Andreev's Theorem on hyperbolic polyhedra

In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of Andreev's Theorem, because Andreev's paper has the reputation of being ``unreadable''.Comment: To appear les Annales de l'Institut Fourier. 47 pages and many figures. Revision includes significant modification to section 4, making it shorter and more rigorous. Many new references include

Extracting the depolarization coefficient D_NN from data measured with a full acceptance detector

The spin transfer from vertically polarized beam protons to Lambda or Sigma hyperons of the associated strangeness production pp -> pK Lambda (Sigma) is described with the depolarization coefficient D_NN. As the polarization of the hyperons is determined by their weak decays, detectors, which have a large acceptance for the decay particles, are needed. In this paper a formula is derived, which describes the depolarization coefficient D_NN by count rates of a 4 pi detector. It is shown, that formulas, which are given in publications for detectors with restricted acceptance, are specific cases of this formula for a 4 pi detector.Comment: Accepted for publication by Nuclear Instruments and Methods in Physics Research Section

Modification of Structure and Tribological Properties of the Surface Layer of Metal-Ceramic Composite under Electron Irradiation in the Plasmas of Inert Gases

Metal-ceramic composites are the main materials for high-load parts in tribomechanical systems. Modern approaches to extend the operation life of tribomechanical systems are based on increasing the strength and tribological properties of the surface layer having 100 to 200 microns in depth. The essential improvement of the properties occurs when high dispersed structure is formed in the surface layer using high-energy processing. As a result of the dispersed structure formation the more uniform distribution of elastic stresses takes place under mechanical or thermal action, the energy of stress concentrators emergence significantly increases and the probability of internal defects formation reduces. The promising method to form the dispersed structure in the surface layer is pulse electron irradiation in the plasmas of inert gases combining electron irradiation and ion bombardment in one process. The present work reports upon the effect of pulse electron irradiation in plasmas of different inert gases with different atomic mass and ionization energy on the structure and tribological properties of the surface layer of TiC/(Ni-Cr) metal-ceramic composite with the volume ratio of the component being 50:50. It is experimentally shown that high-dispersed heterophase structure with a fraction of nanosized particles is formed during the irradiation. Electron microscopy study reveals that refining of the initial coarse TiC particles occurs via their dissolution in the molten metal binder followed by the precipitation of secondary fine particles in the interparticle layers of the binder. The depth of modified layer and the fraction of nanosized particles increase when the atomic number of the plasma gas increases and ionization energy decreases. The wear resistance of metal-ceramic composite improves in accordance to the formation of nanocrystalline structure in the surface layer

An empirically observed pitch-angle diffusion eigenmode in the Earth\u27s electron belt near L* = 5.0

Abstract Using data from NASA\u27s Van Allen Probes, we have identified a synchronized exponential decay of electron flux in the outer zone, near L* = 5.0. Exponential decays strongly indicate the presence of a pure eigenmode of a diffusion operator acting in the synchronized dimension(s). The decay has a time scale of about 4 days with no dependence on pitch angle. While flux at nearby energies and L* is also decaying exponentially, the decay time varies in those dimensions. This suggests the primary decay mechanism is elastic pitch angle scattering, which itself depends on energy and L *. We invert the shape of the observed eigenmode to obtain an approximate shape of the pitch angle diffusion coefficient and show excellent agreement with diffusion by plasmaspheric hiss. Our results suggest that empirically derived eigenmodes provide a powerful diagnostic of the dynamic processes behind exponential decays

Adaptive auditory risk assessment in the dogbane tiger moth when pursued by bats

Moths and butterflies flying in search of mates risk detection by numerous aerial predators; under the cover of night, the greatest threat will often be from insectivorous bats. During such encounters, the toxic dogbane tiger moth, Cycnia tenera uses the received intensity, duration and emission pattern of the bat's echolocation calls to determine when, and how many, defensive ultrasonic clicks to produce in return. These clicks, which constitute an acoustic startle response, act as warning signals against bats in flight. Using an integrated test of stimulus generalization and dishabituation, here we show that C. tenera is able to discriminate between the echolocation calls characteristic of a bat that has only just detected it versus those of a bat actively in pursuit of it. We also show that C. tenera habituates more profoundly to the former stimulus train (‘early attack’) than to the latter (‘late attack’), even though it was initially equally responsive to both stimuli. Matched sensory and behavioural data indicate that reduced responsiveness reflects habituation and is not merely attributable to sensory adaptation or motor fatigue. In search of mates in the face of bats, C. tenera's ability to discriminate between attacking bats representing different levels of risk, and to habituate less so to those most dangerous, should function as an adaptive cost–benefit trade-off mechanism in nature

Nuclear structure beyond the neutron drip line: the lowest energy states in 9^9He via their T=5/2 isobaric analogs in 9^9Li

The level structure of the very neutron rich and unbound $^9$He nucleus has been the subject of significant experimental and theoretical study. Many recent works have claimed that the two lowest energy $^9$He states exist with spins $J^\pi=1/2^+$ and $J^\pi=1/2^-$ and widths on the order of hundreds of keV. These findings cannot be reconciled with our contemporary understanding of nuclear structure. The present work is the first high-resolution study with low statistical uncertainty of the relevant excitation energy range in the $^8$He$+n$ system, performed via a search for the T=5/2 isobaric analog states in $^9$Li populated through $^8$He+p elastic scattering. The present data show no indication of any narrow structures. Instead, we find evidence for a broad $J^{\pi}=1/2^+$ state in $^9$He located approximately 3 MeV above the neutron decay threshold

Population of bound excited states in intermediate-energy fragmentation reactions

Fragmentation reactions with intermediate-energy heavy-ion beams exhibit a wide range of reaction mechanisms, ranging from direct reactions to statistical processes. We examine this transition by measuring the relative population of excited states in several sd-shell nuclei produced by fragmentation with the number of removed nucleons ranging from two to sixteen. The two-nucleon removal is consistent with a non-dissipative process whereas the removal of more than five nucleons appears to be mainly statistical.Comment: 5 pages, 6 figure