Determination of the Galaxy age by the method of uranium–thorium–plutonium isotopic ratios

The dependence of the Galaxy age (Т _G), as determined by the method of uranium–thorium isotopic ratios, on the parameters of the nucleosynthesis model is studied within the theory of galactic nucleosynthesis. It is shown that ТG depends strongly both on the scenario of the production of nuclei in the r-process and those features of neutron-rich nuclei that are used in the respective analysis and on galactic-nucleosynthesis parameters. The effect of a sudden nucleosynthesis spike before the formation of a solar system on the Galaxy age is evaluated. The region of admissible values of the parameters of galacticnucleosynthesis theory is discussed. The method of uranium–thorium isotopic ratios is supplemented with the ²⁴⁴Pu/²³⁸U ratio for yet another cosmochronometer pair, and the Galaxy age is estimated on the basis of the model modified in this way.     

Breeding of 233U in the thorium–uranium fuel cycle in VVER reactors using heavy water

A method is proposed for achieving optimal neutron kinetics and efficient isotope transmutation in the ²³³U–²³²Th oxide fuel of water-moderated reactors with variable water composition (D₂O, H₂O) that ensures breeding of the ²³³U and ²³⁵U isotopes. The method is comparatively simple to implement.     

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.     

Nuclear power plant types and the management of plutonium and minor actinides – in search of fuel cycle flexibility

Transuranics management concerns all NPP types, because of the specifications for a sustainable development. Multiple recycling is mandatory. Neutronic abundance can be obtained in fast spectrum, or by adding external neutrons or (temporarily) with additional ²³⁵U. The LWRs can control the plutonium inventory and significantly reduce the amount of transuranics transferred to the geological repository, thanks to the use of innovative nuclear fuel in a limited part of the NPP fleet. HTR adapted to transuranics burning can help. In the future, in addition to the liquid metal FBR, a strategy based on a gas cooled technological line and advanced fuel opens a second path towards fast spectra. Strategies for defining the optimal mix of reactor types in the nuclear fleet at a given time and demonstrating the fuel cycle flexibility are under study. To cite this article: J.-B. Thomas, C. R. Physique 3 (2002) 783–796.     

Equilibrium composition for the reaction of plutonium hydride with air

There are six independent constituents with 4 chemical elements, i.e. PuH2.7(s), PuN(s), Pu2O3(s), N2, O2 and H2, therefore , the system described involves of 2 independent reactions ,both those of the experimental, which indicates that the chemical equilibrium is nearly completely approached. Therefore, it is believed that the reaction rate of plutonium hydride with air is extremely rapid. The present paper has briefly discussed the simultaneous reactions and its thermodynamic coupling effect.     

On the stability of the shear–free condition

The evolution equation for the shear is reobtained for a spherically symmetric anisotropic, viscous dissipative fluid distribution, which allows us to investigate conditions for the stability of the shear–free condition. The specific case of geodesic fluids is considered in detail, showing that the shear–free condition, in this particular case, may be unstable, the departure from the shear–free condition being controlled by the expansion scalar and a single scalar function defined in terms of the anisotropy of the pressure, the shear viscosity and the Weyl tensor or, alternatively, in terms of the anisotropy of the pressure, the dissipative variables and the energy density inhomogeneity.     

On the Hausdorff Dimension of the Spectrum of the Thue–Morse Hamiltonian

We show that the Hausdorff dimension of the spectrum of the Thue–Morse Hamiltonian has a common positive lower bound for all coupling.     

On the algebraic types of the Bel–Robinson tensor

The Bel–Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov–Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov–Bel types and the additional ones are intrinsically characterized in terms of the sole Bel–Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel–Robinson tensor in regular cases.     

On the Non-Integrability of the Stark–Zeeman Hamiltonian System

In this paper we present a proof of the non-integrability in the Liouvillian sense of the Stark–Zeeman Hamiltonian. In particular, we generalize the result of Kummer and Saenz about the non-integrability of the pure Zeeman Hamiltonian. The proof we give is an application of the theorem of Morales and Ramis (1998) about non-integrability, based on differential Galois theory. Received: 30 March 1999 / Accepted: 16 May 1999     

Mechanical properties of the thermal equilibrium Friedmann–Robertson–Walker universe model

The mechanical property of the thermal-equilibrium Friedmann-Robertson-Walker （TEFRW） universe is first studied. The equation of state and the scale factor of the TEFRW universe take the forms ofw = w（a;zT） and a = a（a;zT,Ho）. For the universe consisting of the nonrelativistic matter and the dark energy, the behavior of the dark energy depends on the value of the present-day matter fraction. For the TEFRW universe consisting of N ingredients, the effective temperature is introduced. Lastly, a simple TEFRW universe model is analyzed.     

On the Diffuse Structure of the Toluene–Water Interface

The electric density profile along the normal to the phase interface between aromatic hydrocarbon toluene and water has been studied by X-ray reflectometry using synchrotron radiation. According to the experimental data, the width of the interface under normal conditions is (3.9 ± 0.1) Å. This value is much larger than a theoretical value of (5.7 ± 0.2) Å predicted by the theory of capillary waves with an interphase tension of (36.0 ± 0.1) mN/m. The observed broadening of the interface is attributed to its own diffuse near-surface structure with a width no less than Å, which is about the value previously discussed for (high-molecular-weight saturated hydrocarbon–water) and (1,2-dichloroethane–water) interfaces.     

On the Eigenstates of the Elliptic Calogero–Moser Model

It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (–1) of the elliptic Calogero–Moser model, where (1, ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero–Sutherland model, if exp(2–1) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero–Moser model which converge to the ones of the Calogero–Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2–1). With some assumptions, we show analogous results for N-particle and l is positive integer cases.     

On the Instability Intervals of the Mathieu–Hill Operator

Consider the Mathieu–Hill operator

14C in uranium and thorium minerals: a signature of cluster radioactivity?

Various uranium and thorium minerals have been analysed with accelerator mass spectrometry to determine their ¹⁴C content. It is found that, whenever the contribution from secondary reactions such as the ¹¹B(α,p)¹⁴C is sufficiently low, the ¹⁴C concentration is consistent with that expected from ¹⁴C (spontaneous) cluster radioactivity from radium isotopes of the uranium and thorium natural series. Received: 15 February 1999     

On the Effect of Stochastic Fluctuations in the Dynamics of the Lifshitz–Slyozov–Wagner Model

In this paper the dynamics of a system of spherical particles that fill a small volume fraction of the space and that evolves in a concentration field is discussed. Corrections to the Lifshitz–Slyozov–Wagner (LSW) model that take into account the stochastic character of the problem are computed. It is proved, under suitable smallness assumptions for the volume fraction filled by the particles, that the effect of these corrections does not modify much the dynamics of the self-similar solutions of the LSW system of equations.     

On the Orthocomplementation of State–Property–Systems of Contextual Systems

We adopt an operational approach to quantum mechanics in which a physical system is defined by the mathematical structure of its set of states and properties. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the case N=2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the two states involved, but also on the measurement context which induces the state transition.     

On the global character of some restricted equilibrium conditions—A remark on metastability

For classical lattice systems with finite-range interactions it is proven that if a state minimizes a free-energy functional at nonzero temperature with respect to variations of the state inside all regions of limited size (for instance, all regions with only one lattice site!) then it is a Gibbs state. This result rules out the possibility of defining metastable states atT 0 as those which satisfy the thermodynamical stability conditions for regions with small volume-to-surface ratio, unlike theT=0 case.Partial financial support by CNPq.Financial support by FAPESP.     

On the structural properties of B–C–N nanotubes

We apply a first-principles method, based on the density functional theory, to calculate the structural stability of B–C–N armchair nanotubes, comparing such results with the ones obtained for zigzag configuration. Analysis of the corresponding strain energies confirm that the stability of BC₂N nanotubes is independent of their chirality and demonstrate that such nanostructures have lower strain than BCN and carbon nanotubes. The results show that the formation energy decreases with the tube diameter and indicate that the most stable nanotubes have the maximum number of B–N and C–C bonds. Therefore, from the experimental point of view, larger diameter BC₂N model-I nanotubes should be more probable to be synthesized.     

On the level-dependence of Wess–Zumino–Witten three-point functions

Three-point functions of Wess–Zumino–Witten models are investigated. In particular, we study the level-dependence of three-point functions in the models based on algebras su(3) and su(4). We find a correspondence with Berenstein–Zelevinsky triangles. Using previous work connecting those triangles to the fusion multiplicities, and the Gepner–Witten depth rule, we explain how to construct the full three-point functions. We show how their level-dependence is similar to that of the related fusion multiplicity. For example, the concept of threshold level plays a prominent role, as it does for fusion.