A study of thin domain wall with spherical symmetry

It is known that for a thin domain wall the pressure in the perpendicular direction to the wall is negligible. In this paper, we have evaluated solutions for thin domain walls with spherical symmetry following two different approaches. The exact solutions are obtained using functional separability of the metric coefficients. This revised version was published online in July 2006 with corrections to the Cover Date.     

On Plane Symmetric Domain Walls and Cosmic Strings in Bimetric Theory

Plane symmetric thick domain walls and cosmic strings are considered in Rosen's (General Relativity and Gravitation 4, 435, 1973) bimetric theory of gravitation. It is shown that, in this theory, thick domain walls and cosmic strings do not exist. Hence, the vacuum solutions in both the cases are presented. PACS No.:98.80     

Gravitational Field of Domain Walls in Higher Dimension

In this paper, we study the gravitational field of domain wall in fivedimensional space-time. Exact solutions of Einstein's equations for a scalarfield with a potential V(Ø) are presented, describing thegravitational field of plane symmetric domain walls. The solution showsthat the energy density as well as pressure in the perpendicular directionon both sides of the walls to be reflection symmetric with respect to thewalls.PACS numbers: 98.80 cq, 0450     

Higher dimensional domain wall in Lyra geometry

Thick domain walls with time dependent displacement vector based on Lyra's geometry are considered. Their exact solutions are obtained in the background of a five-dimensional space time. The field theoretic energy-momentum tensor is considered assuming with $$T_t^t = T_x^x = T_y^y = T_\psi ^\psi .$$ Acceleration due to the domain wall has been evaluated by studyinggeodesic equation.     

Thin Domain Walls in Lyra Geometry

This paper studies thin domain walls within the frame work of Lyra Geometry. We have considered two models. First one is the thin domain wall with negligible pressures perpendicular and transverse direction to the wall and secondly, we take a particular type of thin domain wall where the pressure in the perpendicular direction is negligible but transverse pressures are existed. It is shown that the thin domain walls have no particle horizon and the gravitational force due to them is attractive.     

Chemically reacting flow of a compressible thermally radiating two-component plasma

The paper studies the compressible flow of a hot two-component plasma in the presence of gravitation and chemical reaction in a vertical channel. For the optically thick gas approximation, closed form analytical solutions are possible. Asymptotic solutions are also obtained for the general differential approximation when the temperatures of the two bounding walls are the same. In the general case the problem is reduced to the solution of standard nonlinear integral equations which can be tackled by iterative precedure. The results are discussed quantitatively. The problem may be applicable to the understanding of explosive hydrogen-burning model of solar flares.     

Primordial black holes from monopoles connected by strings

Primordial black holes (PBHs) are known to be produced from collapsing cosmic defects such as domain walls and strings. In this paper we show how PBHs are produced in monopole-string networks.     

What is the most simple solution of Wheeler-DeWitt equation?

The Wheeler-DeWitt equation in Vilenkin model is solved via the ansatz approach when all terms related to vacuum, domain walls, strings, dust, relativistic matter, bosons and fermions and ultra stiff matter are present.     

Domain walls in Lyra geometry

In this paper we have discussed two models of domain walls within the framework of Lyra geometry. An exact solution is obtained for a thick non static domain wall. The space time is non singular both in its spatial and temporal behavior and the gravitational field experienced by a test particle is attractive. It is found that these exists no particle horizon in our case. Also we have presented a spherical domain wall with nonvanishing stress components in the direction perpendicular to the plane of the wall. The gravitational field of the domain wall is shown to be attractive in nature. This revised version was published online in July 2006 with corrections to the Cover Date.     

Axially symmetric cosmological models in a scalar tensor theory based on Lyra manifold

Axially symmetric cosmological models are obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra manifold with time dependent β in the presence of string source, perfect fluid distribution, dust distribution and thick domain walls. Some physical and geometrical properties of these models are discussed.     

An asymptotic representation of unstable gravity modes in stars

An asymptotic representation is developed for high order unstable gravity modes in a star which are associated with a convective zone enclosed between two radiative layers. In the domain which contains both turning points of the differential equation, the solutions are represented by a single asymptotic expansion in terms of Weber functions.     

Axially symmetric non-static domain walls in scalar–tensor theories of gravitation

An axially symmetric non-static space-time is considered in the presence of thick domain walls in the scalar–tensor theories formulated by Brans and Dicke (Phys. Rev. 124:925, 1961) and Saez and Ballester (Phys. Lett. A 113:467, 1985). Exact cosmological models, in both the theories, are presented with the help of special law of variation proposed by Berman (Nuovo Cim. B 74:182, 1983), for Hubble’s parameter. Some physical and kinematical properties of the models are discussed.      

Domain walls with spherical symmetry

In this paper, we have evaluated solutions for Domain walls with sphericalsymmetry in four and five dimensional space time. Exact solutions ofEinstein equations coupled to scalar field with a potential V() are presented. Here scalar field depends both on radial and timecoordinates. Pressures perpendicular to the wall are taken to benon-zero. The solutions are obtained using functional separability ofmetric coefficients. Also we study the gravitational effects on testparticles.Pacs Nos: 04.20jb, 98.80 Bp     

Evidence for silicate dissolution on Mars from the Nakhla meteorite

Veins containing carbonates, hydrous silicates, and sulfates that occur within and between grains of augite and olivine in the Nakhla meteorite are good evidence for the former presence of liquid water in the Martian crust. Aqueous solutions gained access to grain interiors via narrow fractures, and those fractures within olivine whose walls were oriented close to (001) were preferentially widened by etching along [001]. This orientation selective dissolution may have been due to the presence within olivine of shock‐formed [001](100) and [001]{110} screw dislocations. The duration of etching is likely to have been brief, possibly less than a year, and the solutions responsible were sufficiently cool and reducing that laihunite did not form and Fe liberated from the olivine was not immediately oxidized. The pores within olivine were mineralized in sequence by siderite, nanocrystalline smectite, a Fe‐Mg phyllosilicate, and then gypsum, whereas only the smectite occurs within augite. The nanocrystalline smectite was deposited as submicrometer thick layers on etched vein walls, and solution compositions varied substantially between and sometimes during precipitation of each layer. Together with microcrystalline gypsum the Fe‐Mg phyllosilicate crystallized as water briefly returned to some of the veins following desiccation fracturing of the smectite. These results show that etching of olivine enhanced the porosity and permeability of the nakhlite parent rock and that dissolution and secondary mineralization took place within the same near‐static aqueous system.     

The behaviour of neutral lines in two-dimensional magnetohydrodynamic equilibria

Nonlinear equilibrium solutions for two-dimensional magnetic arcades (/z = 0) using a Grad-Shafranov equation in which the axial magnetic field and the pressure are specified as functions of the component of the vector potential in the z direction are re-examined.To compute nonlinear solutions one is restricted to seeking solutions on finite computational domains with specified boundary conditions. We consider two basic models which have appeared in the literature. In one model the field is laterally restricted by means of Dirichlet boundary conditions and free to extend vertically by means of a Neumann condition at the top of the domain. For such fields, bifurcating solutions only appear for a narrow range of values for the parameter (the ratio of a typical length scale of the field to the gravitational scale height). Nevertheless, we show that the presence of this parameter is essential for bifurcating solutions in such domains. For the second model with Neumann conditions on three sides of the domain representing the region above the photosphere we do not find bifurcating solutions. Instead high-energy solutions with detached field lines evolve smoothly from low-energy solutions which have all field lines attached to the photosphere. Again the presence or absence of detached flux is dependent on the magnitude of for those fields which are evolved quasi-statically via an increase in the plasma pressure.     

The solution of a time-dependent problem in radiative transfer

The time-dependent equation of radiative transfer for a finite, plane-parallel, non-radiating, and isotropically scattering atmosphere of arbitrary stratification is solved by using the integral equation method. The medium is taken to be inhomogeneous. The Laplace transform is used in the time domain. It is seen that the obtained solutions are reducible to the corresponding ones for steady-state problems by simply changing the Laplace transform parameter to zero.     

A SOLAR α - ω DYNAMO STUDY AND ITS TRANSITION TO CHAOS

In this contribution we present a nonlinear dynamo model, described by an infinite dimensional system of differential equations, whose solutions depend on the essential parameter D, the dynamo number. The solutions and the bifurcation points of the system are determined with the help of a new developed computer code. We show that, depending on D, stationary, oscillatory and chaotic solutions, which are characterized by Lyapunov exponents, result. We find that the solar dynamo may operate either in the chaotic or in the stable limit cycle domain, depending on the characteristic value of the dynamo number or the motion of the convection zone.     

A Method for locating Singularities in the Complex Time Domain for Integrable Dynamical Systems

A simple method for the determination of the position of singularities in the complex time domain for dynamical systems which are described by ordinary differential equations is presented. The method is designed for integrable separable systems whose solutions are not expressible in closed form. A direct consequence of this method is that it ‘closes’ the phase space. Simple physical meaning is given to the singularity position. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamic portrait of the planetary 2/1 mean-motion resonance – I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (σ-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (  Δϖ  -family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system.
The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low–moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions.
Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.     

Criteria for shear flow instability in the magnetopause boundary layer region

Shear flow instability is studied in the planar magnetopause boundary layer region by treating the plasma as compressible. A necessary criterion for instability near the Alfvén resonance is obtained. Sufficient criterion for instability is derived from the solution of a six degree polynomial for the cases of constant and antisymmetric velocity profiles when there is no Alfvén resonance. Both the criteria are obtained analytically for the first time. The necessary criterion generalises the well-known inflexion point theorem and Rayleigh's criterion in the hydrodynamic case to magnetohydrodynamic case for incompressible plasma provided both the Alfvén surfaces lie in the boundary layer. The Alfvén resonant surfaces are similar to the boundary walls in hydrodynamics. A semi-hyperbola theorem for the unstable situation is derived which represents the domain of Doppler shifted real frequency and imaginary frequency. From the sufficient criterion for instability it is observed that plasma shear should be more for a compressible plasma in order to make the plasma unstable. The growth rate for instability is obtained. A thin layer around Alfvén resonance effectively determines how fast the flow could attain instability.