Inelastic Effects in Low-Energy Electron Reflectivity of Two-dimensional Materials

A simple method is proposed for inclusion of inelastic effects (electron absorption) in computations of low-energy electron reflectivity (LEER) spectra. The theoretical spectra are formulated by matching of electron wavefunctions obtained from first-principles computations in a repeated vacuum-slab-vacuum geometry. Inelastic effects are included by allowing these states to decay in time in accordance with an imaginary term in the potential of the slab, and by mixing of the slab states in accordance with the same type of distribution as occurs in a free-electron model. LEER spectra are computed for various two-dimensional materials, including free-standing multilayer graphene, graphene on copper substrates, and hexagonal boron nitride (h-BN) on cobalt substrates.Comment: 21 pages, 7 figure

Radiative and Collisional Jet Energy Loss in a Quark-Gluon Plasma

We calculate radiative and collisional energy loss of hard partons traversing the quark-gluon plasma created at RHIC and compare the respective size of these contributions. We employ the AMY formalism for radiative energy loss and include additionally energy loss by elastic collisions. Our treatment of both processes is complete at leading order in the coupling, and accounts for the probabilistic nature of jet energy loss. We find that a solution of the Fokker-Planck equation for the probability density distributions of partons is necessary for a complete calculation of the nuclear modification factor $R_{AA}$ for pion production in heavy ion collisions. It is found that the magnitude of $R_{AA}$ is sensitive to the inclusion of both collisional and radiative energy loss, while the average energy is less affected by the addition of collisional contributions. We present a calculation of $R_{AA}$ for $\pi^0$ at RHIC, combining our energy loss formalism with a relativistic (3+1)-dimensional hydrodynamic description of the thermalized medium.Comment: 4 pages, 4 figures, contributed to Quark Matter 2008, Jaipur, Indi

Morphology and Orientation Selection of Non-Metallic Inclusions in Electrified Molten Metal

The effect of electric current on morphology and orientation selection of non-metallic inclusions in molten metal has been investigated using theoretical modelling and numerical calculation. Two geometric factors, namely the circularity (fc) and alignment ratio (fe) were introduced to describe the inclusions shape and configuration. Electric current free energy was calculated and the values were used to determine the thermodynamic preference between different microstructures. Electric current promotes the development of inclusion along the current direction by either expatiating directional growth or enhancing directional agglomeration. Reconfiguration of the inclusions to reduce the system electric resistance drives the phenomena. The morphology and orientation selection follows the routine to reduce electric free energy. The numerical results are in agreement with our experimental observations

Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories

Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in plasma physics --- the flow of magnetic field lines and the guiding center motion of magnetized charged particles --- resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates, i.e., coordinates lacking the familiar $(q, p)$ partitioning. Recent efforts made progress toward non-canonical symplectic integration of these systems by appealing to the variational integration framework; however, those integrators were multistep methods and later found to be numerically unstable due to parasitic mode instabilities. This work eliminates the multistep character and, therefore, the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem ``degenerate variational integration''. Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that their resultant Euler-Lagrange equations are systems of first-order ODEs. We show that retaining the same degree of degeneracy when constructing a discrete Lagrangian yields one-step variational integrators preserving a non-canonical symplectic structure on the original Hamiltonian phase space. The advantages of the new algorithms are demonstrated via numerical examples, demonstrating superior stability compared to existing variational integrators for these systems and superior qualitative behavior compared to non-conservative algorithms

Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology

The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop quantum gravity. The path integrals can be formulated in both timeless and deparameterized frameworks. It turns out that the effective Hamiltonians derived from the two different viewpoints are equivalent to each other. Moreover, the first-order modified Friedmann equations are derived and predict quantum bounces for contracting universe, which coincide with those obtained in canonical theory.Comment: 8 pages. arXiv admin note: substantial text overlap with arXiv:1102.475

Dependence of the flux creep activation energy on current density and magnetic field for MgB2 superconductor

Systematic ac susceptibility measurements have been performed on a MgB$_2$ bulk sample. We demonstrate that the flux creep activation energy is a nonlinear function of the current density $U(j)\propto j^{-0.2}$, indicating a nonlogarithmic relaxation of the current density in this material. The dependence of the activation energy on the magnetic field is determined to be a power law $U(B)\propto B^{-1.33}$, showing a steep decline in the activation energy with the magnetic field, which accounts for the steep drop in the critical current density with magnetic field that is observed in MgB$_2$. The irreversibility field is also found to be rather low, therefore, the pinning properties of this new material will need to be enhanced for practical applications.Comment: 11 pages, 6 figures, Revtex forma