On spherical twisted conjugacy classes

Let G be a simple algebraic group over an algebraically closed field of good odd characteristic, and let theta be an automorphism of G arising from an involution of its Dynkin diagram. We show that the spherical theta-twisted conjugacy classes are precisely those intersecting only Bruhat cells corresponding to twisted involutions in the Weyl group. We show how the analogue of this statement fails in the triality case. We generalize to good odd characteristic J-H. Lu's dimension formula for spherical twisted conjugacy classes.Comment: proof of Lemma 6.4 polished. The journal version is available at http://www.springerlink.com/content/k573l88256753640

Adaptive hard and tough mechanical response in single-crystal B1 VNx ceramics via control of anion vacancies

High hardness and toughness are generally considered mutually exclusive properties for single-crystal ceramics. Combining experiments and ab initio molecular dynamics (AIMD) atomistic simulations at room temperature, we demonstrate that both the hardness and toughness of single-crystal NaCl-structure VNx/MgO(001) thin films are simultaneously enhanced through the incorporation of anion vacancies. Nanoindentation results show that VN0.8, here considered as representative understoichiometric VNx system, is ~20% harder, as well as more resistant to fracture than stoichiometric VN samples. AIMD modeling of VN and VN0.8 supercells subjected to [001] and [110] elongation reveal that the tensile strengths of the two materials are similar. Nevertheless, while the stoichiometric VN phase systematically cleaves in a brittle manner at tensile yield points, the understoichiometric compound activates transformation-toughening mechanisms that dissipate accumulated stresses. AIMD simulations also show that VN0.8 exhibits an initially greater resistance to both {110} and {111} shear deformation than VN. However, for progressively increasing shear strains, the VN0.8 mechanical behavior gradually evolves from harder to more ductile than VN. The transition is mediated by anion vacancies, which facilitate {110} and {111} lattice slip by reducing activation shear stresses by as much as 35%. Electronic-structure analyses show that the two-regime hard/tough mechanical response of VN0.8 primarily stems from its intrinsic ability to transfer d electrons between 2nd-neighbor and 4th-neighbor (i.e., across vacancy sites) V-V metallic states. Our work offers a route for electronic-structure design of hard materials in which a plastic mechanical response is triggered with loading

Machine-learning potentials for nanoscale simulations of deformation and fracture: example of TiB2_2 ceramic

Machine-learning interatomic potentials (MLIPs) offer a powerful avenue for simulations beyond length and timescales of ab initio methods. Their development for investigation of mechanical properties and fracture, however, is far from trivial since extended defects -- governing plasticity and crack nucleation in most materials -- are too large to be included in the training set. Using TiB$_2$ as a model ceramic material, we propose a strategy for fitting MLIPs suitable to simulate mechanical response of monocrystals until fracture. Our MLIP accurately reproduces ab initio stresses and failure mechanisms during room-temperature uniaxial tensile deformation of TiB$_2$ at the atomic scale ($\approx{10}^3$ atoms). More realistic tensile tests (low strain rate, Poisson's contraction) at the nanoscale ($\approx{10}^4$--10$^6$ atoms) require MLIP up-fitting, i.e. learning from additional ab initio configurations. Consequently, we elucidate trends in theoretical strength, toughness, and crack initiation patterns under different loading directions. To identify useful environments for further up-fitting, i.e., making the MLIP applicable to a wider spectrum of simulations, we asses transferability to other deformation conditions and phases not explicitly trained on

Cosmological Feedback from High-Redshift Dwarf Galaxies

We model how repeated supernova explosions in high-redshift dwarf starburst galaxies drive superbubbles and winds out of the galaxies. We compute the efficiencies of metal and mass ejection and energy transport from the galactic potentials, including the effect of cosmological infall of external gas. The starburst bubbles quickly blow out of small, high-redshift, galactic disks, but must compete with the ram pressure of the infalling gas to escape into intergalactic space. We show that the assumed efficiency of the star formation rate dominates the bubble evolution and the metal, mass, and energy feedback efficiencies. With star formation efficiency f*=0.01, the ram pressure of infall can confine the bubbles around high-redshift dwarf galaxies with circular velocities v_c>52 km/s. We can expect high metal and mass ejection efficiencies, and moderate energy transport efficiencies in halos with v_c~30-50 km/s and f*~0.01 as well as in halos with v_c~100 km/s and f*>>0.01. Such haloes collapse successively from 1-2 sigma peaks in LambdaCDM Gaussian density perturbations as time progresses. These dwarf galaxies can probably enrich low and high-density regions of intergalactic space with metals to 10^-3-10^-2 Zsun as they collapse at z~8 and z<5 respectively. They also may be able to provide adequate turbulent energy to prevent the collapse of other nearby halos, as well as to significantly broaden Lyman-alpha absorption lines to v_rms~20-40 km/s. We compute the timescales for the next starbursts if gas freely falls back after a starburst, and find that, for star formation efficiencies as low as f*<0.01, the next starburst should occur in less than half the Hubble time at the collapse redshift. This suggests that episodic star formation may be ubiquitous in dwarf galaxies.Comment: Accepted for ApJ v613, 60 pages, 15 figure

Solubility limit and precipitate formation in Al-doped 4H-SiC epitaxial material

Heavily Al-doped 4H–SiC structures have been prepared by vapor phase epitaxy. Subsequent anneals have been carried out in an Ar atmosphere in a rf-heated furnace between 1500 °C and 2000 °C for 0.5 to 3 h. Secondary ion mass spectrometry has been utilized to obtain Al concentration versus depth as well as lateral distributions (ion images). Transmission electron microscopy(TEM) has been employed to study the crystallinity and determine phase composition after heat treatment. A solubility limit of ∼2×10²⁰ Al/cm³ (1900 °C) is extracted. Three-dimensional ion images show that the Al distribution does not remain homogeneous in layers heat treated at 1700 °C or above when the Al concentration exceeds 2×10²⁰ cm⁻³. Al-containing precipitates are identified by energy-filtered TEM.Financial support was partly received from the Swedish Foundation for Strategic Research (SSF) SiCEP program

Raman scattering in C_{60} and C_{48}N_{12} aza-fullerene: First-principles study

We carry out large scale {\sl ab initio} calculations of Raman scattering activities and Raman-active frequencies (RAFs) in ${\rm C}_{48}{\rm N}_{12}$ aza-fullerene. The results are compared with those of ${\rm C}_{60}$. Twenty-nine non-degenerate polarized and 29 doubly-degenerate unpolarized RAFs are predicted for ${\rm C}_{48}{\rm N}_{12}$. The RAF of the strongest Raman signal in the low- and high-frequency regions and the lowest and highest RAFs for ${\rm C}_{48}{\rm N}_{12}$ are almost the same as those of ${\rm C}_{60}$. The study of ${\rm C}_{60}$ reveals the importance of electron correlations and the choice of basis sets in the {\sl ab initio} calculations. Our best calculated results for ${\rm C}_{60}$ with the B3LYP hybrid density functional theory are in excellent agreement with experiment and demonstrate the desirable efficiency and accuracy of this theory for obtaining quantitative information on the vibrational properties of these molecules.Comment: submitted to Phys.Rev.

Do Child Soldiers Influence UN Peacekeeping?

The use of child soldiers in conflicts has received increasing academic attention in recent years. This article examines post-conflict periods to see whether the use of child soldiers mobilizes United Nations peacekeeping operations (UN PKO) in the aftermath of a conflict. Taking into consideration how child soldiers affect conflict and how important their reintegration is to sustainable peace and post-conflict development, we analyse whether the presence of child soldiers in a civil war increases the likelihood of the presence of a PKO. We argue that the UN deems a conflict with child soldiers as a difficult case for conflict resolution, necessitating a response from the international community. This is in line with our empirical results confirming that the use of child soldiers significantly increases the likelihood of peacekeeping