly connected local clusters that serve as reservoir for the virus. We validate this picture by studying both processes on two real temporal networks.

Extended s-wave pairing symmetry on the triangular lattice heavy fermion system

Abstract: We investigate the pairing symmetry of the Kondo-Heisenberg model on triangular lattice, which is believed to capture the core competition of Kondo screening and local magnetic exchange interaction in heavy electron compounds. On the dominant background of the heavy fermion state, the introduction of the Heisenberg antiferromagnetic interaction (J H ) leads to superconducting pairing instability. Depending on the strength of the interactions, it is found that the pairing symmetry favours an extended s-wave for small J H and high conduction electron density but a chiral $$d_{x^2 - y^2 } + id_{xy}$$ -wave for large J H and low conduction electron density, which provides a phase diagram of pairing symmetry from the calculations of the ground-state energy. The transition between these two pairing symmetries is found to be first-order. Furthermore, we also analyze the phase diagram from the pairing strengths and find that the phase diagram obtained is qualitatively consistent with that based on the ground-state energy. In addition, we propose an effective single-band BCS Hamiltonian, which is able to describe the low-energy thermodynamic behaviors of the heavy fermion superconducting states. These results further deepen the understanding of the antiferromagnetic interaction which results in a geometric frustration for the model studied. Our work may provide a possible scenario to understand the pairing symmetry of the heavy fermion superconductivity, which is one of active issues in very recent years.

Modeling electron dynamics coupled to continuum states in finite volumes with absorbing boundaries

Abstract: Absorbing boundaries are frequently employed in real-time propagation of the Schrodinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for the calculation of observables involving infinitely extended continuum states in finite volumes. In the literature, several boundary absorbers have been proposed. They mostly fall into three main families: mask function absorbers, complex absorbing potentials, and exterior complex-scaled potentials. To date none of the proposed absorbers is perfect, and all present a certain degree of reflections. Characterization of such reflections is thus a critical task with strong implications for time-dependent simulations of atoms and molecules. We introduce a method to evaluate the reflection properties of a given absorber and present a comparison of selected samples for each family of absorbers. Further, we discuss the connections between members of each family and show how the same reflection curves can be obtained with very different absorption schemes.

The relationship between the detrendend fluctuation analysis and the autocorrelation function of a signal

Abstract: We derive an analytical expression for the fluctuation function of the detrended fluctuation analysis and state the relationship with the autocorrelation function for stationary processes. With this result we can investigate the scaling of the fluctuation function for short-range and long-range correlated processes. Furthermore we show that short-range correlated processes always exhibit a crossover between regions of different scaling. We also extend our results to processes with additive trends and discuss the effect of measurement noise.

A continuum framework for mechanics of fractal materials I: from fractional space to continuum with fractal metric

Abstract: This paper is devoted to the mechanics of fractally heterogeneous media. A model of fractal continuum with a fractional number of spatial degrees of freedom and a fractal metric is suggested. The Jacobian matrix of the fractal continuum deformation is defined and the kinematics of deformations is elucidated. The symmetry of the Cauchy stress tensor for continua with the fractal metric is established. A homogenization framework accounting for the connectivity, topological, and metric properties of fractal domains in heterogeneous materials is developed. The mapping of mechanical problems for fractal media into the corresponding problems for the fractal continuum is discussed. Stress and strain distributions in elastic fractal bars are analyzed. An approach to fractal bar optimization is proposed. Some features of acoustic wave propagation and localization in fractal media are briefly highlighted.

Measuring economic complexity of countries and products: which metric to use?

Abstract: Evaluating the economies of countries and their relations with products in the global market is a central problem in economics, with far-reaching implications to our theoretical understanding of the international trade as well as to practical applications, such as policy making and financial investment planning. The recent Economic Complexity approach aims to quantify the competitiveness of countries and the quality of the exported products based on the empirical observation that the most competitive countries have diversified exports, whereas developing countries only export few low quality products – typically those exported by many other countries. Two different metrics, Fitness-Complexity and the Method of Reflections, have been proposed to measure country and product score in the Economic Complexity framework. We use international trade data and a recent ranking evaluation measure to quantitatively compare the ability of the two metrics to rank countries and products according to their importance in the network. The results show that the Fitness-Complexity metric outperforms the Method of Reflections in both the ranking of products and the ranking of countries. We also investigate a generalization of the Fitness-Complexity metric and show that it can produce improved rankings provided that the input data are reliable.

Temporal condensation and dynamic λ-transition within the complex network: an application to real-life market evolution

Abstract: We fill a void in merging empirical and phenomenological characterisation of the dynamical phase transitions in complex networks by identifying and thoroughly characterising a triple sequence of such transitions on a real-life financial market. We extract and interpret the empirical, numerical, and analytical evidences for the existence of these dynamical phase transitions, by considering the medium size Frankfurt stock exchange (FSE), as a typical example of a financial market. By using the canonical object for the graph theory, i.e. the minimal spanning tree (MST) network, we observe: (i) the (initial) dynamical phase transition from equilibrium to non-equilibrium nucleation phase of the MST network, occurring at some critical time. Coalescence of edges on the FSE’s transient leader (defined by its largest degree) is observed within the nucleation phase; (ii) subsequent acceleration of the process of nucleation and the emergence of the condensation phase (the second dynamical phase transition), forming a logarithmically diverging temporal λ-peak of the leader’s degree at the second critical time; (iii) the third dynamical fragmentation phase transition (after passing the second critical time), where the λ-peak logarithmically relaxes over three quarters of the year, resulting in a few loosely connected sub-graphs. This λ-peak (comparable to that of the specific heat vs. temperature forming during the equilibrium continuous phase transition from the normal fluid I 4He to the superfluid II 4He) is considered as a prominent result of a non-equilibrium superstar-like superhub or a dragon-king’s abrupt evolution over about two and a half year of market evolution. We capture and meticulously characterise a remarkable phenomenon in which a peripheral company becomes progressively promoted to become the dragon-king strongly dominating the complex network over an exceptionally long period of time containing the crash. Detailed analysis of the complete trio of the dynamical phase transitions constituting the λ-peak allows us to derive a generic nonlinear constitutive equation of the dragon-king dynamics describing the complexity of the MST network by the corresponding inherent nonlinearity of the underlying dynamical processes.

The spin-1/2 square-lattice J 1 -J 2 model: the spin-gap issue

Abstract: We use the coupled cluster method to high orders of approximation in order to calculate the ground-state energy, the ground-state magnetic order parameter, and the spin gap of the spin-1/2 J 1-J 2 model on the square lattice. We obtain values for the transition points to the magnetically disordered quantum paramagnetic phase of J 2 c1 = 0.454J 1 and J 2 c2 = 0.588J 1. The spin gap is zero in the entire parameter region accessible by our approach, i.e. for J 2 ≤ 0.49J 1 and J 2> 0.58J 1. This finding is in favor of a gapless spin-liquid ground-state in this parameter regime.

First-principles study of electronic and magnetic properties in Co doped BaTiO3

Abstract: The electronic and magnetic properties of Co doped BaTiO3 have been investigated using the first-principle calculations within density functional theory. The nature of magnetism is mainly from the dopant Co atom with magnetic moment 3.15μB, suggesting the Co impurity atom with a high-spin configuration. With the increasing doping concentration, there exist mid-gap states at the Fermi level that increases the probability of electron transitions from valence band to conduction band. On the other hand, the O vacancy has a significant influence on the electronic and magnetic properties in doped BaTiO3 systems. The presence of O vacancy leads to the elapse of system magnetism from 4.78μB to 1.0μB, indicating the transition of the spin configuration of Co atom from a high-spin state to a low-spin one. The results are in good agreement with the experimental observations.

Effect of external periodic regulations on Brownian motor

Abstract: Effect of external periodic regulations on a symmetric Brownian motor performing between two temperature sources was investigated. By means of numerical calculations, we found that: (i) The regulations can control magnitude and direction of the motor’s current to a large degree. As one of the motor’s compartments is regulated, the motor’s current can be both inversed and maximized, dependent on amplitude and frequency of the periodic driving force. If two periodic driving forces with identical amplitudes and frequencies are employed to regulate respectively two compartments of the Brownian motor, the current’s magnitude and direction will make periodic oscillations with phase difference between them. In addition, the external periodic regulation can also change direction of thermal rectifier of the system as a switch. (ii) Optimal regulating parameters of the external periodic forces can enhance pronouncedly conversion efficiency of energy of the Brownian motor.

A density functional (PBE, PBEsol, HSE06) study of the structural, electronic and optical properties of the ternary compounds AgAlX 2 (X = S, Se, Te)

Abstract: First principles density functional theory (DFT) calculations for bulk structural, electronic and optical properties of ternary compounds AgAlX2 (X = S, Se, Te) were performed with two flavours of generalised gradient approximations (PBE and PBEsol) and the hybrid functional HSE06. Using cohesive energy as a stability criterion, we found that the chalcopyrite structure is the favoured phase for these materials. PBEsol gives structural properties closer to the experimental values when compared to the results of PBE. Tetragonal distortion and anion displacement were calculated and we found them to be the cause of the crystal field splitting. Reduction of the bandgap and band splitting around the Γ in the Brillouin zone was noted when spin-orbit coupling was included in our study especially in the case of AgAlTe2. The HSE06 bandgap and frequency dependent dielectric function were in very good agreement with experimental results. We have also shown that the maximum absorption peak lies in the ultraviolet range irrespective of the functional used. The refractive index is also discussed.

Imperfect spreading on temporal networks

Abstract: We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential. We consider a process of imperfect spreading, where transmission is successful with a determined probability at each contact. We first derive an expression for the inter-success time distribution, determining the speed of the propagation, and then focus on a problem related to epidemic spreading, by estimating the epidemic threshold in a system where nodes remain infectious during a finite, random period of time. Finally, we discuss the implications of our work to design an efficient strategy to enhance spreading on temporal networks.

Exploring temporal networks with greedy walks

Abstract: Temporal networks come with a wide variety of heterogeneities, from burstiness of event sequences to correlations between timings of node and link activations. In this paper, we set to explore the latter by using temporal greedy walks as probes of temporal network structure. Given a temporal network (a sequence of contacts), temporal greedy walks proceed from node to node by always following the first available contact. Because of this, their structure is particularly sensitive to temporal-topological patterns involving repeated contacts between sets of nodes. This becomes evident in their small coverage per step taken as compared to a temporal reference model – in empirical temporal networks, greedy walks often get stuck within small sets of nodes because of correlated contact patterns. While this may also happen in static networks that have pronounced community structure, the use of the temporal reference model takes the underlying static network structure out of the equation and indicates that there is a purely temporal reason for the observations. Further analysis of the structure of greedy walks indicates that burst trains, sequences of repeated contacts between node pairs, are the dominant factor. However, there are larger patterns too, as shown with non-backtracking greedy walks. We proceed further to study the entropy rates of greedy walks, and show that the sequences of visited nodes are more structured and predictable in original data as compared to temporally uncorrelated references. Taken together, these results indicate a richness of correlated temporal-topological patterns in temporal networks.

Structural and electronic properties of MX3 (M = Ti, Zr and Hf; X = S, Se, Te) from first principles calculations

Abstract: The structural and electronic properties of layered TiS3, TiSe3, TiTe3, HfS3, HfSe3, HfTe3, ZrS3, ZrSe3 and ZrTe3 with structure P21/m have been investigated using density functional theory for the first time at the atomic level within the vdW-DF and vdW-TS approximations to account for long range dispersive forces, which is important in predicting layered material interlayer spacing accurately. To get reasonable estimates of the band gaps, MBJ band structure calculations were performed. With exception of the tellurides and TiSe3, which are found to be metallic, the compounds are indirect band gap semiconductors with band gap in the range of 0.44 to 2.04 eV. The minimum direct band gaps were found to be in a similar range. The elastic constants of these structures confirm their mechanical stability by satisfying all the stability criteria for monoclinic structures. Phonon band structure and thermal properties were calculated using density functional perturbation theory. The phonon dispersion relations show that the structures are stable under small atomic displacements.

First-principle investigation of half-metallic ferromagnetism in octahedrally bonded Cr-doped rock-salt SrS, SrSe, and SrTe

Abstract: We have investigated the electronic structure and half-metallic ferromagnetism of Sr1−x Cr x Z (Z = S, Se, and Te) in rock-salt structure at concentrations x (x = 0.125, 0.25, 0.5, 0.75 and 0.875) of Cr, using first-principles calculations of density functional theory. The electronic and magnetic properties show that Sr1−x Cr x Z (Z = S and Se) at x = 0.125, 0.25, 0.5, 0.75 and Sr1−x Cr x Te at all concentrations are half-metallic ferromagnets (HMF) with spin polarization of 100% and total magnetic moments of 4μ B per Cr atom, whereas the HMF character destroyed for Sr1−x Cr x Z (Z = S and Se) at x = 0.875. The integrals Bohr magneton of total magnetic moments confirm the half-metallic ferromagnetic behavior of Sr1−x Cr x Z. We have found that the ferromagnetic state is stable by the 3d-eg (Cr) partially filled states associated with the double-exchange mechanism. Therefore, the Sr1−x Cr x S, Sr1−x Cr x Se, and Sr1−x Cr x Te at low concentration are predicted to be new potential candidates for spintronic applications.

Synchronizability of two-layer networks

Abstract: In this paper, we investigate the synchronizability of two-layer networks according to the master stability method. We define three particular couplings: positively correlated, randomly correlated and negatively correlated couplings. When the inter-layer coupling strength is fixed, negatively correlated coupling leads to the best synchronizability of a two-layer network, and synchronizability of networks with randomly and positively correlated couplings follow consecutively. For varying inter-layer coupling strength, the trend of network synchronizability with an unbounded synchronous region differs from that with a bounded one. If the synchronous region is unbounded, synchronizability of the two-layer network keeps enhancing, but it has a threshold. If the synchronous region is bounded, the synchronizability of the two-layer network keeps improving until the inter-layer coupling strength reaches a certain value, and then the synchronizability gets weakened with ever-increasing inter-layer coupling strength. To summarise, there exists an optimal value of the inter-layer coupling strength for maximising synchronizability of two-layer networks, regardless of the synchronous region types and coupling patterns. The findings provided in this paper shed new light on understanding synchronizability of multilayer networks, and may find potential applications in designing optimal inter-layer couplings for synchronization of two-layer networks.

Infection propagator approach to compute epidemic thresholds on temporal networks: impact of immunity and of limited temporal resolution

Abstract: The epidemic threshold of a spreading process indicates the condition for the occurrence of the wide spreading regime, thus representing a predictor of the network vulnerability to the epidemic. Such threshold depends on the natural history of the disease and on the pattern of contacts of the network with its time variation. Based on the theoretical framework introduced in [E. Valdano, L. Ferreri, C. Poletto, V. Colizza, Phys. Rev. X 5, 21005 (2015)] for a susceptible-infectious-susceptible model, we formulate here an infection propagator approach to compute the epidemic threshold accounting for more realistic effects regarding a varying force of infection per contact, the presence of immunity, and a limited time resolution of the temporal network. We apply the approach to two temporal network models and an empirical dataset of school contacts. We find that permanent or temporary immunity do not affect the estimation of the epidemic threshold through the infection propagator approach. Comparisons with numerical results show the good agreement of the analytical predictions. Aggregating the temporal network rapidly deteriorates the predictions, except for slow diseases once the heterogeneity of the links is preserved. Weight-topology correlations are found to be the critical factor to be preserved to improve accuracy in the prediction.

Enhancing and controlling single-atom high-harmonic generation spectra: a time-dependent density-functional scheme

Abstract: High harmonic generation (HHG) provides a flexible framework for the development of coherent light sources in the extreme-ultraviolet and soft X-ray regimes. However it suffers from low conversion efficiencies as the control of the HHG spectral and temporal characteristics requires manipulating electron trajectories on attosecond time scale. The phase matching mechanism has been employed to selectively enhance specific quantum paths leading to HHG. A few important fundamental questions remain open, among those how much of the enhancement can be achieved by the single-emitter and what is the role of correlations (or the electronic structure) in the selectivity and control of HHG generation. Here we address those questions by examining computationally the possibility of optimizing the HHG spectrum of isolated hydrogen and helium atoms by shaping the slowly varying envelope of a 800 nm, 200-cycles long laser pulse. The spectra are computed with a fully quantum mechanical description, by explicitly computing the time-dependent dipole moment of the systems using a time-dependent density-functional approach (or the single-electron Schrodinger equation for the case of H), on top of a one-dimensional model. The sought optimization corresponds to the selective enhancement of single harmonics, which we find to be significant. This selectivity is entirely due to the single atom response, and not to any propagation or phase-matching effect. Moreover, we see that the electronic correlation plays a role in the determining the degree of optimization that can be obtained.

Anti-synchronization for stochastic memristor-based neural networks with non-modeled dynamics via adaptive control approach

Abstract: In this paper, exponential anti-synchronization in mean square of an uncertain memristor-based neural network is studied. The uncertain terms include non-modeled dynamics with boundary and stochastic perturbations. Based on the differential inclusions theory, linear matrix inequalities, Gronwall’s inequality and adaptive control technique, an adaptive controller with update laws is developed to realize the exponential anti-synchronization. Adaptive controller can adjust itself behavior to get the best performance, according to the environment is changing or the environment has changed, which has the ability to adapt to environmental change. Furthermore, a numerical example is provided to validate the effectiveness of the proposed method.

Description of a dissipative quantum spin dynamics with a Landau-Lifshitz/Gilbert like damping and complete derivation of the classical Landau-Lifshitz equation

Abstract: The classical Landau-Lifshitz equation has been derived from quantum mechanics. Starting point is the assumption of a non-Hermitian Hamilton operator to take the energy dissipation into account. The corresponding quantum mechanical spin dynamics along with the time dependent Schrodinger, Liouville and Heisenberg equation has been described and the similarities and differences between classical and quantum mechanical spin dynamics have been discussed. Furthermore, a time dependent Schrodinger equation corresponding to the classical Landau-Lifshitz-Gilbert equation and two ways to include temperature into the quantum mechanical spin dynamics have been proposed.

The fluctuation function of the detrended fluctuation analysis – investigation on the AR(1) process

Abstract: We derive an analytical expression for the fluctuation function of the first order autoregressive process AR(1) by means of the detrended fluctuation analysis (DFA). This process is short-range correlated and therefore the fluctuation exponent should be α = 1/2. However, the fluctuation function exhibits a crossover between a region with α > 1/2 and the expected 1/2. We calculate the crossover point and compare it with the characteristic correlation time of the process. We conclude that DFA is data consuming and requires one to two orders of magnitude more data than the estimation of the autocorrelation function.

Thermal transport in free-standing silicon membranes: influence of dimensional reduction and surface nanostructures

Abstract: Nanostructuring provides a viable route to improve the thermoelectric performance of materials, even of those that in bulk form have very low figure of merit. This strategy would potentially enable the fabrication of thermoelectric devices based on silicon, the cheapest, most integrable and easiest to dope Earth-abundant semiconductor. A drastic reduction of the thermal conductivity, which would lead to a proportional enhancement of the figure of merit, was observed for silicon low-dimensional nanostructures, such as nanowires and ultra-thin membranes. Here we provide a detailed analysis of the phononic properties of the latter, and we show that dimensionality reduction alone is not sufficient to hinder heat transport to a great extent. In turn, the presence of surface roughness at the nanoscale reduces the thermal conductivity of sub-10 nm membranes up to 10 times with respect to bulk.