Narrow Results

In this paper, we investigated new solutions for the anisotropic compact stellar model in Einstein–Gauss–Bonnet (EGB) theory. In this context, we established a set of field equations with the help of anisotropic matter configuration. The relation between pressure in the radial direction and the energy density is taken by using a linear equation of state (EoS). A well-known Boulware–Deser exterior spacetime is matched with interior spherically symmetric spacetime at the boundary of the star to determine the unknown parameters. Different physical parameters are investigated, namely, these are density, radial pressure and transversal pressure, anisotropy, mass function, compactness and surface redshift. We discussed Herrera’s cracking condition, Tolman–Oppenheimer–Volkoff (TOV), and the adiabatic index. The values of some physical quantities like density (at center and surface), compactness and surface redshift are calculated numerically for three compact stars PSR J0348+0432, PSR J0740+6620 and PSR J0030+0451. A graphical analysis of these physical quantities for a representative compact star candidate PSR J0348+0432 is also presented with various values of EGB parameter $\alpha$. The energy conditions for anisotropic compact star PSR J0348+0432 are satisfied, surface redshift remains within the limit and also all the stability conditions that we discussed in this work are satisfied, this validates our presented model. The effects of the GB coupling parameter $\alpha$ on the physical parameters are depicted graphically and numerically.

The six quark state(uuddss) called H dibaryon(J^P = 0⁺,S = -2) has been calculated to study its existence and stability. The simulations are performed in quenched QCD on 8³ × 24 and 16³ × 48 anisotropic lattices with Symanzik improved gauge action and Clover fermion action. The gauge coupling is β = 2.0 and aspect ratio ξ = a_s/a_t = 3.0. Preliminary results indicate that mass of H dibaryon is 2134(100)Mev on 8³ × 24 lattice and 2167(59)Mev on 16³ × 48 respectively. It seems that the radius of H dibaryon is very large and the finite size effect is very obvious.

The electromagnetic field in an anisotropic and inhomogeneous magnetodielectric medium is quantized by modelling the medium with two independent quantum fields. Maxwell and constitutive equations of the medium are obtained using a minimal coupling scheme. The electric and magnetic susceptibility tensors of the medium are calculated. Finally the efficiency of the approach is elucidated by some examples.

Since the discovery of accelerated expansion of the universe, it was necessary to introduce a new component of matter distribution called dark energy. The standard cosmological model considers isotropy of the pressure and assumes an equation of state p = ωρ, relating the pressure p and the energy density ρ. The interval of the parameter ω defines the kind of matter of the universe, related to the fulfillment, or not, of the energy conditions of the fluid. The recent interest in this kind of fluid with anisotropic pressure, in the scenario of the gravitational collapse and star formation, imposes a careful analysis of the energy conditions and the role of the components of the pressure. Here, in this work, we show an example where the classification of dark energy for isotropic pressure fluids is used incorrectly for anisotropic fluids. The correct classification and its consequences are presented.

The cosmological behavior is investigated for ten-dimensional scalar–tensor theory with matter. The matter is taken as an anisotropic fluid. As a simple ansatz, the anisotropic fluid for each four and six dimensions satisfies the same type of the equation of state with different coefficients, p_x,y = γ_x,yρ. Following the ansatz of the anisotropic matter, the spacetime then has a product structure which means that the spacetime is decomposed as four-dimensional spacetime (M_x) and six-dimensional transverse space (M_y). We focus on the solution such that the scale factors in each four and six dimensions behave differently. The corresponding cosmological solutions are obtained for general γ_x,y. By giving specific numeric values for the coefficients of the equation of state γ_x,y, we find the solution which behaves in such a way that the spatial three dimensions are expanding while the extra six dimensions are contracting.

We consider the effect of matter in the anisotropic universe of the scalar–tensor theory. We study Brans–Dicke model as a scalar–tensor theory. The matter is treated as perfect fluid type one. Just as the spacetime is anisotropic, the matter is also considered to be anisotropic. In order to give the present universe which is isotropic, the spacetime should be filled with the particular type of matter.

Locally Rotationally Symmetric (LRS) Bianchi type-I metric is examined in the presence of perfect fluid. Exact solutions of Einstein’s field equations (EFE) have been studied by taking into account a hyperbolic scale factor. We observed that the model has initial singularity. It is found that the Universe approaches isotropy at late times. Through state finder pair $\{r,s\}$, it is observed that at late cosmic time, the model behaves analogous to $\mathrm{\Lambda }$CDM model. Energy conditions of the model are studied and it is found that null energy condition (NEC), weak energy condition (WEC) and dominant energy conditions (DEC) are satisfied for our model while SEC is violated. We investigate some physically and geometrically realistic models in order to develop a viable cosmological model.

It is shown that in a single-axis antiferromagnetic semiconductor placed in a strong magnetic field, dispersionless magnons start emitting at any arbitrarily small velocity of an electron occurring in a spinpolaron state. If magnons are dispersed they are generated when the spinpolaron velocity exceeds the minimum phase velocity of magnons. The maximum power of magnon generation caused by the drift of spinpolarons is estimated.

This paper presents the results of a study on the production of nanofiber anisotropic nanoporous materials based on silk fibroin and cotton cellulose by electrospinning using a rotating screen-receiver of nanofibers in the form of a thin material. The difference in the anisotropic properties of the nanofiber material is shown by the method of birefringence, sorption of water vapor and filtration of a liquid-phase mixture. The possibility of using nanofiber nanoporous fibroin and cotton cellulose materials as a nanofilter of gaseous and liquid-phase mixtures has been shown.

In this paper, we study the two-body problem that describes the motion of two-point masses in an anisotropic space under the influence of a Newtonian force-law with two relativistic correction terms. We will show that the set of initial conditions leading to collisions and ejections and leading to escapes and captures have positive measure. Using the infinity manifold, we study capture and escape solutions in the zero-energy case. We also show that the flow on the zero energy manifold of a two-body problem given by the sum of the Newtonian potential and three anisotropic perturbations (corresponding to three relativistic correction terms) is chaotic.

This paper deals with an analysis of a nonlinear monotone conduction problem posed on a medium which we assume to be anisotropic and periodically reinforced by thin fibers also assumed to be anisotropic. We consider the case where the conductivity in the fibers are more important than in the material which surrounds it so that the operator we have to consider loses his uniform ellipticity with respect to the size ε of the period; we then investigate the effect of the anisotropy in the homogenization process.

Models with a vanishing anisotropic viscosity in the vertical direction are of relevance for the study of turbulent flows in geophysics. This motivates us to study the two-dimensional Boussinesq system with horizontal viscosity in only one equation. In this paper, we focus on the global existence issue for possibly large initial data. We first examine the case where the Navier–Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transport–diffusion equation with diffusion in the horizontal direction only. For both systems, we construct global weak solutions à la Leray and strong unique solutions for more regular data. Our results rest on the fact that the diffusion acts perpendicularly to the buoyancy force.

The effect of anisotropic surface tension on the growth of columnar crystals in ternary melt is studied, and the approximate analytical solution of the growth morphology of columnar crystals is given. It is found that in the initial stage of growth, some parts of the interface grow outward, while some parts first grow inward, and grow outward together with other parts after reaching a certain depth, which makes the columnar crystal interface form a remarkable concave and convex formation. Compared with the case in the pure melt and ternary alloy melt, the component added in the ternary alloy melt decreases the effect of the anisotropic surface tension.

In this paper, we will present an approach to constructing of dynamical spatial Green’s function (elementary solutions, dominant function) for a thin infinite elastic plate of constant thickness. The plate material is anisotropic with a single plane of symmetry, geometrically coinciding with plate’s middle plane. The Timoshenko theory was used for describing the plate movement. Transient spatial Green’s functions for normal displacements and angles of orthogonal alteration to middle surface before deformation of material fiber are built in the Cartesian coordinate system.

To construct Green’s function, direct and inverse Laplace and Fourier integral transformations are applied. The originals of Laplace Green’s functions were analytically found with the theorem of residues. To construct Fourier originals, a specific method was used based on Fourier series transformation inversion integral connection with Fourier series on a variable interval.

Green’s function found for normal displacement made it possible to represent the normal transient function as three-fold convolution of Green function with distant load function. The functions of normal distant displacements were constructed in case of the impact of transient total loads concentrated and distributed across rectangular courts. The numerical method of rectangles was used to calculate the convolution integrals. The influence of the concentrated load speed on transient normal displacements of the anisotropic plate was analyzed.

As a verification of constructed transient spatial Green’s functions, the results of numerical solutions were compared with the results found using known transient Green’s functions for isotropic thin elastic rectangular simply supported Timoshenko’s plate which solutions are constructed using Laplace integral transformation in time and its decomposition into Fourier series on coordinates. Besides, its confidence was proved analyzing the nature of waves in anisotropic, orthotropic and isotropic plate, found in the process of numerical calculations. The results are represented as diagrams. Examples of calculations are given.

Fatigue failure of anisotropic structure of the artificial articular has been implicated in a number of clinical failure scenarios, especially the fatigue behaviour of the articular surface is poorly understood, At the same time, there is no established design and procedure, which is applicable to all load-bearing implants. However, materials degradation significantly may also be increased the life of sample by reducing the peak stresses and redistributing the load to the surrounding tissue. This paper presents the effect of the structural integrity of the shape and stresses distribution on the global material behaviour of articular cartilage. Then modulus degradation appears to be a result of trabecular fracture rather than as a result of tissue level material degradation. Furthermore, we found that Young's modulus normal to the contact surface increases from the superficial to the deep zone in articular cartilage.

The presentation is mainly devoted to the research on the regularized boundary integral equations (BIEs) with indirect unknowns for torsion problem of the anisotropic uniform bar. Based on a new view and idea, a novel regularization technique is pursued, in which the nonsingular indirect BIE (IBIE) excluding the CPV and HFP integrals is established. Such torsion problems can be solved directly by using the presented technique without transforming them into isotropic ones, for this reason, no inverse transform is required. Moreover, a unique feature of the shear stress BIEs expressed by density functions is that they are independent of the warp BIEs and, as such, can be collocated at the same locations as the warp BIEs. This provides additional and concurrently useable equations for various purposes. Besides, in the numerical implementation, the boundary geometric is depicted by exact elements, while the distribution of the boundary quantity on each element is approximated by a discontinuous quadratic element. Some numerical examples will be applied to validate the current scheme. It is shown that a better precision and high-computational efficiency can be achieved by the presentation.

We propose a novel computational model for the high fidelity prediction of failure mechanisms in brittle polycrystalline materials. A three-dimensional finite element model of the polycrystalline structure is reconstructed to explicitly account for the micro-features such as grain sizes, grain orientations, and grain boundary misorientations. Grain boundaries are explicitly represented by a thin layer of elements with non-zero misorientation angles. In addition, the Eigen-fracture algorithm is employed to predict the crack nucleation and propagation in the grain structure. In the framework of variational fracture mechanics, an equivalent energy release rate is defined at each finite element to evaluate the local failure state by comparing to the critical energy release rate, which varies at the grain boundaries and the interior of grains. Moreover, constitutive models are considered as functions of the local microstructure features. As a result, a direct mesoscale simulation model is developed to resolve the anisotropic response, intergranular and transgranular fractures during the microstructure evolution of brittle materials under general loading conditions. A micromechanics-based interpretation for the rate dependent strength of brittle materials is derived and verified in examples of dynamic compression tests. In specific, the compressive dynamic response of hexagonal SiC with equiaxed grain structures is studied under different strain rates.

Here, we have investigated the interaction of Bianchi type-I anisotropic cloud string cosmological model universe with electromagnetic field in the context of general relativity. In this paper, the energy-momentum tensor is assumed to be the sum of the rest energy density and string tension density with an electromagnetic field. To obtain exact solution of Einstein’s field equations, we take the average scale factor as an integrating function of time. Also, the dynamics and significance of various physical parameters of model are discussed.

This paper is focused on the in/stability of a collapsing anisotropic self-gravitating spherically symmetric compact fluid under the influence of non-minimally coupled f(R, T) gravitational theory, where R and T are traces of Ricci tensor and stress-energy tensor, respectively. We explore the f(R, T) equations of motion as well as conservation equations. We utilize the perturbation technique on dynamical equations, and physical quantities to get the collapse equation in a similar scenario. In the presence of considered f(R, T)-function (i.e. $f(R,T)=R-\zeta R_{c}tanh(\frac{R}{R_c})+\lambda RT$), to explain the dynamical behavior of the considered anisotropic relativistic fluid system. Furthermore, to address the issue of in/stability, the conditions on adiabatic index $\mathrm{\Gamma }$ i.e. stiffness parameter of fluid, are developed for Newtonian $(\mathrm{\text{N}})$-$epoch$ and post-Newtonian ($p\mathrm{\text{N}})$-$epoch$. Several physical constraints are imposed to maintain the un/stable fluid structure.

This paper reviews the current state of conductive adhesive technology. Most work to date has been carried out with isotropically-conductive adhesives which conduct electricity in any direction. In this review, particular attention has been paid to recently-developed anisotropically-conductive adhesives which are electrically conductive along one axis only. Patents filed in this area have been surveyed and the key points relating to the technology employed are summarized. A survey of the market was carried out and is presented. Adhesive processing techniques were studied and reliability issues relating to adhesives in general and to conductive adhesives in particular investigated. Voids in the adhesive leading to reduced adhesion and stress concentration were seen to be an area of concern while the effect of moisture leading to increased joint resistance and reduced strength was concluded to be the key limiting factor in the long-term reliability of conductive adhesives.