International Journal of Modern Physics C

Our study emphasizes the efficacy of employing matrices resembling Wishart matrices, derived from magnetization time series data within specific dynamics, to elucidate phase transitions and critical phenomena in the Q-state Potts model. Through the application of appropriate statistical methods, we not only identify second-order transitions but also distinguish weaker first-order transitions by carefully analyzing the density of eigenvalues and their fluctuations. Additionally, we investigate the method’s sensitivity to stronger first-order transition points. Notably, we establish a robust correlation between the system’s actual thermodynamics and the spectral thermodynamics encapsulated within the eigenvalues. Our findings are further supported by correlation histograms of the time series data, revealing insightful patterns. Building upon our core results, we provide a didactic analysis that draws parallels between the spectral properties of criticality in a spin system and matrices intentionally imbued with correlations (a toy model). Within this framework, we observe a universal behavior characterized by the distribution of eigenvalues into two distinct groups, separated by a gap dependent on the level of correlation, influenced by temperature-induced changes in the spin system.

To understand, predict and control the motion of the solid particles, the motion of a neutrally buoyant circular particle with thermal convection in a square cavity is studied with the lattice Boltzmann method, where the effects of the initial position of the circular particle, Rayleigh number and particle size are investigated. Under the effect of thermal convection, the obvious feature of the motion of the circular particle in the square cavity is the existence of the limit cycle, which is created by the inertia of the circular particle, confinement of the boundaries of the square cavity and centrifugal force. Interestingly, the limit cycle is insensitive to the initial position of the circular particle. The effect of the Rayleigh number on the motion of the circular particle is obvious, with the increase of the Rayleigh number, the limit cycle expands toward the boundaries of the square cavity first, then shrinks and migrates toward the bottom left corner, which is caused by the combined effects of the centrifugal force and vortex behavior. The effect of the particle size on the motion of the circular particle is significant, with the increase of the particle size, the inertia of the circular particle becomes larger, which is more difficultly dragged by the fluid, thus, the limit cycle shrinks toward the bottom left corner of the square cavity.

In this research, we regard a miniature significant for many cell types and activates stimulants against external interventions, thereby causing calcium oscillation. We stage the dependent variables regarding the Atangana–Balenau derivative operator in terms of Caputo so that the model can be physically interpreted better. The study investigates the existence and uniqueness of solutions using fixed point theory, stability in terms of Hyers–Ulam, positivity and numerical solutions. In addition, spacetime, phase diagrams and three-dimensional graphic simulations are presented due to the Lagrange interpolation technique for parameter selections that match the existence and uniqueness condition of the solution.

We examine the imbalance thermodynamics of uncontaminated decoherence in graphene. In a uncontaminated decoherence process, no exchange of energy takes place directly between graphene and the surroundings. It is seen that due to decoherence heat dissolution takes place due to which energy of the environment cannot remain conserved. In this paper, we find out the energy eigenvalues and wave function in the graphene from the perturbed Hamiltonian to find out the density matrix and entropy of the system and their unique relation between the density matrix, momentum of the graphene and entropy where the graphene is taken as an open system. In graphene, the behavior of electrons is controlled by the massless Hamiltonian and ($2+1$) Dirac equation.

In this work, we employ simulations to investigate deterministic and stochastic dynamics of a system governed by four coupled nonlinear ordinary differential equations (ODEs) derived from the canonical three-dimensional Chua model, replacing the piecewise nonlinearity with a cubic function. We employed two simulation approaches: (i) using software — where we performed numerical simulations (digital computation) in the ODEs model, and (ii) using hardware — where we performed experimental studies (analog computation) in the ODEs model. In the initial software-based approach for simulations, we performed stability and bifurcation analyses of the trivial equilibrium point, which were analytically conducted, along with the numerical continuation method. We solved the model using digital computation and explored its intricate dynamical behavior through nonlinear dynamics techniques applied to the parameter planes. In the second approach, employing hardware for simulations through analog computation, we designed an electronic circuit using analog electronics to solve the model in a continuous-time integration. The experimental setup mirrored the numerical simulations, yielding comparable results in terms of dynamical behaviors. This study underscores significant agreement between numerical and experimental findings, highlighting the robustness of the model across digital and analog contexts and offering practical insights into the various nonlinear dynamics presented in this system.

The paper devotes to the synthesis of local and global analysis of a discrete model describing the second-order digital filter with nonlinear signal processors. The discrete model gives rise to a two-dimensional non-invertible map, whose basins of attraction have complicated topological structures due to the intrinsic multi-stability. The influences of joint parameters on the local dynamics are presented in great details. Both theoretical and numerical results are plotted on the two-dimensional parametric planes. To show more detailed bifurcation structure, the isoclines are extended to higher periodic orbits for detecting the cusps of resonant entrainments. Invariant manifolds and critical curves are employed to illustrate the global dynamics of the model vividly. The tangency and intersections of invariant manifolds expound the process of erosions of basins of attraction. The global bifurcations of basins of attraction are deduced dynamically by critical curves.

With the rapid development of the mobile Internet, online social networks are playing an increasingly vital role in the dissemination of information. Accurately predicting the size of information cascades in advance has become a crucial issue, particularly in the realms of viral marketing, risk management and resource allocation. There are numerous studies that have tackled this prediction task, but the outcomes are unsatisfactory. In this paper, we explore the predictability of information cascade size through the lens of percolation theory. Our investigation reveals that the accuracy of cascade size prediction is notably diminished in the proximity of the threshold, evident in both artificial and empirical networks. Moreover, we observe a degradation and an user-level difference in prediction performance as social media platforms undergo evolution. Our findings underscore the necessity for additional factors to enhance prediction accuracy.

In this study, we utilize the coherence spectrum and structure-function methods to examine the multi-scale coherence and multifractal characteristics of financial time series. The phase spectrum reveals the temporal shift between two indices, indicating whether one leads or lags by several days within a region of high correlation that is scale-dependent. This information can serve as a predictive model for quantitative analysis. The Fourier power spectrum and scaling exponents, derived from the structure-function method, exhibit universal patterns across indices from various countries. Our findings suggest that stock market indices display behavior akin to turbulence, as demonstrated by the structure-function, power-law scaling and multifractal movements. Our results suggest that the fluctuations of indices could be accurately represented by a multifractal random walk model, offering a complex and insightful view of the financial market.

This study describes the Casson (a non-Newtonian fluid) nanofluid bioconvection flow across a spinning disc in the presence of gyrotactic microorganisms, many slips and thermal radiation. Also, the flow is considered as a reversible flow. The esterification process is taken into account. Using the proper variables, a system of extremely nonlinear PDEs is converted into a system of ODEs. To arrive to the solution of such equations, a numerical approach is used. Using the bvp4c approach, nonlinear flow equations can be numerically solved. Investigated are the effects of different numbers on the thermal field, volumetric concentration of nanoparticles and microbiological field. The key characteristics of the parameters in relation to the profiles of the velocity, temperature, concentration and microorganisms are graphically assessed with appropriate physical effects. A graphical explanation is provided for the wall shear stress, local Nusselt number, local Sherwood number and local motile density number. Rate of motile density number shows a prominent difference between reversible and irreversible flows for Brownian motion and Peclet number. The results of the theoretical simulations have dynamic applications in the fields of biotechnology and thermal engineering.

The pseudo-random number generator (PRNG) based on chaos has been widely used in the fields of digital communication, cryptography and computer simulation. In this paper, we study a new PRNG based on spatial surface chaotic system (SSCS), which is constructed based on coupling mapping lattice (CML) and one-dimensional Logistic chaotic map. To verify the performance of this generator, we study its nonlinear dynamic properties, including the Lyapunov exponent, ergodicity and bifurcation phenomena. Moreover, we analyze the cryptographic properties such as key space, key sensitivity, correlation, histogram and information entropy, while performing NIST SP800-22 test and TestU01 test for the randomness of this system. Theoretical analysis and numerical simulation results show that the PRNG proposed in this paper has good complexity, ergodicity, sensitivity and randomness. Moreover, the key space can increase dynamically with the increase of encrypted data, especially suitable for the protection of big data such as multimedia, which is more advantageous than most existing chaotic mapping. The results of this paper will provide a new idea for the study of chaotic cryptography, and motivate the study of new discrete chaotic models with desirable statistical properties.

Cellular automaton (CA) is a computing model which is emerging rapidly. It is largely used in different types of scientific applications and simulations due to its ability to solve complex problems using simple rule(s). Cellular automata (CAs) are used in different types of applications like cryptography, VLSI systems, fault detection, etc. Typically, most of these applications utilize one-dimensional, 2-state, 3-neighborhood CAs. This paper explores the concept of Next State RMT Transition Diagram (NSRTD) for characterization of all the Elementary Cellular Automata (ECA) rules in periodic boundary condition leading to the identification of all ECA rules forming more than two fixed points (referred to as Single Length Cycle Multi-Attractor CA (MACA)) for an arbitrary CA length (n). For this, the 88 Wolfram classification rules and their equivalent rules have been utilized to reduce the search complexity by avoiding exhaustive searching on all the 256 ECA rules.

Nowadays, technology has shifted the way individuals access news from conventional media sources to social media platforms. The active engagement of people with social media platforms leads them to consume news without confirming its source or legitimacy. This facilitated the dissemination of more manipulated and false information in the form of rumors and fake news. Fake news can affect public opinion and create chaos and panic among the population. Thus, it is essential to employ an advanced methodology to identify fake news with high precision. This research work has proposed the concept of the quantum-inspired firefly algorithm with the ant miner plus algorithm (QFAMP) for more effective fake news detection. The proposed QFAMP algorithm utilizes the attributes of quantum computing (QC), the firefly algorithm (FA), and the ant miner plus algorithm (AMP). Here, the QFA approach ensures the effective exploitation of the firefly agents until the agents are able to search for the brighter firefly. Further, the AMP algorithm utilizes the best ants with higher pheromone concentrations for global exploration, which also avoids the premature convergence of the QFA agents. In addition, the AMP algorithm serves as an efficient data mining variant that is effective for the classification of fake news. The efficacy of the proposed QFAMP algorithm is evaluated for the dataset of FakeNewsNet, which is composed of two sub-categories: BuzzFeed and PolitiFact. The experimental evaluations indicate the effective performance of the proposed algorithm compared to the other techniques.

The unstable time fractional Schrödinger model (UTFSM) is studied through the development of disturbances in marginally stable or unstable media. A modified Sardar-sub equation technique (MSSE) for a conformable fractional-order nonlinear evolution model is presented in this paper. The objective here is to construct new wave solutions for UTFSM. These solutions have particular relevance in quantum physics and assume several forms such as rational, exponential, trigonometric and hyperbolic functions, as well as combo solutions. This technique produces various shapes of dark, kink-type solitons and periodic solitary waves by setting proper parametric values. These discrete physical frameworks contribute to an understanding from analysis of unstable dynamical models. Additionally, we investigate modulation instability and stability analysis to ensure that obtained solutions are highly stable. The multiplicity of waves and solutions emphasizes how this technique can be used for different nonlinear fractional models in quantum physics and other areas.

We introduce the modified Picard–Ishikawa hybrid iterative scheme and establish some strong convergence results for the class of asymptotically generalized $\varphi$-pseudocontractive mappings in the intermediate sense in Banach spaces and approximate the fixed point of this class of mappings via the newly introduced iteration scheme. We construct some numerical examples to support our results. Furthermore, we apply the Picard–Ishikawa hybrid iteration scheme in solving the nonlinear Caputo type fractional differential equations. Our results generalize, extend and unify several existing results in literature.