FRW Cosmological Models with Bulk-Viscosity in?Barber’s Second Self-Creation Theory

We have studied the evolution of spatially homogeneous and isotropic FRW cosmological model with bulk-viscosity in the frame work of Barber’s (Gen. Relativ. Gravit. 14: 117, 1982) second self-creation theory of gravitation. The cosmological models are obtained with the help of special law of variation for Hubble parameter proposed by Bermann (Nuovo Cimento 74B: 182, 1983). Physical parameters of the models have been discussed in case of false vacuum model, Zel’dovich fluid and radiation dominated fluid.     

Role of Brans-Dicke Theory with?or?without?Self-Interacting Potential in?Cosmic?Acceleration

In this work we have studied the possibility of obtaining cosmic acceleration in Brans-Dicke theory with varying or constant ω (Brans-Dicke parameter) and with or without self-interacting potential, the background fluid being barotropic fluid or Generalized Chaplygin Gas. Here we take the power law form of the scale factor and the scalar field. We show that accelerated expansion can also be achieved for high values of ω for closed Universe.     

Inverse Spectral Problem with Partial Information¶on the Potential: The Case of the Whole Real Line

The Schrödinger operator -d²/dx²+q(x)-d^2/dx^2+q(x) is considered on the real axis. We discuss the inverse spectral problem where discrete spectrum and the potential on the positive half-axis determine the potential completely. We do not impose any restrictions on the growth of the potential but only assume that the operator is bounded from below, has discrete spectrum, and the potential obeys q(-|x|) 3 q(|x|)q(-|x|)\geq q(|x|). Under these assertions we prove that the potential for xS 0 and the spectrum of the problem uniquely determine the potential on the whole real axis. Also, we study the uniqueness under slightly different conditions on the potential. The method employed uses Weyl m-function techniques and asymptotic behavior of the Herglotz functions.     

Cosmological Models with Bulk Viscosity in the Presence of Adiabatic Matter Creation and with Variable G, c, and Λ

Some properties of cosmological models with a time variable bulk viscous coefficient in the presence of adiabatic matter creation and variable G, c, are investigated in the framework of a specifically flat FRW line element. We trivially find a set of solutions through Dimensional Analysis. In all the studied cases it is found that the behaviour of these "constants" is inversely proportional to the cosmic time. It is found that with the solution obtained our model verifies the principles of general covariance and Lorentz invariance. Finally we emphasize that the envisaged models are free of the horizon and entropy problem.     

Feynman’s Proof of Maxwell Equations: in?the?Context?of Quantum Gravity

Many of us are familiar with Feynman’s “proof” of 1948, as revealed by Dyson, which demonstrates that Maxwell equations of electromagnetism are a consequence of Newton’s laws of motion of classical mechanics and the commutation relations of coordinate and momentum of quantum mechanics. It was Feynman’s purpose to explore the universality of dynamics of particles while making the fewest assumptions. We re-examine this formulation in the context of quantum gravity and show how Feynman’s derivation can be extended to include quantum gravity.     

Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group

We showed in Part I that the Hopf algebra ℋ of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group G and that the renormalized theory is obtained from the unrenormalized one by evaluating at ɛ= 0 the holomorphic part γ₊(ɛ) of the Riemann–Hilbert decomposition γ₋(ɛ)^{− 1}γ₊(ɛ) of the loop γ(ɛ)∈G provided by dimensional regularization. We show in this paper that the group G acts naturally on the complex space X of dimensionless coupling constants of the theory. More precisely, the formula g ₀=gZ ₁ Z ₃ ^−3/2 for the effective coupling constant, when viewed as a formal power series, does define a Hopf algebra homomorphism between the Hopf algebra of coordinates on the group of formal diffeomorphisms to the Hopf algebra ℋ. This allows first of all to read off directly, without using the group G, the bare coupling constant and the renormalized one from the Riemann–Hilbert decomposition of the unrenormalized effective coupling constant viewed as a loop of formal diffeomorphisms. This shows that renormalization is intimately related with the theory of non-linear complex bundles on the Riemann sphere of the dimensional regularization parameter ɛ. It also allows to lift both the renormalization group and the β-function as the asymptotic scaling in the group G. This exploits the full power of the Riemann–Hilbert decomposition together with the invariance of γ₋(ɛ) under a change of unit of mass. This not only gives a conceptual proof of the existence of the renormalization group but also delivers a scattering formula in the group G for the full higher pole structure of minimal subtracted counterterms in terms of the residue. Received: 21 March 2000 / Accepted: 3 October 2000     

Bianchi Type-II, VIII & IX Cosmological Models with Strange Quark Matter Attached to String Cloud in Brans–Dicke and General Theory of Gravitation

We have obtained and presented spatially homogeneous Bianchi type-II, VIII & IX cosmological models with strange quark matter attached to string cloud in Brans and Dicke (Phys. Rev. C 71:054905, 1961) scalar tensor theory and general theory of gravitation. Some important features of the models, thus obtained, have been discussed. We noticed that these universes always expand isotropically and the presence of scalar field doesn’t affect the geometry of the space-time but changes the matter distribution.     

On the Brazil Nuts Problem: Is It of Relevance to Hydrodynamics?

A recent advance in understanding the Brazil nuts phenomenon together with insight into the relative motion of different-size particles in a lattice fluid makes this phenomenon amenable to an approach based on hydrodynamic concept. Here we use this conjecture as a stimulus for solving the equation describing asymmetric transport of particles in a medium moving with constant velocity. We also consider a method for constructing invariant solutions, which enables us to study the dependence of the probability density function on the parameters controlling the asymmetry of the flow. Physical realizations of the invariant solutions are in agreement with recent computer simulations by Alexander and Lebowitz.     

The Archaic Universe: Big Bang,Cosmological Term and the Quantum Origin of Time in Projective Cosmology

This article proposes some cosmological reflections at the qualitative and conjectural level, suggested by the Fantappié-Arcidiacono projective relativity theory. The difference will firstly be discussed between two types of singularity in this theory: geometric (de Sitter horizon) and physical (big bang, big crunch). The reasons for the existence of geometric singularities are deeply rooted in the principle of inertia and in the principle of relativity, while physical singularities are associated with the creation or destruction of matter. In this framework, quantum mechanics is introduced through a particular interpretation of Bohm’s holomovement. Finally, a possible mechanism is discussed for the genesis of the cosmological term. No form of inflation appears in the scenario described.     

The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?

We show that the strong form of Heisenberg’s inequalities due to Robertson and Schrödinger can be formally derived using only classical considerations. This is achieved using a statistical tool known as the “minimum volume ellipsoid” together with the notion of symplectic capacity, which we view as a topological measure of uncertainty invariant under Hamiltonian dynamics. This invariant provides a right measurement tool to define what “quantum scale” is. We take the opportunity to discuss the principle of the symplectic camel, which is at the origin of the definition of symplectic capacities, and which provides an interesting link between classical and quantum physics.     

The Stochastic Limit of the Fröhlich Hamiltonian: Relations with the Quantum Hall Effect

We propose a model of an approximatively two-dimensional electron gas in a uniform electric and magnetic field and interacting with a positive background through the Fröhlich Hamiltonian. We consider the stochastic limit of this model and we find the quantum Langevin equation and the generator of the master equation. This allows us to calculate the explicit form of the conductivity and the resistivity tensors and to deduce a fine tuning condition (FTC) between the electric and the magnetic fields. This condition shows that the x-component of the current is zero unless a certain quotient, involving the physical parameters, takes values in a finite set of physically meaningful rational numbers. We argue that this behavior is quite similar to that observed in the quantum Hall effect. We also show that, under some conditions on the form factors entering in the definition of the model, also the plateaux and the almost linear behavior of the Hall resistivity can be recovered. Our FTC does not distinguish between fractional and integer values.     

The dominant deformation mechanism of nanocrystalline materials with the finest grains: grain boundary sliding or grain boundary migration?

We report an efficient room-temperature synthesis of Au nanoparticles (NPs) using carbon dots (C-dots) as mediator in poly(ethylene glycol). The synthesis does not require any irradiation or heating for the reduction of the metal precursor and it yields smaller sized particles of ~15 nm, mostly octahedron in shape. The effect of varying concentrations of the Au precursor and C-dots on the synthesis was studied, which demonstrated the variation in particle size and shape with change in either the precursor or C-dots concentration. Time-resolved absorbance study for the synthesis of Au NPs showed the sigmoidal behavior for the autocatalytic growth having the lagging phase of induction period. The optimum concentration of the precursor and the C-dots were determined for the synthesis of well-dispersed Au NPs. The stability of the prepared Au NPs was also determined, showing that at optimum concentration of the precursor and C-dots, the particles were stable and did not precipitate for several days.     

The Effect of Irradiation of a Titanium Alloy of the Ti–6Al–4V–Н System with Pulsed Electron Beams on Its Creep

Russian Physics Journal - Comparative studies of the effect of pulsed electron beam irradiation of the Ti–6Al–4V titanium alloys with the contents of hydrogen of 0.002 wt.% (VT6 alloy)...     

Hybrid fusion–fission reactor with a thorium blanket: Its potential in the fuel cycle of nuclear reactors

Discussions are currently going on as to whether it is suitable to employ thorium in the nuclear fuel cycle. This work demonstrates that the ²³¹Pa–²³²U–²³³U–Th composition to be produced in the thorium blanket of a hybrid thermonuclear reactor (HTR) as a fuel for light-water reactors opens up the possibility of achieving high, up to 30% of heavy metals (HM), or even ultrahigh fuel burnup. This is because the above fuel composition is able to stabilize its neutron-multiplying properties in the process of high fuel burnup. In addition, it allows the nuclear fuel cycle (NFC) to be better protected against unauthorized proliferation of fissile materials owing to an unprecedentedly large fraction of ²³²U (several percent!) in the uranium bred from the Th blanket, which will substantially hamper the use of fissile materials in a closed NFC for purposes other than power production.