Higher-spin Realisations of the Bosonic String

It has been shown that certain $W$ algebras can be linearised by the inclusion of a spin--1 current. This provides a way of obtaining new realisations of the $W$ algebras. Recently such new realisations of $W_3$ were used in order to embed the bosonic string in the critical and non-critical $W_3$ strings. In this paper, we consider similar embeddings in $W_{2,4}$ and $W_{2,6}$ strings. The linearisation of $W_{2,4}$ is already known, and can be achieved for all values of central charge. We use this to embed the bosonic string in critical and non-critical $W_{2,4}$ strings. We then derive the linearisation of $W_{2,6}$ using a spin--1 current, which turns out to be possible only at central charge $c=390$. We use this to embed the bosonic string in a non-critical $W_{2,6}$ string.Comment: 8 pages. CTP TAMU-10/95

Graphical Tensor Product Reduction Scheme for the Lie Algebras so(5) = sp(2), su(3), and g(2)

We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2), su(3), and g(2). This leads to an efficient practical method to reduce tensor products of irreducible representations into sums of such representations. For this purpose, the 2-dimensional weight diagram of a given representation is placed in a "landscape" of irreducible representations. We provide both the landscapes and the weight diagrams for a large number of representations for the three simple rank 2 Lie algebras. We also apply the algebraic "girdle" method, which is much less efficient for calculations by hand for moderately large representations. Computer code for reducing tensor products, based on the graphical method, has been developed as well and is available from the authors upon request.Comment: 43 pages, 18 figure

Kinematic Constraints to the Transition Redshift from SNe Ia Union Data

The kinematic approach to cosmological tests provides a direct evidence to the present accelerating stage of the universe which does not depend on the validity of general relativity, as well as on the matter-energy content of the Universe. In this context, we consider here a linear two-parameter expansion for the decelerating parameter, $q(z)=q_0+q_1z$, where $q_0$ and $q_1$ are arbitrary constants to be constrained by the Union supernovae data. By assuming a flat Universe we find that the best fit to the pair of free parameters is ($q_0,q_1$) = ($-0.73,1.5)$ whereas the transition redshift is $z_t = 0.49^{+0.14}_{-0.07}$ ($1\sigma$) $^{+0.54}_{-0.12}$ ($2\sigma$). This kinematic result is in agreement with some independent analyzes and accommodates more easily many dynamical flat models (like $\Lambda$CDM).Comment: 10 pages, 4 figures, 1 tabl

One-dimensional nonlinear stability of pathological detonations

In this paper we perform high-resolution one-dimensional time-dependent numerical simulations of detonations for which the underlying steady planar waves are of the pathological type. Pathological detonations are possible when there are endothermic or dissipative effects in the system. We consider a system with two consecutive irreversible reactions A[rightward arrow]B[rightward arrow]C, with an Arrhenius form of the reaction rates and the second reaction endothermic. The self-sustaining steady planar detonation then travels at the minimum speed, which is faster than the Chapman–Jouguet speed, and has an internal frozen sonic point at which the thermicity vanishes. The flow downstream of this sonic point is supersonic if the detonation is unsupported or subsonic if the detonation is supported, the two cases having very different detonation wave structures. We compare and contrast the long-time nonlinear behaviour of the unsupported and supported pathological detonations. We show that the stability of the supported and unsupported steady waves can be quite different, even near the stability boundary. Indeed, the unsupported detonation can easily fail while the supported wave propagates as a pulsating detonation. We also consider overdriven detonations for the system. We show that, in agreement with a linear stability analysis, the stability of the steady wave is very sensitive to the degree of overdrive near the pathological detonation speed, and that increasing the overdrive can destabilize the wave, in contrast to systems where the self-sustaining wave is the Chapman–Jouguet detonation

Symmetry breaking and unconventional charge ordering in single crystal Na2.7_{2.7}Ru4_4O9_9

The interplay of charge, spin, and lattice degrees of freedom in matter leads to various forms of ordered states through phase transitions. An important subclass of these phenomena of complex materials is charge ordering (CO), mainly driven by mixed-valence states. We discovered by combining the results of electrical resistivity ($\rho$), specific heat, susceptibility $\chi$ (\textit{T}), and single crystal x-ray diffraction (SC-XRD) that Na$_{2.7}$Ru$_4$O$_9$ with the monoclinic tunnel type lattice (space group $C$2/$m$) exhibits an unconventional CO at room temperature while retaining metallicity. The temperature-dependent SC-XRD results show successive phase transitions with super-lattice reflections at \textbf{q}$_1$=(0, $\frac{1}{2}$, 0) and \textbf{q}$_2$=(0, $\frac{1}{3}$, $\frac{1}{3}$) below $T_{\textrm{C2}}$ (365 K) and only at \textbf{q}$_1$=(0, $\frac{1}{2}$, 0) between $T_{\textrm{C2}}$ and $T_{\textrm{C1}}$ (630 K). We interpreted these as an evidence for the formation of an unconventional CO. It reveals a strong first-order phase transition in the electrical resistivity at $T_{\textrm{C2}}$ (cooling) = 345 K and $T_{\textrm{C2}}$ (heating) = 365 K. We argue that the origin of the phase transition is due to the localized 4$d$ Ru-electrons. The results of our finding reveal an unique example of Ru$^{3+}$/Ru$^{4+}$ mixed valance heavy \textit{d}$^4$ ions.Comment: 10 pages, 9 figure

On computation of the first Baues--Wirsching cohomology of a freely-generated small category

The Baues--Wirsching cohomology is one of the cohomologies of a small category. Our aim is to describe the first Baues--Wirsching cohomology of the small category generated by a finite quiver freely. We consider the case where the coefficient is a natural system obtained by the composition of a functor and the target functor. We give an algorithm to obtain generators of the vector space of inner derivations. It is known that there exists a surjection from the vector space of derivations of the small category to the first Baues--Wirsching cohomology whose kernel is the vector space of inner derivations.Comment: 11 page