Approximate minimum-time trajectories for 2-link flexible manipulators

Powell's nonlinear programming code, VF02AD, was used to generate approximate minimum-time tip trajectories for 2-link semi-rigid and flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for an n-link, m-joint system with horizontal-plane bending only. Constraints on the trajectory include boundary conditions on position and energy for a rest-to-rest maneuver, straight-line tracking between boundary positions, and motor torque limits. Trajectory comparisons utilize a change in the link stiffness, EI, to transition from the semi-rigid to flexible case. Results show the level of compliance necessary to excite significant modal behavior. Quiescence of the final configuration is examined with the finite-element model

Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200

Exact results for `bouncing' Gaussian wave packets

We consider time-dependent Gaussian wave packet solutions of the Schrodinger equation (with arbitrary initial central position, x_0, and momentum, p_0, for an otherwise free-particle, but with an infinite wall at x=0, so-called bouncing wave packets. We show how difference or mirror solutions of the form psi(x,t)-psi(-x,t) can, in this case, be normalized exactly, allowing for the evaluation of a number of time-dependent expectation values and other quantities in closed form. For example, we calculate _t explicitly which illustrates how the free-particle kinetic (and hence total) energy is affected by the presence of the distant boundary. We also discuss the time dependence of the expectation values of position, _t, and momentum, _t, and their relation to the impulsive force during the `collision' with the wall. Finally, the x_0,p_0 --> 0 limit is shown to reduce to a special case of a non-standard free-particle Gaussian solution. The addition of this example to the literature then expands on the relatively small number of Gaussian solutions to quantum mechanical problems with familiar classical analogs (free particle, uniform acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic field) available in closed form.Comment: 14 pages, 1 embedded .eps figur

Leptoquark production in ultrahigh-energy neutrino interactions revisited

The prospects for producing leptoquarks (LQs) in ultrahigh-energy (UHE) neutrino nucleon collisions are re-examined in the light of recent interpretations of HERA data in terms of leptoquark production. We update predictions for cross-sections for the production of first- and second-generation leptoquarks in UHE nu-N and nubar-N collisions including (i) recent experimental limits on masses and couplings from the LEP and TEVATRON colliders as well as rare processes, (ii) modern parton distributions, and (iii) radiative corrections to single leptoquark production. If the HERA events are due to an SU(2) doublet leptoquark which couples mainly to (e+,q) states, we argue that there are likely other LQ states which couple to neutrinos which are close in mass, due to constraints from precision electroweak measurements.Comment: 12 pages, LaTeX, 3 separate postscript figures. Added 1 reference plus discussion, updated another referenc

The Stark effect in linear potentials

We examine the Stark effect (the second-order shift in the energy spectrum due to an external constant force) for two 1-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z>0 and V(z) infinite for z<0) and the symmetric linear potential (given by V(z) = F|z|). We show how straightforward use of the most obvious properties of the Airy function solutions and simple Taylor expansions give closed form results for the Stark shifts in both systems. These exact results are then compared to other approximation techniques, such as perturbation theory and WKB methods. These expressions add to the small number of closed-form descriptions available for the Stark effect in model quantum mechanical systems.Comment: 15 pages. To appear in Eur. J. Phys. Needs Institute of Physics (iopart) style file

Spin-Spin Asymmetries in Large Transverse Momentum Higgs Boson Production

We examine the spin-dependence of standard model Higgs boson production at large transverse momentum via the processes $gg \rightarrow gH^0$, $qg \rightarrow qH^0$, and $q\overline{q} \rightarrow gH^0$. The partonic level spin-spin asymmetries ($\hat{a}_{LL}$) for these processes are large at SSC/LHC energies.Comment: 10 pages, 4 figures (not included), LaTeX; PSU/TH/113, MAD/PH/70

Reconstruction of the Extended Gauge Structure from Z′Z' Observables at Future Colliders

The discovery of a new neutral gauge boson $Z'$ with a mass in the TeV region would allow for determination of gauge couplings of the $Z'$ to ordinary quarks and leptons in a model independent way. We show that these couplings in turn would allow us to determine the nature of the extended gauge structure. As a prime example we study the $E_6$ group. In this case two discrete constraints on experimentally determined couplings have to be satisfied. If so, the couplings would then uniquely determine the two parameters, $\tan \beta$ and $\delta$, which fully specify the nature of the $Z'$ within $E_6$. If the $Z'$ is part of the $E_6$ gauge structure, then for $M_{Z'}=1$ TeV $\tan \beta$ and $\delta$ could be determined to around $10\%$ at the future colliders. The NLC provides a unique determination of the two constraints as well as of $\tan \beta$ and $\delta$, though with slightly larger error bars than at the LHC. On the other hand, since the LHC primarily determines three out of four normalized couplings, it provides weaker constraints for the underlying gauge structure.Comment: 14 pages LaTeX using RevTeX and psfig.sty. TeX source and 3 PS figures, tarred, compressed and uuencoded; also available via anonymous ftp to ftp://dept.physics.upenn.edu/pub/Cvetic/UPR-636-T

Forward-Backward Asymmetries in Hadronically Produced Lepton Pairs

It has now become possible to observe appreciable numbers of hadronically produced lepton pairs in mass ranges where the contributions of the photon and $Z^0$ are comparable. Consequently, in the reaction $p \bar p \to \ell^- \ell^+ + \ldots$, substantial forward-backward asymmetries can be seen. These asymmetries provide a test of the electroweak theory in a new regime of energies, and can serve as diagnostics for any new neutral vector bosons coupling both to quarks and to charged lepton pairs.Comment: 11 pages, latex, 4 uuencoded figures sent separately, Fig. 2 revise

Supersymmetric Sum Rules for Electromagnetic Multipoles

We derive model independent, non-perturbative supersymmetric sum rules for the magnetic and electric multipole moments of any theory with N=1 supersymmetry. We find that in any irreducible N=1 supermultiplet the diagonal matrix elements of the l-multipole moments are completely fixed in terms of their off-diagonal matrix elements and the diagonal (l-1)-multipole moments.Comment: 10 pages, plain Te