International Journal of Modern Physics B

This paper presents a novel tracking model to detect a $d$-dimensional random walk radionuclides and toxic chemicals in a fractured medium with minimum time and maximum probability. This model improves the physical and chemical properties of a fractured medium for a long time. It depends on a coordinated search technique with multiple sensors. The radionuclide particle has a linear flows on one direction from $d$-directions to spread. We consider this particle dispersed through a cylinder path in a very small time. The tracking or searching process in each cylinder path will be done by two sensors which start from any point in the fractured medium (space). The particle’s initial position is a vector of random variables with a known probability distribution. More than presenting the analytical solution which shows the existence of a finite tracking technique, we derive some auxiliary results related to optimal tracking technique. Besides that, we derive this optimal tracking technique which minimizes the expected value of the first meeting time between one of the sensors and the radionuclide or the toxic chemical particle. The effectiveness of this model appears in some numerical results.

In this paper, we study different analytical solutions for long water-wave equation (LWWE) like lump, breathers, rogue waves, periodic cross-kink, periodic wave, lump with one and two-kink, multiwave and periodic-cross lump. We compute the essential relationship between interaction between lump periodic and kink wave, periodic cross-kink and other types of exact solutions by studying the unknown nonlinear evolution equations (NLEEs) for long water wave. We show the graphical representation for our retrieve analytical solutions to observe the behavior of effective waves.

In this paper, a new corresponding state principle (CSP)-based model is proposed to calculate the surface tension of hydrocarbons based on the National Institute of Standards and Technology (NIST) database. This model requires the critical point temperature, the lowest temperature available for surface tension data and the corresponding maximum surface tension value as inputs. It includes two adjustable coefficients which are fitted by using NIST data of three hydrocarbons. To test the applicability of this model, we applied it to predict the surface tension values of other 16 hydrocarbons. For all the 19 hydrocarbons available in NIST database, the average absolute deviations of 16 hydrocarbons are less than 5%. We also compared this new proposed model with other three existing corresponding state models, and found that this model is the best in predicting the surface tension data of hydrocarbons.

Nowadays, research on social networks has attracted a large amount of attention from both academic and industrial societies. To understand the diffusion process and guide viral marketing, it is of importance to model and then estimate the influence of a seed user on a target user, which is defined as target influence in this paper. In famous diffusion models like independent cascade model and linear threshold model, tremendous computational costs are usually required in estimating influence probability through simulation. In this paper, we adopt duplicate forwarding model, and propose two measurements for the target influence, which can be analyzed theoretically. The former is the average number of duplicates the target user receives, and the latter is the probability of the target user receiving at least one duplicate. We further find the former will approach infinity if the spread intensity exceeds some threshold, but the latter can be adopted without this constraint. We also seek to use the latter to estimate the influence probability in the independent cascade model, and find it achieves much better accuracy than other heuristic metrics. All results are verified through simulations in real-world social networks, and we believe approach proposed here can provide insights to solve the problems like target influence maximization and influence maximization.

The particles in condensed matter physics are almost characterized by Brownian motion. This phenomenon is the basis for a very important understanding of the particles motion in condensed matter. For our previous research, there is already applied and confirmed the complex fractal correction which includes influence of parameters from grains and pores surface and also effects based on particles’ Brownian motion. As a chaotic structure of these motions, we have very complex research results regarding the particles’ trajectories in three-dimension (3D). In our research paper, we applied fractal interpolation within the idea to reconstruct the above mentioned trajectories in two dimensions at this stage. Because of the very complex fractional mathematics on Brownian motion, we found and developed much simpler and effective mathematization. The starting point is within linear interpolation. In our previous research, we presented very original line fractalization based on tensor product. But, in this paper, we applied and successfully confirmed that by fractal interpolation (Akimo polynomial method) that is possible to reconstruct the chaotical trajectories lines structures by several fractalized intervals and involved intervals. This novelty is very important because of the much more effective procedure that we can reconstruct and in that way control the particles’ trajectories. This is very important for further advanced research in microelectronics, especially inter-granular micro capacitors.

Characterizing and quantifying quantum entanglement in states of open quantum systems are at the heart of quantum information theory. In this work, we study the mixedness and entanglement of a two-mode symmetrical Gaussian state evolving in a thermal Markovian environment. The considered state is that of two movable end-mirrors of two distant Fabry–Pérot cavities coupled via a two-mode squeezed light and driven by coherent lasers. We use the logarithmic negativity to consistently quantify the degree of entanglement between the two mechanical modes. The purity is employed as a witness of mixedness and characterize of entanglement in the two-mode mechanical bi-partition. By comparing the behavior of the logarithmic negativity with that of the purity under the effect of various parameters and based on the entanglement classification established in [G. Adesso, A. Serafini and F. Illuminati, Phys. Rev. Lett. 92, 087901 (2004)], we found that the purity can be used as a characterize and measure of entanglement in the two-mode symmetrical state when the squeezing parameter is fixed. The effects of thermal noise, squeezing and optomechanical coupling are also discussed in detail.

In this paper, we focused on time-dependent flow of micropolar fluid between parallel permeable plates. Fluid is electrically conducting. Magnetic field is applied in the transverse direction to flow. Energy equation is modeled in the presence of viscous dissipation, thermal radiation and Joule heating. Suction is considered at lower plate while injection is considered at upper plate. Appropriate dimensionless variables are employed to reduce the governing PDE’s system into dimensionless one. Nondimensional PDE system is tackled numerically by finite difference technique. Effects of flow parameters on velocity, micro-rotation, temperature, couple and shear stresses at plates and Nusselt number are discussed. The obtained outputs show that for nonzero electric field parameter the velocity increases with Hartmann number. For zero electric field parameter the velocity decreases with Hartmann number. Temperature increases with both electric and magnetic field parameters. Micro-rotation decreases with micro-rotation material parameter and it increases with time.

This paper designs a thermal waveguide using thermal phonon insulators, to manipulate the loss of thermal radiation. Two-dimensional (2D) photonic crystals with dielectric background and air holes have been used in the waveguide clad to suppress thermal radiation so that thermal radiation cannot escape out from the waveguide clad. The photonic crystals may reduce the loss of thermal radiation through waveguide clad which surges the thermal energy confinement in the waveguide core and propagation along the longitudinal axis. The photonic crystals have been designed with the bandgap covering the thermal phonon frequency range and thus can be used to construct thermal phonon insulators to suppress or trap thermal emission generated through phonon wave propagation. The finite-difference-time-domain simulation results demonstrate that electromagnetic bandgap in photonic crystals has enough width in the thermal phonon frequency range to confine the thermal energy within the core of the waveguide and effective transmission of thermal radiation can be conquered within the waveguide core.

In this paper, a specific consideration is paid to the nonlinear dynamics of solitary waves to kinetics of phase separation in iron $(\mathrm{\text{Fe-Cr}}-X(X=\mathrm{\text{Mo, Cu}}))$ based on ternary alloys. The convective–diffusive Cahn–Hilliard (CH) equation is used as a mathematical model to describe the dynamics of the separation phase for the ternary alloys of iron. A variety of solitary wave solutions with unknown parameters are extracted in different shapes like kink-type, bell-shape, shock-type, combine soliton, trigonometric, hyperbolic and Jacobi’s elliptic function solutions with the assistant of recently computational tools, namely, extended Fan-sub equation method (EFSEM) and extended auxiliary equation method (EAEM). In addition, 3D, 2D, and their corresponding contour profiles of earned results are sketched in order to observe their dynamics with the choices of involved parameters. On the bases of achieved results, we may claim that the proposed computational methods are direct, dynamics, well organized, and will be useful for solving the more complicated nonlinear problems in diverse areas together with symbolic computations.

This paper presents a newly developed method, namely, the rational sine-Gordon expansion method to find novel exact solutions to nonlinear differential equations. This method is based on the sine-Gordon expansion method. To generalize the approach, we utilize the ansatz, which is a rational function as different to a polynomial function. In this way, we have more general wave solutions for nonlinear dynamic systems. We apply this method to the ($2+1$)-dimensional conformable Zakharov–Kuznetsov modified equal width (ZK-MEW) equation and the modified regularized long wave (MRLW) equation. Some new solutions are reported. Consequently, we submit the new soliton solutions to the literature.