Restricted Three-Body Problem Under the Effect of Albedo When Smaller Primary is a Finite Straight Segment

This paper addresses the dynamics of the infinitesimal body in the restricted three-body problem under the effect of Albedo when the smaller primary is a finite straight segment and bigger one is a source of radiation. The measure of diffusive reflection of solar radiation out of the total solar radiation received by a body is Albedo which is measured on a scale from 0 to 1. The equations of motion of the infinitesimal body are derived and it is found that there exist five libration points, out of which three are collinear and the rest are non-collinear with the primaries. All the collinear libration points are found to be unstable while the non-collinear libration points are stable for a critical value of the mass parameter. The perturbation of libration points and its stability due to the effect of Albedo and straight segment in the present problem are investigated. Further, it is found that the effect of Jacobian constant, length of the straight segment and Albedo parameter has a substantial influence on the possible regions of motion of the infinitesimal body. It is observed that when the value of the Jacobian constant decreases, the region of possible motion increases. When the length of the straight segment increases, the region of possible motion increases. Further, it is observed that as we increase the Albedo parameter, the region of possible motion decreases

A Study of Small Perturbations in the Coriolis and Centrifugal Forces in RR3BP with Finite Straight Segment

In this paper, the effect of small perturbations in the Coriolis and centrifugal forces on the existence and stability of the equilibrium point in the Robe’s restricted three-body problem (RR3BP) by taking the smaller primary as a finite straight segment is introduced. In the present structure the density rho1 of the fluid filled in the bigger primary of mass m1*and the density rho3 of the infinitesimal body of mass m3 are considered to be equal. It is worth mentioning that the location of the equilibrium point is affected by a small perturbation in the centrifugal force. The present model possesses one equilibrium point L1 which is collinear with the center of mass of the primaries. It lies towards the right or left of the center of the shell according as the perturbation pi2 in the centrifugal force is positive or negative. Further, the stability of L1 is analyzed. The range of stability is affected not only by the perturbations in the Coriolis and centrifugal forces but also by the length of the finite straight segment. For 0 \u3c mu less than or equal to mu*, L1 is unstable whereas for mu* \u3c mu \u3c 1 it becomes stable. It is observed that the Coriolis force is a stabilizing force provided the centrifugal force is kept constant while the centrifugal force is a destabilizing force when the Coriolis force is kept constant

Outcomes of Aspheric Primaries in Robe’s Circular Restricted Three-body Problem

We consider the Robe’s restricted three-body problem in which the bigger primary is assumed to be a hydrostatic equilibrium figure as an oblate spheroid filled with a homogeneous incompressible fluid, around which a circular motion is described by the second primary, that is a finite straight segment. The aim of this note is to investigate the effect of oblateness and length parameters on the motion of an infinitesimal body that lies inside the bigger primary. The locations of the equilibrium points are approximated by the series expansions and it is found that two collinear equilibrium points lying on the line segment joining the centers of the primaries, exist. The non- collinear equilibrium points lie on a circle and are infinite in number. No out-of-plane equilibrium point exists. Based on the linear stability analysis, it is observed that the collinear equilibrium points can be stable under certain conditions whereas the non-collinear ones are always unstable

Stability Analysis of Circular Robe’s R3BP with Finite Straight Segment and Viscosity

In this paper, the effect of viscous force on the linear stability of equilibrium points of the circular Robe’s restricted three-body problem (CRR3BP) with smaller primary as a finite straight segment is studied. The present model comprises of a bigger primary m*1 which is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ1 and the smaller primary m2 lies outside the shell. The infinitesimal mass m3 is a small solid sphere of density ρ3 moving inside m*1. The pertinent equations of motion of m3 are derived and solved for the equilibrium points. Routh-Hurwitz criterion is used to detect the stability of the obtained equilibrium points. The stability of the collinear equilibrium points has been studied systematically in the different regions for the various values of the parameters involved. These points are found to be conditionally stable, whereas the non-collinear and out-of-plane equilibrium points are always unstable for all the values of the parameters. We observed that viscosity has no effect on the location of equilibrium points. However, its effect along with the length parameter l is evident on the stability of equilibrium points

Physical-Mathematical modeling and numerical simulations of stress-strain state in seismic and volcanic regions

The strain-stress state generated by faulting or cracking and influenced by the strong heterogeneity of the internal earth structure precedes and accompanies volcanic and seismic activity. Particularly, volcanic eruptions are the culmination of long and complex geophysical processes and physical processes which involve the generation of magmas in the mantle or in the lower crust, its ascent to shallower levels, its storage and differentiation in shallow crustal chambers, and, finally, its eruption at the Earth’s surface. Instead, earthquakes are a frictional stick-slip instability arising along pre-existing faults within the brittle crust of the Earth. Long-term tectonic plate motion causes stress to accumulate around faults until the frictional strength of the fault is exceeded. The study of these processes has been traditionally carried out through different geological disciplines, such as petrology, structural geology, geochemistry or sedimentology. Nevertheless, during the last two decades, the development of physical of earth as well as the introduction of new powerful numerical techniques has progressively converted geophysics into a multidisciplinary science. Nowadays, scientists with very different background and expertises such as geologist, physicists, chemists, mathematicians and engineers work on geophysics. As any multidisciplinary field, it has been largely benefited from these collaborations. The different ways and procedures to face the study of volcanic and seismic phenomena do not exclude each other and should be regarded as complementary. Nowadays, numerical modeling in volcanology covers different pre-eruptive, eruptive and post-eruptive aspects of the general volcanic phenomena. Among these aspects, the pre-eruptive process, linked to the continuous monitoring, is of special interest because it contributes to evaluate the volcanic risk and it is crucial for hazard assessment, eruption prediction and risk mitigation at volcanic unrest. large faults. The knowledge of the actual activity state of these sites is not only an academic topic but it has crucial importance in terms of public security and eruption and earthquake forecast. However, numerical simulation of volcanic and seismic processes have been traditionally developed introducing several simplifications: homogeneous half-space, flat topography and elastic rheology. These simplified assumptions disregards effects caused by topography, presence of medium heterogeneity and anelastic rheology, while they could play an important role in Moreover, frictional sliding of a earthquake generates seismic waves that travel through the earth, causing major damage in places nearby to the modeling procedure This thesis presents mathematical modeling and numerical simulations of volcanic and seismic processes. The subject of major interest has been concerned on the developing of mathematical formulations to describe seismic and volcanic process. The interpretation of geophysical parameters requires numerical models and algorithms to define the optimal source parameters which justify observed variations. In this work we use the finite element method that allows the definition of real topography into the computational domain, medium heterogeneity inferred from seismic tomography study and the use of complex rheologies. Numerical forward method have been applied to obtain solutions of ground deformation expected during volcanic unrest and post-seismic phases, and an automated procedure for geodetic data inversion was proposed for evaluating slip distribution along surface rupture

REGULATORY GUIDELINES FOR APPROVAL OF BIOSIMILARS IN INDIA, EUROPE, BRAZIL AND CHINA: A COMPREHENSIVE OVERVIEW

A biosimilar is a biological medicinal product that contains a version of the active substance of an already authorized original biological medicinal product (reference medicinal product). A biosimilar demonstrates similarity to the reference biological product in terms of quality characteristics, biological activity, safety and efficacy based on a comprehensive comparability exercise. EMA (European Medicines Agency) was the first to introduce the guidelines for biosimilar approval, effective from June 2006. Biosimilar guideline was released in 2010 in Brazil and 2012 in India. Recently China published its guideline for biosimilar approval in 2015.This article summarizes the regulatory requirements for approval of biosimilars in India, Europe, Brazil, and China. These countries require comparability exercise of a biosimilar with reference biological product for generating comparative analytical, non-clinical and clinical data (usually one or two phase 1 and phase 3 comparative studies). A case study of infliximab biosimilar approval in India, Brazil and Europe has also been included