arXiv subjects

Roberto F. S. Andrade

Publications and source records attributed to Roberto F. S. Andrade.

At least 19 recordsLinked to original sources

arXiv2022

Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network

The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction-diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction-diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction-diffusion model for describing local dynamics.

q-bio.PE↗

arXiv2019

Prime stars multiplexes

This work investigates the class of prime star multiplexes, in which each of its layers $i$, $i=1,2, \ldots M$, consists of a regular cycle graph where any node has $2J_i$ neighbors. In a process that does not affect the cyclic topology, it is assumed that, before the multiplex is assembled, the nodes are labeled differently in each individual layer. As the setup requires that all representations of the same node in the different $M$ layers must be linked by inter-layers connections, the resulting multiplex pattern can be highly complex. This can be better visualized if one assumes that in one layer the nodes are labeled in the sequentially ascending order and that the nodes with the same label are drawn on the top of the other, so that all inter-layer connections are represented by vertical lines. In such cases, the other $M-1$ layers are characterized by long distance shortcuts. As a consequence, in spite of sharing the same internal topological structure, the multiplex ends up with very dissimilar layers. For prime number of nodes, a regular star geometry arises by requiring that the neighbor labels of the $M-1$ layers differ by a constant value $p_i>1$. For $M=2$, we use analytical and numerical approaches to provide a thorough characterization of the multiplex topological properties, of the inter layer dissimilarity, and of the diffusive dynamical processes taking place on them. For the sake of definitiveness, it is considered that each node in the sequentially labeled layer is characterized by $J_1\geq1$. In the other layer, we fix $J_2\equiv1$, while $p>1$ becomes a proxy of layer dissimilarity.

physics.soc-ph↗

arXiv2019

Fractional dynamics on circulant multiplex networks: optimal coupling and long-range navigation for continuous-time random walks

This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends on the connection weight. Synthetic multiplexes with well known topology are used to illustrate dynamical features obtained by numerical simulations, while exact analytical expressions are presented for multiplexes assembled by circulant layers with finite number of nodes. Special attention is given to the effect of inter- $D_x$ and intra-layer $D_i$ coefficients on the system's behavior. In opposition to usual discrete time dynamics, the relaxation time has a well defined minimum at an optimal value of $D_x/D_i$. It is found that, even for the enhanced diffusion condition, the walkers mean square displacement increases linearly with time.

physics.soc-ph↗

arXiv2019

Markov chain approach to anomalous diffusion on Newman-Watts networks

A Markov chain (MC) formalism is used to investigate the mean-square displacement (MSD) of a random walker on Newman-Watts (NW) networks. It leads to a precise analysis of the conditions for the emergence of anomalous sub- or super-diffusive regimes in such random media. Whereas results provided by most numerical approaches used so far base their results on the computation of a large number of independent runs over many equivalent substrates, the MC framework is applied only once to each equivalent sample. Starting from the simple cycle graph with $2k$ nearest neighbor connections, for which exact MSD expressions within the MC formalism can be derived, the randomness and complexity of the substrate is easily controlled by the number $x$ of added links. Results for different values of $k$, $x$, and the number $N$ of nodes make it possible to distinguish actual anomalous regimes from transient behavior and finite size effects. Albeit the high computing cost restricts the size of our networks to $N\leq1500$ nodes, our very precise results justify a new and more comprehensive scaling ansatz for walker dynamics, from which the behavior for very large networks can be derived.

physics.soc-ph↗

arXiv2018

Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one-dimension

We report local roughness exponents, $α_{\text{loc}}$, for three interface growth models in one dimension which are believed to belong the non-linear molecular-beam-epitaxy (nMBE) universality class represented by the Villain-Lais-Das Sarma (VLDS) stochastic equation. We applied an optimum detrended fluctuation analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801 (2017)] and compared the outcomes with standard detrending methods. We observe in all investigated models that ODFA outperforms the standard methods providing exponents in the narrow interval $α_{\text{loc}}\in[0.96,0.98]$ consistent with renormalization group predictions for the VLDS equation. In particular, these exponent values are calculated for the Clarke-Vvdensky and Das Sarma-Tamborenea models characterized by very strong corrections to the scaling, for which large deviations of these values had been reported. Our results strongly support the absence of anomalous scaling in the nMBE universality class and the existence of corrections in the form $α_{\text{loc}}=1-ε$ of the one-loop renormalization group analysis of the VLDS equation.

cond-mat.stat-mech↗

arXiv2018

First-principles analysis of nanoelectromechanical systems using Loewner equation

The Loewner equation (LE) is used to obtain conformal mappings that lead to exact and analytical expressions for several electrostatic properties of realistic quasi-unidimensional nanoelectromechanical systems (NEMS). The LE approach also embraces curved geometries, impossible to be addressed by traditional methods such as the Schwarz-Christoffel transformation, often used in this scenario. Among the possible applications of the formalism, we show that it allows for an exact evaluation of the field enhancement factor (FEF) close to the apex of different emitters. Despite its key role in the demodulation process for radio-receiver nano-devices, actual FEF values have been mostly obtained via numerical and/or phenomenological approaches. This work extends the already huge universe of applications of the LE and provides an analytical method to evaluate the FEF, even for curved emitters. Furthermore, our results provide a signature of the varying emitted current's response due to the nanostructure oscillation, justifying its role in the demodulation process of radio-frequency.

cond-mat.mes-hall↗

arXiv2018

Superdiffusion on complex networks: the role of shortcuts and long-range interactions

This work addresses the superdiffusive motion of a discrete time random walker on ordered discrete substrates and complex networks with the presence of long-range interactions (LRIs). In ordered regular lattices, where LRIs have a clear geometrical meaning, their presence allow for hoppings between more distant sites, yet with a smaller probability. In such cases, it is found that LRIs do not affect the dependency of the mean square displacement (MSD) traveled by the walker: exact analytical results for the the cycle graph within the Markov chain framework shows that MSD follows the same linearly increasing behavior with time when LRIs are absent, independently of the strength of LRI. This contrasts with the superdiffusive scenario in complex networks. When they have very short diameter ($\sim \log N$), the analysis of the time dependency of MSD becomes quite difficult, as it saturates very quickly even when LRIs are absent. The presence of a faster than linearly increasing growth phase can be noticed, but it can hardly be measured with precision. This effect is sidestepped on small-world Newman-Watts (NW) networks, where the network diameter can be controlled by the number of new links (shortcuts) that are added to the cycle graph. The time duration $t_f$ of the superdiffusive regime and the power law exponent can be adequately evaluated by numerical methods. They depend on the number of nodes and shortcuts, as well as the strength of LRIs. Although the later causes a strong reduction in $t_f$ when shortcuts are present, their presence by itself is not sufficient to trigger a superdiffusive behavior.

physics.soc-ph↗

arXiv2017

Schramm-Loewner evolution and perimeter of percolation clusters of correlated random landscapes

Motivated by the fact that many physical landscapes are characterized by long-range height-height correlations that are quantified by the Hurst exponent H, we investigate the statistical properties of the iso-height lines of correlated surfaces in the framework of Schramm-Loewner evolution (SLE). We show numerically that in the continuum limit the external perimeter of a percolating cluster of correlated surfaces with H between -1 and zero is statistically equivalent to SLE curves. Our results suggest that the external perimeter also retains the Markovian properties, confirmed by the absence of time correlations in the driving function and the fact that the latter is Gaussian distributed for any specific time. We also confirm that for all H the variance of the winding angle grows logarithmically with size.

cond-mat.stat-mech↗

arXiv2017

Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators

This work considers the timescales associated with the global order parameter and the interlayer synchronization of coupled Kuramoto oscillators on multiplexes. For the two-layer multiplexes with initially high degree of synchronization in each layer, the difference between the average phases in each layer is analyzed from two different perspectives: the spectral analysis and the non-linear Kuramoto model. Both viewpoints confirm that the prior timescales are inversely proportional to the interlayer coupling strength. Thus, increasing the interlayer coupling always shortens the transient regimes of both the global order parameter and the interlayer synchronization. Surprisingly, the analytical results show that the convergence of the global order parameter is faster than the interlayer synchronization, and the latter is generally faster than the global synchronization of the multiplex. The formalism also outlines the effects of frequencies on the difference between the average phases of each layer, and identifies the conditions for an oscillatory behavior. Computer simulations are in fairly good agreement with the analytical findings and reveal that the timescale of the global order parameter is at least half times smaller than timescale of the multiplex.

physics.soc-ph↗

arXiv2017

Thermodynamic Framework for Compact q-Gaussian Distributions

Recent works have associated systems of particles, characterized by short-range repulsive interactions and evolving under overdamped motion, to a nonlinear Fokker-Planck equation within the class of nonextensive statistical mechanics, with a nonlinear diffusion contribution whose exponent is given by $ν=2-q$. The particular case $ν=2$ applies to interacting vortices in type-II superconductors, whereas $ν>2$ covers systems of particles characterized by short-range power-law interactions, where correlations among particles are taken into account. In the former case, several studies presented a consistent thermodynamic framework based on the definition of an effective temperature $θ$ (presenting experimental values much higher than typical room temperatures $T$, so that thermal noise could be neglected), conjugated to a generalized entropy $s_ν$ (with $ν=2$). Herein, the whole thermodynamic scheme is revisited and extended to systems of particles interacting repulsively, through short-ranged potentials, described by an entropy $s_ν$, with $ν>1$, covering the $ν=2$ (vortices in type-II superconductors) and $ν>2$ (short-range power-law interactions) physical examples. The main results achieved are: (a) The definition of an effective temperature $θ$ conjugated to the entropy $s_ν$; (b) The construction of a Carnot cycle, whose efficiency is shown to be $η=1-(θ_2/θ_1)$, where $θ_1$ and $θ_2$ are the effective temperatures associated with two isothermal transformations, with $θ_1>θ_2$; (c) Thermodynamic potentials, Maxwell relations, and response functions. The present thermodynamic framework, for a system of interacting particles under the above-mentioned conditions, and associated to an entropy $s_ν$, with $ν>1$, certainly enlarges the possibility of experimental verifications.

cond-mat.stat-mech↗

arXiv2016

Modularity map of the network of human cell differentiation

Cell differentiation in multicellular organisms is a complex process whose mechanism can be understood by a reductionist approach, in which the individual processes that control the generation of different cell types are identified. Alternatively, a large scale approach in search of different organizational features of the growth stages promises to reveal its modular global structure with the goal of discovering previously unknown relations between cell types. Here we sort and analyze a large set of scattered data to construct the network of human cell differentiation (NHCD) based on cell types (nodes) and differentiation steps (links) from the fertilized egg to a crying baby. We discover a dynamical law of critical branching, which reveals a fractal regularity in the modular organization of the network, and allows us to observe the network at different scales. The emerging picture clearly identifies clusters of cell types following a hierarchical organization, ranging from sub-modules to super-modules of specialized tissues and organs on varying scales. This discovery will allow one to treat the development of a particular cell function in the context of the complex network of human development as a whole. Our results point to an integrated large-scale view of the network of cell types systematically revealing ties between previously unrelated domains in organ functions.

q-bio.CB↗

arXiv2016

The consequences of dependence between the formal area efficiency and the macroscopic electric field on linearity behavior in Fowler-Nordheim plots

This work presents a theoretical explanation for a crossover in the linear behavior in Fowler-Nordheim (FN) plots based on cold field electron emission (CFE) experimental data. It is characterized by a clear change in the decay rate of usually single-slope FN plots, and has been reported when non-uniform nano-emitters are subject to high macroscopic electric field $F_M$. We assume that the number of emitting spots, which defines an apparent formal area efficiency of CFE surfaces, depends on the macroscopic electric field. Non-uniformity is described by local enhancement factors $\left\{γ_j\right\}$, which are randomly assigned to each distinct emitter of a conducting CFE surface, from a discrete probability distribution $ρ{(γ_{j})}$, with $j=1,2$. It is assumed that $ρ{(γ_{1})} < ρ{(γ_{2})}$, and that $γ_{1} > γ_{2}$. The local current density is evaluated by considering a usual Schottky-Nordheim barrier. The results reproduce the two distinct slope regimes in FN plots when $F_M \in $ $[2,20]$ V/$μ$m and are analyzed by taking into account the apparent formal area efficiency, the distribution $ρ$, and the slopes in the corresponding FN plot. Finally, we remark that our results from numerical solution of Laplace's equation, for an array of conducting nano-emitters with uniform apex radii $50$ nm but different local height, supports our theoretical assumptions and could used in orthodox CFE experiments to test our predictions.

cond-mat.mtrl-sci↗

arXiv2015

A percolation model with continuously varying exponents

This work analyzes a percolation model on the diamond hierarchical lattice (DHL), where the percolation transition is retarded by the inclusion of a probability of erasing specific connected structures. It has been inspired by the recent interest on the existence of other universality classes of percolation models. The exact scale invariance and renormalization properties of DHL leads to recurrence maps, from which analytical expressions for the critical exponents and precise numerical results in the limit of very large lattices can be derived. The critical exponents $ν$ and $β$ of the investigated model vary continuously as the erasing probability changes. An adequate choice of the erasing probability leads to the result $ν=\infty$, like in some phase transitions involving vortex formation. The percolation transition is continuous, with $β>0$, but $β$ can be as small as desired. The modified percolation model turns out to be equivalent to the $Q\rightarrow1$ limit of a Potts model with specific long range interactions on the same lattice.

cond-mat.stat-mech↗

arXiv2013

A dynamical programming approach for controlling the directed abelian Dhar-Ramaswamy model

A dynamical programming approach is used to deal with the problem of controlling the directed abelian Dhar-Ramaswamy model on two-dimensional square lattice. Two strategies are considered to obtain explicit results to this task. First, the optimal solution of the problem is characterized by the solution of the Bellman equation obtained by numerical algorithms. Second, the solution is used as a benchmark to value how far from the optimum other heuristics that can be applied to larger systems are. This approach is the first attempt on the direction of schemes for controlling self-organized criticality that are based on optimization principles that consider explicitly a tradeoff between the size of the avalanches and the cost of intervention.

physics.comp-ph↗

arXiv2013

Controlling self-organized criticality in sandpile models

We introduce an external control to reduce the size of avalanches in some sandpile models exhibiting self organized criticality. This rather intuitive approach seems to be missing in the vast literature on such systems. The control action, which amounts to triggering avalanches in sites that are near to be come critical, reduces the probability of very large events, so that energy dissipation occurs most locally. The control is applied to a directed Abelian sandpile model driven by both uncorrelated and correlated deposition. The latter is essential to design an efficient and simple control heuristic, but has only small influence in the uncontrolled avalanche probability distribution. The proposed control seeks a tradeoff between control cost and large event risk. Preliminary results hint that the proposed control works also for an undirected sandpile model.

physics.comp-ph↗

arXiv2013

Controlling self-organized criticality in complex networks

A control scheme to reduce the size of avalanches of the Bak-Tang-Wiesenfeld model on complex networks is proposed. Three network types are considered: those proposed by Erdős-Renyi, Goh-Kahng-Kim, and a real network representing the main connections of the electrical power grid of the western United States. The control scheme is based on the idea of triggering avalanches in the highest degree nodes that are near to become critical. We show that this strategy works in the sense that the dissipation of mass occurs most locally avoiding larger avalanches. We also compare this strategy with a random strategy where the nodes are chosen randomly. Although the random control has some ability to reduce the probability of large avalanches, its performance is much worse than the one based on the choice of the highest degree nodes. Finally, we argue that the ability of the proposed control scheme is related to its ability to reduce the concentration of mass on the network.

physics.soc-ph↗

arXiv2010

Protein Interaction Networks are Fragile against Random Attacks and Robust against Malicious Attacks

The capacity to resist attacks from the environment is crucial to the survival of all organisms. We quantitatively analyze the susceptibility of protein interaction networks of numerous organisms to random and malicious attacks. We find for all organisms studied that random rewiring improves protein network robustness, so that actual networks are more fragile than rewired surrogates. This unexpected fragility contrasts with the behavior of networks such as the Internet, whose robustness decreases with random rewiring. We trace this surprising effect to the modular structure of protein networks.

physics.comp-ph↗

arXiv2010

q-state Potts model on the Apollonian network

The q-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the Transfer Matrix method. The spontaneous magnetization, correlation length, entropy, and specific heat are analyzed as a function of temperature for different number of states, $q$. Different scaling functions in temperature and $q$ are proposed. A quantitative agreement is found between results from both methods. No critical behavior is observed in the thermodynamic limit for any number of states.

cond-mat.stat-mech↗