International Journal of Modern Physics C

Prof. Dr. H. C. Dietrich Stauffer passed away on August 6, 2019 after a long battle with cancer. He was for many years the Managing Editor of International Journal of Modern Physics C. The scientific community of statistical and computational physics has lost one of its prominent figures, who has shaped the field for over almost five decades.

We derive explicit closed-form matrix representations of Hamiltonians drawn from tensored algebras, such as quantum spin Hamiltonians. These formulas enable us to soft-code generic Hamiltonian systems and to systematize the input data for uniformly structured as well as for un-structured Hamiltonians. The result is an optimal computer code that can be used as a black box that takes in certain input files and returns spectral information about the Hamiltonian. The code is tested on Kitaev’s toric model deployed on triangulated surfaces of genus 0 and 1. The efficiency of our code enables these simulations to be performed on an ordinary laptop. The input file corresponding to the minimal triangulation of genus 2 is also supplied.

The fractional calculus is useful to model nonlocal phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution of ordinary fractional differential equations. Due to the nonlocality of the fractional derivative, we may establish an equivalence between fractional oscillators and ordinary oscillators with a dissipative term.

This paper is devoted to introduce an efficient solver using the Hermite collocation technique (HCT), of the coupled system of fractional differential equations (FDEs). The given systems are of basic importance in modeling various phenomena like Cascades and Compartment Analysis, Pond Pollution, Home Heating, Chemostats, and Microorganism Culturing, Nutrient Flow in an Aquarium, Biomass Transfer, Forecasting Prices, Electrical Network, Earthquake Effects on Buildings. The proposed method reduces the system of FDEs to a system of algebraic equations in the coefficients of the expansion using the Hermite polynomials. The introduced method is computer oriented and provides highly accurate solution. To demonstrate the efficiency of the method, two examples are solved and the results are displayed graphically. Finally, we convert the presented coupled systems from the case of its standard form to a first-order ordinary differential equations to compare the obtained numerical solutions with those solutions using the fourth-order Runge–Kutta method (RK4).

Many real-world systems can be abstracted as networks. As those systems always change dynamically in nature, the corresponding networks also evolve over time in general, and detecting communities from such time-evolving networks has become a critical task. In this paper, we propose an incremental detection method, which can stably detect high-quality community structures from time-evolving networks. When the network evolves from the previous snapshot to the current one, the proposed method only considers the community affiliations of partial nodes efficiently, which are either newborn nodes or some active nodes from the previous snapshot. Thus, the first phase of our method is determining active nodes that should be reassigned due to the change of their community affiliations in the evolution. Then, we construct subgraphs for these nodes to obtain the preliminary communities in the second phase. Finally, the final result can be obtained through optimizing the primary communities in the third phase. To test its performance, extensive experiments are conducted on both some synthetic networks and some real-world dynamic networks, the results show that our method can detect satisfactory community structure from each of snapshot graphs efficiently and steadily, and outperforms the competitors significantly.

In this work, we implement multiplicative noise to the Duffing oscillator with variable coefficients. The stochastic differential equations are solved using the fourth-order Runge–Kutta method with the Box-Müller algorithm and the corresponding integral of motion is obtained. Some numerical experiments are performed and the results show that the integral of motion is highly unaffected by the multiplicative noise.

As an elementary task in statistical physics and network science, link prediction has attracted great attention of researchers from many fields. While numerous similarity-based indices have been designed for undirected networks, link prediction in directed networks has not been thoroughly studied yet. Among several representative works, motif predictors such as “feed-forward-loop” and Bi-fan predictor perform well in both accuracy and efficiency. Nevertheless, they fail to explicitly explain the linkage motivation of nodes, nor do they consider the unequal contributions of different neighbors between node pairs. In this paper, motivated by the investment theory in economics, we propose a universal and explicable model to quantify the contributions of nodes on driving link formation. Based on the analysis on two typical investment relationships, namely “follow-up” and “co-follow”, an investment-profit index is designed for link prediction in directed networks. Empirical studies on 12 static networks and four temporal networks show that the proposed method outperforms eight mainstream baselines under three standard metrics. As a quasi-local index, it is also suitable for large-scale networks.

Traffic flow models are important tools for traffic management applications such as traffic incident detection and traffic control. In this paper, we propose a novel numerical approximation method for second-order macroscopic traffic flow models. The method is based on the semi-discrete central-upwind numerical flux and high-order reconstructions for spatial discretizations. We then apply the designed high-resolution schemes to three representative types of second-order traffic flow models and perform a variety of numerical experiments to validate the proposed methods. The simulation results illustrate the effectiveness, simplicity and universality of the central-upwind scheme as numerical approximation method for macroscopic traffic flow models.

We study opinion formation by uncovering the relevant aspects hiding in the distribution of micro-configurations in a 2-D Ising model. The external field denotes the external influence such as guiding viewpoint, and temperature represents randomness of the agents. The full-positive configuration or the full-negative configuration means consensus. We find that the probability of the full-positive configuration and the full-negative configuration can reach $0.5$ (which implies the equal splitting of a group) if the interaction is strong enough and the system is free from external field; the probability of the full-positive configuration can reach 1 (which means consensus) if the positive external field is strong enough under condition of given interaction and temperature. These phenomena are regarded as the reversing mechanism of the full-negative configuration induced by the external field — an opinion reversal. The equal splitting and consensus can be broken down as temperature rises. We discuss the dependence of interaction strength $J_c$ (with which the equal splitting occurs) on temperature $T$, the dependence of external field strength $B_c$ (with which the consensus occurs) on interaction strength $J$ at a certain temperature, as well as the scaling relations responsible for the probability of the full-negative configuration varying with temperature under different conditions. The findings provide us with a good description to understand opinion formation.

An interesting fact which was used in the construction of targeted essentially non-oscillatory (TENO) schemes is that a $(n+1)$th order accurate scheme can be written as a linear combination of two $n$th order accurate schemes. Taking advantage of this fact, we propose a formula to determine the ideal weights used in developing finite difference WENO/WENO-like schemes. Such quantitative results are helpful for further discussion on finite difference WENO/WENO-like schemes.

Explicit formulas for orbital carriers of periods 4, 5 and 6 are reported for discrete-time quadratic dynamics. A systematic investigation of orbital inheritance for periods as high as $k\le 12$ is also reported. Inheritance means that unknown orbits may be obtained by nonlinear transformations of known orbits. Such nested orbit within orbit stratification shows orbits not to be necessarily independent of each other as generally assumed. Orbital stratification is potentially significant to rearrange trajectories sums in trace formulas underlying modern semiclassical interpretations of atomic physics spectra. The stratification seems to dominate as the orbital period grows.

In this age of Facebook, Instagram, and Twitter, there is rapidly growing interest in understanding network-enabled opinion dynamics in large groups of autonomous agents. The phenomena of opinion polarization, the spread of propaganda and fake news, and the manipulation of sentiment is of interest to large numbers of organizations and people. Whether it is the more nefarious players such as foreign governments that are attempting to sway elections or it is more open and above board, such as researchers who want to make large groups of people aware of helpful innovations, what is at stake is often significant.

In this paper, we review opinion dynamics including the extensions of many classical models as well as some new models that deepen understanding. For example, we look at models that track the evolution of an individual’s power, that include noise, and that feature sequentially dependent topics, to name a few.

While the first papers studying opinion dynamics appeared over 60 years ago, there is still a great deal of room for innovation and exploration. We believe that the political climate and the extraordinary (even unprecedented) events in the sphere of politics in the last few years will inspire new interest and new ideas.

It is our aim to help those interested researchers understand what has already been explored in a significant portion of the field of opinion dynamics. We believe that in doing this, it will become clear that there is still much to be done.

In order to characterize the disturbance fluctuation of pedestrian flow caused by the disturbance during evacuation and the state change of pedestrian flow, this paper improves the social force model by introducing disturbance fluctuation force. First, a momentum equation is established to describe the change of pedestrian flow under the influence of disturbance fluctuation, and the mathematical expression of disturbance fluctuation force is given. Second, the evacuation processes of pedestrian flow with and without “queue jumpers” are simulated with the simulation experimental platform, and the key factors influencing the performance of the model are deeply studied through numerical analysis. The results showed that: when the expected velocity is the same, the bigger the angle between the cross-section position vector and the initial expected velocity is, the more serious the congestion occurs at the exit. In addition, when the crowd density is small, the larger the angle, the higher the evacuation efficiency and vice versa.

To evaluate the effectiveness of the containment on the epidemic spreading of the new Coronavirus disease 2019, we carry on an analysis of the time evolution of the infection in a selected number of different Countries, by considering well-known macroscopic growth laws, the Gompertz law, and the logistic law. We also propose here a generalization of Gompertz law. Our data analysis permits an evaluation of the maximum number of infected individuals. The daily data must be compared with the obtained fits, to verify if the spreading is under control. From our analysis, it appears that the spreading reached saturation in China, due to the strong containment policy of the national government. In Singapore a large growth rate, recently observed, suggests the start of a new strong spreading. For South Korea and Italy, instead, the next data on new infections will be crucial to understand if the saturation will be reached for lower or higher numbers of infected individuals.

The Lorenz–Stenflo system is a four-parameter four-dimensional autonomous nonlinear continuous-time dynamical system, derived to model the time evolution of finite amplitude acoustic gravity waves in a rotating atmosphere. In this paper, we propose a modified Lorenz–Stenflo system, where the variable $x$ in the fourth equation of the original Lorenz–Stenflo system was replaced by $ln|x|$. We investigate cross-sections of the parameter-space of this new system, characterizing regions of different dynamical behaviors. We show that the aforementioned replacement may promote the emergence of organized periodic structures in places of these cross-sections, where they did not exist before modification.