In recent decades the effects of magnetic and electric fields on living cells and organisms have gained the increasedattention of researchers. In recent years, dielectrophoresis based microfluidics systems have been used to manipulatebiological micro particles, such as red blood cells, white blood cells, platelets, cancer cells, bacteria, yeast, microorganisms, proteins, DNA, etc. So most previous researchers have studied particle trajectory under theapplication of electric field in order to better design of such micro devices. In the current study the effect of nonuniformelectric field on a single cell is investigated. A neutral particle polarizes in the presence of electric field. It causes localchange in electrostatic potential distribution and local nonuniformity in electric field. These changes are ignored inprevious researches and effective dipole moment (EDM) approximation is applied to predict the DEP force exerted oncells. In the present research the effect of cell on electrostatic potential distribution and electric STRESSes acting on cellsurface is studied. To this end, the cell shape and internal boundary conditions on cell surface must be considered incomputational domain. To do this, Immersed Interface Method (IIM) which is a modified finite difference method isemployed. Some numerical results are presented to show the good accuracy of mentioned numerical method. Theelectric STRESSes on cell surface are calculated by MAXWELL STRESS TENSOR (MST). Also some results are presented tovalidate the numerical solution and investigate the accuracy of EDM approximation. Other electrokinetic effects suchas electrophoresis and electro-osmosis are neglected in this study.

This paper investigates damping ratio in micro-beam resonators based on magneto-thermo-elasticity. A unique aspect of the present study is the effect of permanent magnetic field on the stiffness and thermo-elastic damping of the micro resonators. In our modeling the theory of thermo-elasticity with interacting of an externally applied permanent magnetic field is taken into account. Combined theoretical and numerical studies investigate the permanent magnetic field effect on the damping ratio in clamped-clamped and cantilever micro-beams. Furthermore, the influence of the magnetic field intensity on the frequency of the micro-beams with thermo-elastic damping effect is evaluated. Such evaluations are used to determine the influence of magnetic field on the vibration amplitude of the resonators. The meaningful conclusion is that the magnetic field increases the equivalent stiffness and thermo-elastic damping and consequently the energy consumption of the resonators.

Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction method specifically formulated to deal with TENSOR data. Precisely, the goal of MDA  is to find mode-specific projections that optimally separate TENSOR data from different classes. However, to solve this task, standard MDA methods use alternating optimization heuristics involving the computation of a succession of TENSOR-matrix products. Such approaches are most of the time difficult to solve and not natural, highligthing the difficulty to formulate this problem in fully TENSOR form. In this paper, we propose to solve multilinear discriminant analysis (MDA) by using the concept of transform domain (TD) recently proposed in [15]. We show here that moving MDA to this specific transform domain make its resolution easier and more natural. More precisely, each frontal face of the transformed TENSOR is processed independently to build a separate optimization sub-problems easier to solve. Next, the obtained solutions are converted into projective TENSORs by inverse transform. By considering a large number of experiments, we show the effectiveness of our approach with respect to existing MDA methods.

The governing equations of three dimensional elasticity problems include the six Beltrami– Michell STRESS compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usually used to achieve a solution. STRESS-based formulation methods, and displacement-based formulation methods are two common simplified methods for solving elasticity problems. This work adopts a STRESS-based formulation for a three dimensional elasticity problem. In this work, the MAXWELL’ s STRESS functions for solving three dimensional problems of elasticity theory are derived from fundamental principles. It is shown that the three MAXWELL STRESS functions identically satisfy all the three differential equations of static equilibrium when body force components are ignored. It is further shown that the three MAXWELL STRESS functions are solutions to the six Beltrami-Michell STRESS compatibility equations if the MAXWELL STRESS functions are potential functions. It is also shown that the Airy’ s STRESS functions for two dimensional elasticity problems are special cases of the MAXWELL STRESS functions.

The MAXWELL-Dagum distribution is a continuous statistical distribution suitable for modeling data sets relating to various fields including finance, business, medical sciences, survival analysis, and related areas. This article aimed to propose some important properties of the MAXWELL-Dagum distribution and obtained the parameters of its estimates by using different methods of estimation including maximum likelihood estimation, the maximum product of spacings, least squares estimation, and weighted least squares estimation. The first and second derivatives of this distribution are studied. We present two real data sets relating to the COVID-19 mortality rate belonging to Canada and the waiting time of bank customers to assess the performance of the proposed distribution. It is discovered that the MAXWELL-Dagum distribution can be chosen as the best distribution by having a minimum value of Akaike information and Bayesian information criteria.

The main goal of this research was to evaluate the STRESS produced in tooth, PDM, spongy bone, and cortical bone consequent to force application (1 N) to the crown of an upper central incisor, while the alveolar bone resorbs gradually. Four 3-dimensional FEM models were designed (ARGue 392-5) with the same form except for their alveolar bone support that represented 1, 2.5, 5, and 6.5 mm of reduction. All the output data were compared with a normal model (ARGue 391). Normal STRESS in palato-labial direction (dY) and two shearing STRESSes (Tyz, Tyx) were evaluated. A progressive increase in all STRESS forms were found in all of the involved tissues in gradual steps of alveolar bone loss. Based upon this study, 2.5 mm of alveolar bone loss can be considered as the limit beyond which the normal STRESS changes accelerate. This limit is 5 mm for the shearing STRESSes. There were some clinical suggestions on the manner of force application and the appliance selection, based on the findings of this study, in the article.

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discussed by the authors. We introduce a new class of geometric vector fields and prove some basic facts about them. We call these vector fields affinewise. By contraction of the symmetric curvature, we define two new curvatures which have direct relations to the notions of divergence, Laplacian, and the Ricci TENSOR.

Observation and numerical documents have shown that the protoplanetary discs (PPDs) around the young stellar objects (YSOs) are gravitationally unstable. The self-gravity can be important in PPDs. The gravitational instability and outflow (mass-loss) are dominant mechanisms for transporting outward angular momentum and inward accretion in the disc cold mid-plane. The structure of the self-gravitating accretion discs depends strongly on the rate at which it cools. In this paper, we have studied the hydrodynamical equations in the presence of component of the viscous STRESS TENSOR (t_θφ) in the spherical coordinates (r,θ,φ) by using the semi- analytical self- similar solutions in the steady state and axisymmetric assumptions. This component of the viscous STRESS TENSOR is related to the transport outward of angular momentum by outflows. The solutions indicate that the disc is gravitationally instable. The gravitational instability as a viscose source leads to heat the disc. Our results have shown the toomre parameter (Q) decreases by increasing the cooling rate because the heating supplied by gravitational instability is not enough to counteract cooling and so the disk will fragment and produce planets. The results have shown that t_θφ makes the disc colder, and thinner and outflows form in the regions with lower latitudes. We have shown that the effect of t_θφ in the mid-plane of the disc is more effective than t_rφ (turbulent viscosity).