Volume 12, Issue 8

An approach to model the Martian magnetization can be done using classical source models. Classical models, such as uniformly magnetized spheres and cylinders, allow for the introduction of additional constraints related to the available information of the magnetic field and its sources. The use of a suitable conservative numerical scheme in Cartesian coordinates was carried out for numerical studies. In this work the motion of different charged particles under the influence of different magnetized sources have been analyzed by using the proposed numerical scheme. For that purpose, electron, proton and alpha particles were used. In addition, the impact of the gravitational effect on the particles motion was also studied.

In this paper we investigate the yield condition in the mobilization of yield-stress materials in distensible tubes. We discuss the two possibilities for modeling the yield-stress materials prior to yield: solid-like materials and highly-viscous fluids and identify the logical consequences of these two approaches on the yield condition. Our results reveal that these two modeling approaches have far reaching consequences on the yield bottleneck and hence should be critically examined in the light of experimental evidence. As part of this investigation we derive an analytical expression for the pressure field inside a distensible tube with a Newtonian flow using a one-dimensional Navier-Stokes flow model in conjunction with a pressurearea constitutive relation based on elastic tube wall characteristics. This analytical expression has wider applicability than in the identification of the yield condition of yield-stress material.

The residual symmetries of the famous modified Korteweg-de Vries (mKdV) equation are researched in this paper. The initial problem on the residual symmetry of the mKdV equation is researched. The residual symmetries for the mKdV equation are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries by means of enlarging the mKdV equations. One-parameter invariant subgroups and the invariant solutions for the extended system are listed. Eight types of similarity solutions and the reduction equations are demonstrated. It is noted that we researched the twofold residual symmetries by means of taking the mKdV equation as an example. Similarity solutions and the reduction equations are demonstrated for the extended mKdV equations related to the twofold residual symmetries.

This paper considers the Rayleigh-Ritz variational calculations with non-orthogonal basis sets that exhibit the correct asymptotic behaviour. This approach is illustrated by constructing suitable basis sets for one-dimensional models such as the two double-well oscillators recently considered by other authors. The rate of convergence of the variational method proves to be considerably greater than the one exhibited by the recently developed orthogonal polynomial projection quantization.

The surface relaxation and the formation of a single vacancy in very thin Cu (001) film formed by 2 ∼ 14 atomic layers have been studied by using MAEAM and MD simulation. For the surface relaxtion, the highest surface energy is in the l = 2 atomic layers. The multilayer relaxation mainly occurs between the first two atomic layers, and the maximum contractive displacement is obtained in the very thin Cu (001) film formed by l = 3 atomic layers. For the vacancy formed in l′ = 1 of the very thin Cu (001) film formed by l = 2 ∼ 14 layers, the most difficult site in the film formed by l = 3 atomic layers.

In this paper we apply a new method of analysis of random behavior of chaotic systems based on the Prony decomposition. The generalized Prony spectrum (GPS) is used for quantitative description of a wide class of random functions when information about their probability distribution function is absent. The scaling properties of the random functions that keep their invariant properties on some range of scales help to fit the compressed function based on the Prony’s decomposition. In paper [1] the first author (RRN) found the physical interpretation of this decomposition that includes the conventional Fourier decomposition as a partial case. It has been proved also that the GPS can be used for detection of quasi-periodic processes that are appeared usually in the repeated or similar measurements. A triple physical pendulum is used as a chaotic system to obtain a chaotic behavior of displacement angles with one, two and three positive Lyapunov’s exponents (LEs). The chaotic behavior of these angles can be expressed in the form of amplitude-frequency response (AFR) that is extracted from the corresponding GPS and can serve as a specific ”fingerprint” characterizing the random behavior of the triple-pendulum system studied. This new quantitative presentation of random data opens additional possibilities in classification of chaotic responses and random behaviors of different complex systems.

This paper presents a negative refractive index tunable metamaterial based on F-Shape structure which is capable of achieving dual-band negative permeability and permittivity, thus dual-band negative refractive index. An electromagnetic simulation was performed and effective media parameters were retrieved. Numerical investigations show clear existence of two frequency bands in which permeability and permittivity both are negative. The two negative refractive index bandwidths are from 23.8 GHz to 24.1 GHz and from 28.3 GHz to 34.9 GHz, respectively. The geometry of the structure is simple so it can easily be fabricated. The proposed structure can be used in multiband and broad band devices, as the band range in second negative refractive index region is 7 GHz, for potential applications instead of using complex geometric structures and easily tuned by varying the separation between the horizontal wires.

We study the isoscalar giant monopole resonance for drip-lines and super heavy nuclei in the framework of relativistic mean field theory with a scaling approach. The well known extended Thomas-Fermi approximation in the nonlinear σ-ω model is used to estimate the giant monopole excitation energy for some selected light spherical nuclei starting from the region of proton to neutron drip-lines. The application is extended to the super heavy region for Z=114 and 120, which are predicted by several models as the next proton magic numbers beyond Z=82. We compared the excitation energy obtained by four successful force parameters NL1, NL3, NL3*, and FSUGold. The monopole energy decreases toward the proton and neutron drip-lines in an isotopic chain for lighter mass nuclei, in contrast to a monotonic decrease for super heavy isotopes. The maximum and minimum monopole excitation energies are obtained for nuclei with minimum and maximum isospin in an isotopic chain, respectively.

We have studied anisotropic and homogeneous Bianchi type-II cosmological model with linear equation of state (EoS) p = αρ−β, where α and β are constants, in General Relativity. In order to obtain the solutions of the field equations we have assumed the geometrical restriction that expansion scalar θ is proportional to shear scalar σ. The geometrical and physical aspects of the model are also studied.

Recent direct observations of localization of mRNAs and proteins both in prokaryotic and eukaryotic cells can be related to slowdown of diffusion of these species due to macromolecular crowding and their ability to aggregate and form immobile or slowly mobile complexes. Here, a generic kinetic model describing both these factors is presented and comprehensively analyzed. Although the model is non-linear, an accurate self-consistent analytical solution of the corresponding reaction-diffusion equation has been constructed, the types of localized protein distributions have been explicitly shown, and the predicted kinetic regimes of gene expression have been classified.