69,249 research outputs found

### 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 Na$_{2.7}$Ru$_4$O$_9$

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

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