On the 2D Ericksen–Leslie equations with anisotropic energy and external forces

In this paper we consider the 2D Ericksen–Leslie equations which describe the hydrodynamics of nematic liquid crystal with external body forces and anisotropic energy modeling the energy of applied external control such as magnetic or electric field. Under general assumptions on the initial data, the external data and the anisotropic energy, we prove the existence and uniqueness of global weak solutions with finitely many singular times. If the initial data and the external forces are sufficiently small, then we establish that the global weak solution does not have any singular times and is regular as long as the data are regular.

Neutral physical compact spherically symmetric stars with non-exotic matters in Einstein’s cluster model using Weitzenböck geometry

We revisit the neutral (uncharged) solutions that describe Einstein’s clusters with matters in the frame of Weitzenböck geometry. To this end, we use a tetrad field with non-diagonal spherical symmetry which gives vanishing of the off-diagonal components of the gravitational field equations. The cluster solutions are calculated by using an anisotropic energy–momentum tensor. We solve the field equations using two novel assumptions. First, we use an equation of state that relates density with tangential pressure, and then we assume a specific form of one of the metric potentials in addition to the assumption of the vanishing of radial pressure to make the system of differential equations in a closed-form. The resulting solutions are coincide with the literature $$ however \, \,in\, \,this\, \,study\, \,we\, \,constrain\,\, the\,\, constants \, \,of\, \, integration\, \, from\, \, \,the\, \, matching\,\, of\, \,boundary $$ h o w e v e r i n t h i s s t u d y w e c o n s t r a i n t h e c o n s t a n t s o f i n t e g r a t i o n f r o m t h e m a t c h i n g o f b o u n d a r y $$ condition\, \, in a\,\, way \,\,different\,\, from\,\, that\,\, presented \,\,in \,\,the\,\, literature. $$ c o n d i t i o n i n a w a y d i f f e r e n t f r o m t h a t p r e s e n t e d i n t h e l i t e r a t u r e . Among many things presented in this study, we investigate the static stability specification and show that our model is consistent with a real compact start except that the tangential pressure has a vanishing value at the center of the star which is not accepted from the physical viewpoint of a real compact star. We conclude that the model that has vanishing radial pressure in the frame of Einstein’s theory is not a physical model. Therefore, we extend this study and derive a new compact star without assuming the vanishing of the redial pressure but instead we assume new form of the metric potentials. We repeat our procedure done in the case of vanishing radial pressure and show in details that the new compact star is more realistic from different physical viewpoints of real compact stellar.

The influence of fibre alignment on the fracture toughness of anisotropic soft tissue

Finite element (FE) simulations are performed to investigate the effect of fiber induced anisotropy on the notch behavior in hyperelastic skin type materials. The modified anisotropic (MA) model is used to define the constitutive behavior in FE simulations through Abaqus user defined material model UMAT. A parametric study is carried out to examine the effect of fiber orientation, notch root radius and sample geometry on the stress field ahead of the notch tip. A non-dimensional parameter is defined to characterize the combined effect of J energy and average anisotropic energy on the notch behavior. It is shown that fibre orientation significantly influences the stress state and J-integral at the notch. The findings of the present study will be helpful in determining optimal constitution and orientation of skin grafts at locations of high stress and complex geometries, such as corner of eyes and lips etc.

Measurement of turbulence properties

The aim of the research is to investigate anisotropic turbulence intensities, id est to investigate the distribution of Reynolds stresses and energy spectra in a square cross-section channel, downstream of a semi-active jet turbulence grid generating anisotropic turbulent airflow. In addition to the semi-active jet turbulence grid, another type of turbulence grid was developed and experimentally investigated. This grid contains vertical, flexible strips of aluminum (in this case, there are no perpendicular (horizontal) grid elements), which vibrate at a frequency depending on the velocity of the main airflow. Besides the investigation of the velocity- and turbulence intensity distributions, another main objective of the research is to measure the von Kármán energy spectrum when the turbulence cannot be considered isotropic. This aspiration of ours is justified by the knowledge gap present in the literature in this specific field. Monin has carried out a theoretical study to extend and generalize the von Kármán – Howarth isotropic principal stress equation to the anisotropic regime. The proposed new experimental work aims to provide a solid experimental background for verifying and validating the physical correctness of the Monin equation, which may result in a new theoretical understanding and perception of the major issues and the nature of anisotropic turbulence. Since the anisotropic energy spectra are expected to exhibit different characteristics from the isotropic Kolmogorov spectra, these new experimental results may contribute to the development of new anisotropic and engineering turbulence models that can be used in industrial applications.