Generic scaling relation in the scalar ϕ4\phi^{4} model

The results of analysis of the one--loop spectrum of anomalous dimensions of composite operators in the scalar $\phi^{4}$ model are presented. We give the rigorous constructive proof of the hypothesis on the hierarchical structure of the spectrum of anomalous dimensions -- the naive sum of any two anomalous dimensions generates a limit point in the spectrum. Arguments in favor of the nonperturbative character of this result and the possible ways of a generalization to other field theories are briefly discussed.Comment: 15 pages, Latex, 50 K

Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory

For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP, and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e., its integrand contains only the coordinates of two electron, say r1 and r2, and it has a Dirac delta function -- delta(r1 - r2) -- as a factor. Since Brueckner and Hartree--Fock orbitals are often very similar, any local exchange functional that works well with Hartree--Fock theory is a reasonable approximation with reference-state one-particle density-matrix theory. The LDA approximation is also a reasonable approximation. However, the Colle--Salvetti correlation-energy functional, and the LYP variant, are not ideal for the method, since these are universal functionals. Nevertheless, they appear to provide reasonable approximations. The B3LYP functional is derived using a linear combination of two functionals: One is the BLYP functional; the other uses exact exchange and a correlation-energy functional from the LDA.Comment: 26 Pages, 0 figures, RevTeX 4, Submitted to Mol. Phy

New continuous wave infrared Ar‐Xe laser at intermediate gas pressures pumped by a transverse radio frequency discharge

An atomic Xe laser with a transverse rf excitation has been operated in a cw mode in the intermediate pressure regime. The laser output spectrum consisted of 5 Xe lines with wavelengths of 2.03, 2.63, 2.65, 3.37, and 3.51 μm. The unoptimized total output power of 330 mW was obtained for a gas mixture Ar:He:Xe=59:40:1 at a pressure of 85 Torr and a rf input power of 150 W and excitation frequency of 121 MHz

Numerical Modeling of a Granular Collapse Immersed in a Viscous Fluid

The three-dimensional unsteady collapse of the granular column in a viscous fluid has been investigated with an IBM/DEM approach. Present numerical simulations allow one to confirm quantitatively several experimental observations of Rondon et al. regarding morphology, characteristic sizes of granular deposits and the basal pressure below the column. In the presented simulations, the collapse dynamics is controlled by the viscous time Tv. To our knowledge, a numerical approach, e.g. the IBM/DEM method, is able for the first time to capture the pore pressure feedback phenomenon in flowing fluid-grains mixture. The effect of the initial packing fraction has a great influence of the dynamics of granular collapse in the simulation results as in the experiments of Rondon et al. Furthermore, the IBM/DEM permits to investigate the inner state of the granular column during the collapse, in particular, the evolution of the pressure field inside the granular column can be analyzed which is difficult to do in experiments. Simulations of the collapse of a granular column immersed in a fluid can be performed in the inertial and free-fall regimes as well varying the nature of the fluid and/or the particles

Discrete element simulation and experimental study of powder spreading process in additive manufacturing

Powders used in additive manufacturing (AM) are spread into a compact layer of particles for sintering and this process is repeated layer by layer to form the final products. Spreading of rod-shaped particles in realistic AM settings is simulated using the discrete element method (DEM) to investigate the effects of particle shape and operating conditions on the bed quality, characterised by its surface roughness and solid volume fraction. It is discovered that larger particle aspect ratios, Ar, or higher spreader translational velocities result in a lower bed quality, i.e. a larger surface roughness and a smaller volume fraction. The surface roughness increases monotonically with Ar. However, the volume fraction exhibits a maximum at Ar = 1.5 for randomly packed powder beds that are formed by the roller type spreaders moving at low translational velocities. It is also found that a roller outperforms a blade spreader in terms of the quality of the prepared bed at the same operating conditions. The micro-structural analysis of the beds also shows particle alignment in response to the induced flow, which is qualitatively confirmed by a set of purposely-designed experiments. In addition, a shape segregation is documented for powders with mixed aspect ratios (Ar) such that particles with larger Ar tend to accumulate on the upper layers of the bed

Force Schemes in Simulations of Granular Materials

In computer simulations of granular flow, one widely used technique is classical soft-sphere Molecular Dynamics, where the equations of motion of the particles are numerically integrated. This requires specification of the forces acting between grains. In this paper, we systematically study the properties of the force laws most commonly used and compare them with recent experiments on the impact of spheres. We point out possible problems and give criteria for the right choice of parameters. Finally, two generic problems of soft-sphere simulations are discussed

A novel bidirectional pendulum tuned mass damper using variable homogeneous friction to achieve amplitude‐independent control

Passive tuned mass dampers (TMDs) are widely used in controlling structural vibrations. Although their principle is well established, the search for improved arrangements is still under way. This effort has recently produced an innovative paradigm of bidirectional pendulum TMD (BTMD) that, moving along a specially designed three‐dimensional (3D) surface, can simultaneously control two in‐plane orthogonal structural modes. In existing versions of BTMDs, energy dissipation is provided either by ordinary horizontal viscous dampers or by an original arrangement of vertical friction dampers. In this paper, a new paradigm is proposed, in which energy dissipation comes from the tangential friction arising along the pendulum surface out of an optimal spatially variable friction coefficient pattern. Within this paradigm, if the friction coefficient is taken proportional to the modulus of the pendulum surface gradient, the dissipation model results nonlinear homogeneous in the smalldisplacement domain, and the performance of the absorber, herein called the homogeneous tangential friction BTMD (HT‐BTMD), results independent from the excitation level. The present work introduces this concept, derives the analytical model of the HT‐BTMD, establishes a method for its optimal design, and numerically verifies its seismic effectiveness in comparison with viscously damped devices. The validity and feasibility of the concept are demonstrated through experimental tests on a small‐scale lab prototype, which also show the efficacy of a stepwise approximation of the homogeneous friction pattern. The new device proves a competing alternative to existing BTMDs, and homogeneous tangential friction proves a promising new paradigm to provide pendular systems with amplitude‐independent structural damping