507 research outputs found
Hausdorff dimension of some groups acting on the binary tree
Based on the work of Abercrombie, Barnea and Shalev gave an explicit formula
for the Hausdorff dimension of a group acting on a rooted tree. We focus here
on the binary tree T. Abert and Virag showed that there exist finitely
generated (but not necessarily level-transitive) subgroups of AutT of arbitrary
dimension in [0,1].
In this article we explicitly compute the Hausdorff dimension of the
level-transitive spinal groups. We then show examples of 3-generated spinal
groups which have transcendental Hausdroff dimension, and exhibit a
construction of 2-generated groups whose Hausdorff dimension is 1.Comment: 10 pages; full revision; simplified some proof
The three-loop Adler -function for SQCD regularized by dimensional reduction
The three-loop Adler -function for SQCD in the
\overline{\mbox{DR}} scheme is calculated starting from the three-loop result
recently obtained with the higher covariant derivative regularization. For this
purpose, for the theory regularized by higher derivatives we find a subtraction
scheme in which the Green functions coincide with the ones obtained with the
dimensional reduction and the modified minimal subtraction prescription for the
renormalization of the SQCD coupling constant and of the matter superfields.
Also we calculate the -function in the \overline{\mbox{DR}} scheme for all
renormalization constants (including the one for the electromagnetic coupling
constant which appears due to the SQCD corrections). It is shown that the
results do not satisfy the NSVZ-like equation relating the -function to the
anomalous dimension of the matter superfields. However, the NSVZ-like scheme
can be constructed with the help of a properly tuned finite renormalization. It
is also demonstrated that the three-loop -function defined in terms of the
bare couplings with the dimensional reduction does not satisfy the NSVZ-like
equation for an arbitrary renormalization prescription. We also investigate a
possibility to present the results in the form of the -expansion and the
scheme dependence of this expansion.Comment: 25 pages, 2 figures, 1 table, improved conclusion, version accepted
for publication in JHE
Alpha-nucleus potential for alpha-decay and sub-barrier fusion
The set of parameters for alpha-nucleus potential is derived by using the
data for both the alpha-decay half-lives and the fusion cross-sections around
the barrier for reactions alpha+40Ca, alpha+59Co, alpha+208Pb. The alpha-decay
half-lives are obtained in the framework of a cluster model using the WKB
approximation. The evaluated alpha-decay half-lives and the fusion
cross-sections agreed well with the data. Fusion reactions between
alpha-particle and heavy nuclei can be used for both the formation of very
heavy nuclei and spectroscopic studies of the formed compound nuclei.Comment: 10 pages, 5 figure
Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium
Experiments with acoustic waves guided along the mechanically free surface of
an unconsolidated granular packed structure provide information on the
elasticity of granular media at very low pressures that are naturally
controlled by the gravitational acceleration and the depth beneath the surface.
Comparison of the determined dispersion relations for guided surface acoustic
modes with a theoretical model reveals the dependencies of the elastic moduli
of the granular medium on pressure. The experiments confirm recent theoretical
predictions that relaxation of the disordered granular packing through
non-affine motion leads to a peculiar scaling of shear rigidity with pressure
near the jamming transition corresponding to zero pressure. Unexpectedly, and
in disagreement with the most of the available theories, the bulk modulus
depends on pressure in a very similar way to the shear modulus
Thermodynamic aspects of materials' hardness: prediction of novel superhard high-pressure phases
In the present work we have proposed the method that allows one to easily
estimate hardness and bulk modulus of known or hypothetical solid phases from
the data on Gibbs energy of atomization of the elements and corresponding
covalent radii. It has been shown that hardness and bulk moduli of compounds
strongly correlate with their thermodynamic and structural properties. The
proposed method may be used for a large number of compounds with various types
of chemical bonding and structures; moreover, the temperature dependence of
hardness may be calculated, that has been performed for diamond and cubic boron
nitride. The correctness of this approach has been shown for the recently
synthesized superhard diamond-like BC5. It has been predicted that the
hypothetical forms of B2O3, diamond-like boron, BCx and COx, which could be
synthesized at high pressures and temperatures, should have extreme hardness
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