Status of Lattice QCD

Significant progress has recently been achieved in the lattice gauge theory calculations required for extracting the fundamental parameters of the standard model from experiment. Recent lattice determinations of such quantities as the kaon $B$ parameter, the mass of the $b$ quark, and the strong coupling constant have produced results and uncertainties as good or better than the best conventional determinations. Many other calculations crucial to extracting the fundamental parameters of the standard model from experimental data are undergoing very active development. I review the status of such applications of lattice QCD to standard model phenomenology, and discuss the prospects for the near future.Comment: 20 pages, 8 embedded figures, uuencoded, 2 missing figures. (Talk presented at the Lepton-Photon Symposium, Cornell University, Aug. 10-15, 1993.

Variable Powder Flow Rate Control in Laser Metal Deposition Processes

This paper proposes a novel technique, called Variable Powder Flow Rate Control (VPFRC), for the regulation of powder flow rate in laser metal deposition processes. The idea of VPFRC is to adjust the powder flow rate to maintain a uniform powder deposition per unit length even when disturbances occur (e.g., the motion system accelerates and decelerates). Dynamic models of the powder delivery system motor and the powder transport system (i.e., five–meter pipe, powder dispenser, and cladding head) are first constructed. A general tracking controller is then designed to track variable powder flow rate references. Since the powder flow rate at the nozzle exit cannot be directly measured, it is estimated using the powder transport system model. The input to this model is the DC motor rotation speed, which is estimated on–line using a Kalman filter. Experiments are conducted to examine the performance of the proposed control methodology. The experimental results demonstrate that VPFRC is successful in maintaining a uniform track morphology, even when the motion control system accelerates and decelerates.Mechanical Engineerin

Elliptic CR-manifolds and shear invariant ODE with additional symmetries

We classify the ODEs that correspond to elliptic CR-manifolds with maximal isotropy. It follows that the dimension of the isotropy group of an elliptic CR-manifold can be only 10 (for the quadric), 4 (for the listed examples) or less. This is in contrast with the situation of hyperbolic CR-manifolds, where the dimension can be 10 (for the quadric), 6 or 5 (for semi-quadrics) or less than 4. We also prove that, for all elliptic CR-manifolds with non-linearizable istropy group, except for two special manifolds, the points with non-linearizable isotropy form exactly some complex curve on the manifold

Nucleon-nucleon cross sections in neutron-rich matter and isospin transport in heavy-ion reactions at intermediate energies

Nucleon-nucleon (NN) cross sections are evaluated in neutron-rich matter using a scaling model according to nucleon effective masses. It is found that the in-medium NN cross sections are not only reduced but also have a different isospin dependence compared with the free-space ones. Because of the neutron-proton effective mass splitting the difference between nn and pp scattering cross sections increases with the increasing isospin asymmetry of the medium. Within the transport model IBUU04, the in-medium NN cross sections are found to influence significantly the isospin transport in heavy-ion reactions. With the in-medium NN cross sections, a symmetry energy of $E_{sym}(\rho)\approx 31.6(\rho /\rho_{0})^{0.69}$ was found most acceptable compared with both the MSU isospin diffusion data and the presently acceptable neutron-skin thickness in $^{208}$Pb. The isospin dependent part $K_{asy}(\rho _{0})$ of isobaric nuclear incompressibility was further narrowed down to $-500\pm 50$ MeV. The possibility of determining simultaneously the in-medium NN cross sections and the symmetry energy was also studied. The proton transverse flow, or even better the combined transverse flow of neutrons and protons, can be used as a probe of the in-medium NN cross sections without much hindrance from the uncertainties of the symmetry energy.Comment: 32 pages including 14 figures. Submitted to Phys. Rev.

Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear ODEs and using the original system to replace the second derivative. The procedure developed splits into two cases, those where the coefficients are constant and those where they are variables. Both cases are discussed and examples given

A Group Theoretical Identification of Integrable Equations in the Li\'enard Type Equation x¨+f(x)x˙+g(x)=0\ddot{x}+f(x)\dot{x}+g(x) = 0 : Part II: Equations having Maximal Lie Point Symmetries

In this second of the set of two papers on Lie symmetry analysis of a class of Li\'enard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are smooth functions of their variables, we isolate the equations which possess maximal Lie point symmetries. It is well known that any second order nonlinear ordinary differential equation which admits eight parameter Lie point symmetries is linearizable to free particle equation through point transformation. As a consequence all the identified equations turn out to be linearizable. We also show that one can get maximal Lie point symmetries for the above Li\'enard equation only when $f_{xx} =0$ (subscript denotes differentiation). In addition, we discuss the linearising transformations and solutions for all the nonlinear equations identified in this paper.Comment: Accepted for publication in Journal of Mathematical Physic

Contact symmetry of time-dependent Schr\"odinger equation for a two-particle system: symmetry classification of two-body central potentials

Symmetry classification of two-body central potentials in a two-particle Schr\"{o}dinger equation in terms of contact transformations of the equation has been investigated. Explicit calculation has shown that they are of the same four different classes as for the point transformations. Thus in this problem contact transformations are not essentially different from point transformations. We have also obtained the detailed algebraic structures of the corresponding Lie algebras and the functional bases of invariants for the transformation groups in all the four classes

Realizations of Real Low-Dimensional Lie Algebras

Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of variables. Our classification amends and essentially generalizes earlier works on the subject. Known results on classification of low-dimensional real Lie algebras, their automorphisms, differentiations, ideals, subalgebras and realizations are reviewed.Comment: LaTeX2e, 39 pages. Essentially exetended version. Misprints in Appendix are correcte