ALBERT

Description: 〈h3〉Abstract.〈/h3〉 〈p〉We obtained, by using the proper quantization rule, the approximate solutions of the Schrödinger equation with Manning-Rosen plus Hellmann potential for any l-state. Furthermore, thermodynamic properties, such as the vibrational mean 〈em〉U〈/em〉 , specific heat 〈em〉C〈/em〉, free energy 〈em〉F〈/em〉 and entropy 〈em〉S〈/em〉 for the pure vibrational state in the classical limit for these energy eigenvalues, are studied.〈/p〉

Description: 〈h3〉Abstract.〈/h3〉 〈p〉Aiming at the shortcomings of the current fractional-calculus Fourier transform applied to image processing, it is necessary to artificially specify the differential order. This paper proposes an adaptive fractional differential, which can be applied to the aerobics view with higher real-time requirements and image reconstruction occasions. The adaptive fractional differential derivative Fourier transform selection can represent the fractal dimension of texture detail complexity as a parameter adaptive method to determine the order of the differential, but the commonly used fractional box dimension calculation method has relatively rough results. Its algorithmic shortcomings and an improved algorithm are proposed to make the fractal dimension obtained by the improved algorithm more accurate. An image reconstruction application based on the improved adaptive-tensor small-frame sparse-regularization algorithm was developed, which verified that feature matching can be performed with corner points. Experiments show that the improved fractal-based adaptive fractional-order differential Fourier transform constructed in this paper has better experimental results than the integer-order differential in edge detection and reconstruction of aerobics view images.〈/p〉

Description: 〈h3〉Abstract.〈/h3〉 〈p〉In the present paper, we establish a remarkable connection between the length of the periodic orbit of a classical particle enclosed in a class of 2-dimensional planar billiards and the energy of a quantum particle confined to move in an identical region with infinitely high potential wall on the boundary. We observe that the quantum energy spectrum of the particle is in exact one-to-one correspondence with the spectrum of the amplitude squares of the periodic orbits of a classical particle for the class of integrable billiards considered. We have established the results by geometric constructions and exploiting the method of reflective tiling and folding of classical trajectories. We have further extended the method to 3-dimensional billiards, for which exact analytical results are scarcely available --exploiting the geometric construction, we determine the exact energy spectra of two new tetrahedral domains which we believe are integrable. We test the veracity of our results by comparing them with numerical results.〈/p〉

Description: 〈h3〉Abstract.〈/h3〉 〈p〉A Bohmian analysis of the so-called Schrödinger-Langevin or Kostin nonlinear differential equation is provided to study how thermal fluctuations of the environment affects the dynamics of the wave packet from a quantum hydrodynamical point of view. In this way, after obtaining the Schrödinger-Langevin-Bohm equation from the Kostin equation its application to simple but physically insightful systems such as the Brownian-Bohmian motion, motion in a gravity field and transmission through a parabolic repeller is studied. If a time-dependent Gaussian ansatz for the probability density is assumed, the effect of thermal fluctuations together with thermal wave packets leads to Bohmian stochastic trajectories. From this trajectory based analysis, quantum and classical diffusion coefficients for free particles, thermal arrival times for a linear potential and transmission probabilities and characteristic times, such as arrival and dwell times for a parabolic repeller, are then presented and discussed.〈/p〉

Description: 〈h3〉Abstract.〈/h3〉 〈p〉In this work, we study an implicit numerical scheme for a class of multi-term time-fractional diffusion equation, where the fractional derivatives are described in the Caputo sense. The numerical scheme is constructed based on Crank-Nicolson finite difference method in time and exponential B-spline method in space. It is proved that the proposed scheme is unconditionally stable and convergent with second-order in space and (2 - 〈span〉 〈span〉\( \gamma\)〈/span〉 〈/span〉) order in time. To illustrate the efficiency and accuracy of the present method, few numerical examples are presented and are compared with the other existing methods. Numerical results are presented to support theoretical analysis.〈/p〉

Description: 〈h3〉Abstract.〈/h3〉 〈p〉Graphene is one of the thinnest and hardest elastic nanoscale materials and has opened new horizons in the field of material science for its versatile applications. The thermophoretic motion system is under investigation which describes the propagation of solitons in substrate-supported graphene sheets. A test function of the extended three-soliton method is used to construct the new soliton solutions. The one-order and mixed-order solutions involving solitons and lump waves are constructed. The dynamical behaviour of solitons under reflection, periodic distribution and interaction is depicted. Moreover, the bright and mixed type lump wave soliton propagation and interaction are discussed.〈/p〉

Description: 〈h3〉Abstract.〈/h3〉 〈p〉In this article, the vibration characteristics of high-speed rotating graphene-nanoplatelets (GNP)-reinforced composite cylindrical nanoshell coupled with a piezoelectric actuator (PIAC) are investigated. This composite nanostructure rotates around the axial direction, and the Coriolis and centrifugal effects are considered in the formulation. The material properties of piecewise graphene-reinforced composites (GNPRCs) are assumed to be graded in the thickness direction of the cylindrical nanoshell and estimated through a nanomechanical model. In the current study, the effects of angular velocity, piezoelectric layer, GNPRC and size-effects on the frequency of the spinning GNPRC cylindrical nanoshell coupled with PIAC are studied for the first time. The governing equations and boundary conditions are developed using the minimum potential energy and solved with the aid of generalized differential quadrature (GDQM). In addition, due to existence of piezoelectric layer, Maxwell’s equation is derived. The results show that angular velocity, piezoelectric layer, GNP distribution pattern, length scale parameter and GNP weight function play an important role in the vibrational characteristics of the spinning GNP cylindrical nanoshell coupled with PIAC. The results of the current study are useful for design of materials science, micro-electro-mechanical systems and nanoelectromechanical systems such as nanoactuators and nanosensors.〈/p〉

Description: 〈h3〉Abstract.〈/h3〉 〈p〉The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1 - 〈em〉q〈/em〉) is assumed to be very tiny, is adopted for the limit of large particle number for most normal systems. In this case, Tsallis entropy can be expanded as a function of energy and particle number fluctuation, and thus the power-law forms of the generalized Gibbs distribution and grand canonical distribution can be derived. These new distribution functions can be applied to derive the free energy and grand thermodynamic potential in nonextensive thermodynamics. In order to establish appropriate nonextensive thermodynamic formalism, the dual thermodynamic interpretations are necessary for thermodynamic relations and thermodynamic quantities. By using a new technique of parameter transformation, the single-particle distribution can be deduced from the power-law Gibbs distribution. This technique produces a link between the statistical ensemble and the quasi-independent system with two kinds of nonextensive parameter having quite different physical explanations. Furthermore, the technique is used to construct nonextensive quantum statistics and effectively to avoid the factorization difficulty in the power-law grand canonical distribution.〈/p〉

Description: 〈h3〉Abstract.〈/h3〉 〈p〉A Dy〈sub〉0.5〈/sub〉(Sr〈sub〉0.95〈/sub〉Ca〈sub〉0.05〈/sub〉)〈sub〉0.5〈/sub〉MnO〈sub〉3〈/sub〉 system has been prepared by the sol gel method and sintered at temperatures of 700 〈sup〉°〈/sup〉〈em〉C〈/em〉 and 1350 〈sup〉°〈/sup〉〈em〉C〈/em〉 for a similar period of time. Its electrical and dielectrical data as a function of frequency and temperature have been recorded by means of impedance spectroscopy. It is observed that the contribution of grain boundary to total resistance becomes dominant once increasing sintering temperature. The increase of sintering temperature increases the static dielectric constant by 25 times. Such interesting result is understood in the framework of many reasons including the presence of oxygen vacancies. Unlike sample sintered at 700 〈sup〉°〈/sup〉〈em〉C〈/em〉 , the compound sintered at 1350 〈sup〉°〈/sup〉〈em〉C〈/em〉 reveals two extra relaxation processes. Further, the sample sintered at 1350 〈sup〉°〈/sup〉〈em〉C〈/em〉 possesses the higher value of the dielectric constant as well as a lower value of the loss tangent, which makes it a promising candidate for technological applications. For transport properties, the conduction process is found to be governed by the band gap model.〈/p〉

Description: 〈h3〉Abstract.〈/h3〉 〈p〉Theoretical perspective discussions about negatively charged graphene slabs and their radiation properties are presented. It is shown that additional electrons in graphene, injected in a charging process, can enhance the value of the total cross section of photon radiation interactions, especially for X-rays and lower energies. A detailed discussion about the photoelectric effect on electrons trapped in quantum wells in graphene supplements the investigations on light carbon radiation shields. It is concluded that hundreds of parallel graphene slabs would give a significant contribution to modern radiation protection.〈/p〉