Fourth Order Algorithms for Solving the Multivariable Langevin Equation and the Kramers Equation

We develop a fourth order simulation algorithm for solving the stochastic Langevin equation. The method consists of identifying solvable operators in the Fokker-Planck equation, factorizing the evolution operator for small time steps to fourth order and implementing the factorization process numerically. A key contribution of this work is to show how certain double commutators in the factorization process can be simulated in practice. The method is general, applicable to the multivariable case, and systematic, with known procedures for doing fourth order factorizations. The fourth order convergence of the resulting algorithm allowed very large time steps to be used. In simulating the Brownian dynamics of 121 Yukawa particles in two dimensions, the converged result of a first order algorithm can be obtained by using time steps 50 times as large. To further demostrate the versatility of our method, we derive two new classes of fourth order algorithms for solving the simpler Kramers equation without requiring the derivative of the force. The convergence of many fourth order algorithms for solving this equation are compared.Comment: 19 pages, 2 figure

Extra Spin-Wave mode in Quantum Hall systems. Beyond the Skyrmion Limit

We report on the observation of a new spin mode in a quantum Hall system in the vicinity of odd electron filling factors under experimental conditions excluding the possibility of Skyrmion excitations. The new mode having presumably zero energy at odd filling factors emerges at small deviations from odd filling factors and couples to the spin-exciton. The existence of an extra spin mode assumes a nontrivial magnetic order at partial fillings of Landau levels surrounding quantum Hall ferromagnets other then the Skyrmion crystal.Comment: 9 pages, 4 figure

The nonlinear time-dependent response of isotactic polypropylene

Tensile creep tests, tensile relaxation tests and a tensile test with a constant rate of strain are performed on injection-molded isotactic polypropylene at room temperature in the vicinity of the yield point. A constitutive model is derived for the time-dependent behavior of semi-crystalline polymers. A polymer is treated as an equivalent network of chains bridged by permanent junctions. The network is modelled as an ensemble of passive meso-regions (with affine nodes) and active meso-domains (where junctions slip with respect to their positions in the bulk medium with various rates). The distribution of activation energies for sliding in active meso-regions is described by a random energy model. Adjustable parameters in the stress--strain relations are found by fitting experimental data. It is demonstrated that the concentration of active meso-domains monotonically grows with strain, whereas the average potential energy for sliding of junctions and the standard deviation of activation energies suffer substantial drops at the yield point. With reference to the concept of dual population of crystalline lamellae, these changes in material parameters are attributed to transition from breakage of subsidiary (thin) lamellae in the sub-yield region to fragmentation of primary (thick) lamellae in the post-yield region of deformation.Comment: 29 pages, 12 figure

The use of titanium alloys for details of downhole hammers

The influence of cementation technology of titanium alloy Ti-Al-Mn on its wear resistance is studied. It is established that after lubrication a friction pair with mineral oil the wear resistance of the cemented titanium alloy is comparable to wear resistance of the tempered steel 12HN3A, and in water medium surpasses it by 1.5 times. Decrease in the tendency to seizure with steel is the main reason for increase of wear resistance of titanium alloy. Industrial tests of the ASH43 hammer have shown that the use of titanium alloys for the manufacture of hammer strikers allows to increase impact capacity by 1.5 times and to increase drilling rate by 30 % compared to hammers with steel strikers

Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts.

The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes

High-Energy Approach for Heavy-Ion Scattering with Excitations of Nuclear Collective States

A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach analytical expressions for elastic and inelastic scattering amplitudes are obtained where all the orders in the deformation parameters are included. The multistep effect of the 2$^+$ rotational state excitation on elastic scattering is analyzed. Calculations of inelastic cross sections for the $^{17}$O ions scattered on different nuclei at about hundred Mev/nucleon are compared with experimental data, and important role of the Coulomb excitation is established.Comment: 9 pages; 3 figures. Submitted to the Physics of Atomic Nucle

On the construction of high-order force gradient algorithms for integration of motion in classical and quantum systems

A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the new fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth- and eighth-order-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.Comment: 23 pages, 2 figures; submitted to Phys. Rev.

Kinetic equations for thermal degradation of polymers

Kinetic equations are analyzed for thermal degradation of polymers. The governing relations are based on the fragmentation-annihilation concept. Explicit solutions to these equations are derived in two particular cases of interest. For arbitrary values of adjustable parameters, the evolution of the number-average and mass-average molecular weights of polymers is analyzed numerically. Good agreement is demonstrated between the results of numerical simulation and experimental data. It is revealed that the model can correctly predict observations in thermo-gravimetric tests when its parameters are determined by matching experimental data for the decrease in molecular weight with exposure time

Early Observations and Analysis of the Type Ia SN 2014J in M82

We present optical and near infrared (NIR) observations of the nearby Type Ia SN 2014J. Seventeen optical and twenty-three NIR spectra were obtained from 10 days before ($-$10d) to 10 days after (+10d) the time of maximum $B$-band brightness. The relative strengths of absorption features and their patterns of development can be compared at one day intervals throughout most of this period. Carbon is not detected in the optical spectra, but we identify CI $\lambda$ 1.0693 in the NIR spectra. We find that MgII lines with high oscillator strengths have higher initial velocities than other MgII lines. We show that the velocity differences can be explained by differences in optical depths due to oscillator strengths. The spectra of SN 2014J show it is a normal SN Ia, but many parameters are near the boundaries between normal and high-velocity subclasses. The velocities for OI, MgII, SiII, SII, CaII and FeII suggest that SN 2014J has a layered structure with little or no mixing. That result is consistent with the delayed detonation explosion models. We also report photometric observations, obtained from $-$10d to +29d, in the $UBVRIJH$ and $K_s$ bands. SN 2014J is about 3 magnitudes fainter than a normal SN Ia at the distance of M82, which we attribute to extinction in the host. The template fitting package SNooPy is used to interpret the light curves and to derive photometric parameters. Using $R_V$ = 1.46, which is consistent with previous studies, SNooPy finds that $A_V = 1.80$ for $E(B-V)_{host}=1.23 \pm 0.01$ mag. The maximum $B$-band brightness of $-19.19 \pm 0.10$ mag was reached on February 1.74 UT $\pm 0.13$ days and the supernova had a decline parameter of $\Delta m_{15}=1.11 \pm 0.02$ mag.Comment: 6 figures, 6 tables, submitted to the Ap

Nanometric diamond delta doping with boron

Diamond is desired for active semiconducting device because of it high carrier mobility, high voltage breakdown resistance, and high thermal diffusivity. Exploiting diamond as a semiconductor is hampered by the lack of shallow dopants to create sufficient electronic carriers at room temperature. In this work, nanometer thick, heavily boron doped epitaxial diamond ‘delta doped’ layers have been grown on ultra smooth diamond surfaces which demonstrate p type conduction with enhanced Hall mobilities of up to 120 cm2/Vs and sheet carrier concentrations to 6 × 1013 cm–2, thus enabling a new class of active diamond electronic devices