In this work we have studied the dynamic scaling behavior of two scaling functions and we have shown that scaling functions obey the dynamic finite size scaling rules. Dynamic finite size scaling of scaling functions opens possibilities for a wide range of applications.As an application we have calculated the dynamic critical exponent (z) of Wolff's cluster algorithm for 2-, 3-and 4-dimensional Ising models. Configurations with vanishing initial magnetization are chosen in order to avoid complications due to initial magnetization.The observed dynamic finite size scaling behavior during early stages of the Monte Carlo simulation yields z for Wolff's cluster algorithm for 2-, 3-and 4-dimensional Ising models with vanishing values which are consistent with the values obtained from the autocorrelations. Especially, the vanishing dynamic critical exponent we obtained for d = 3 implies that the Wolff algorithm is more efficient in eliminating critical slowing down in Monte Carlo simulations than previously reported.

The conditions under which entanglement becomes maximal are sought in the general one--dimensional quantum random walk with two walkers. Moreover, a one--dimensional shift operator for the two walkers is introduced and its performance in generating entanglement is analyzed as a function of several free parameters, some of them coming from the shift operator itself and some others from the coin operator. To simplify the investigation an averaged entanglement is defined.Comment: Latex source, 9 pages, 6 figures (revised version, identical to published one

We report a systematic study of asymptotic behavior of entanglement between the position and coin degrees of freedom for a one-dimensional discrete quantum walk. Effects of coin bias, initial coin asymmetry and phase difference and non-locality of initial position state on the fluctuations and asymptotic value of entanglement are investigated by using Fourier approach. Fluctuations in entropy are found to die out as power law in time as t-α with α = 1/2,3/2 and 5/2 depending on the initial state parameters of the system.

A model of opinion dynamics with two types of agents as social actors are presented, using the Ising thermodynamic model as the dynamics template. The agents are considered as opportunists which live at sites and interact with the neighbors, or fanatics/missionaries which move from site to site randomly in persuasion of converting agents of opposite opinion with the help of opportunists. Here, the moving agents act as an external influence on the opportunists to convert them to the opposite opinion. It is shown by numerical simulations that such dynamics of opinion formation may explain some details of consensus formation even when one of the opinions are held by a minority. Regardless the distribution of the opinion, different size societies exhibit different opinion formation behavior and time scales. In order to understand general behavior, the scaling relations obtained by comparing opinion formation processes observed in societies with varying population and number of randomly moving agents are studied. For the proposed model two types of scaling relations are observed. In fixed size societies, increasing the number of randomly moving agents give a scaling relation for the time scale of the opinion formation process. The second type of scaling relation is due to the size dependent information propagation in finite but large systems, namely finite-size scaling.

In this work, dynamics of diffusion of innovation in the smartphone markets is modeled by using an agent-based simulation in a period of 28 quarters starting from 2009. Rapid changes in smartphone technology affected the consumer preferences and two operating systems, namely Android and iOS, out of over 10 operating systems, and dominated the smartphone markets in a period of 6 years. The model aims to study the conditions of competition and adoption among similar high technology products. Relative roles of the essential parameters, namely affordability and social effects have been the main interest points in these studies. For this end, a simple, Cobb–Douglas production relation-based model on simple square lattice is introduced. The model parameters are adjusted to match the simulation results with the actual market shares data obtained from Statista. A clear relation between the model parameter values and global sales of different operating systems is observed.

Pandemics are a growing world-wide threat for all societies. Throughout history, various infectious diseases presented widely spread damage to human life, economic viability and general well-being. The scale of destruction of the most recent pandemic, COVID-19, has yet to be seen. This work aims to introduce intervention methodology for the prevention of global scale spread of infectious diseases. The proposed method combines time-dependent infection spreading data with the social connectivity structure of the society. SIR model simulations provided the dynamic of contamination spread in different sets of network data. Seven centrality measures parameterized the local and global importance of each node in the underlying network. At each time step the calculated values of the correlations between node infection probability and node centrality values are analyzed. Calculations show that correlations increase at the beginning of infection spread and reaches its highest value when spreading starts to become an epidemic. The peak is at the very early stages of the spreading; and with this analysis, it is possible to predict the node infection probability from time-dependent correlations data.

In this work, the spread of a contagious disease on a society where the individuals may take precautions is modeled. The primary assumption is that the infected individuals transmit the infection to the susceptible members of the community through direct contact interactions. In the meantime, the susceptibles gather information from the adjacent sites which may lead to taking precautions. The SIR model is used for the diffusion of infection while the Bass equation models the information diffusion. The sociological classification of the individuals indicates that a small percentage of the population takes action immediately after being informed, while the majority expects to see some real advantage of taking action. The individuals are assumed to take two different precautions. The precursory measures are getting vaccinated or trying to avoid direct contact with the neighbors. A weighted average of states of the neighbors leads to the choice of action. The fully connected and scale-free Networks are employed as the underlying network of interactions. The comparison between the simple contagion diffusion and the diffusion of infection in a responsive society showed that a very limited precaution makes a considerable difference in the speed and the size of the spread of illness. Particularly, highly connected hub nodes play an essential role in the reduction of the spread of disease.

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