Development of a high altitude Stokes flow decelerator Final report

Drag generation theory, design, and drop tests for high altitude Stokes flow decelerato

Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces

We study the general deformed conformal-Poincare (Galilean) symmetries consistent with relativistic (nonrelativistic) canonical noncommutative spaces. In either case we obtain deformed generators, containing arbitrary free parameters, which close to yield new algebraic structures. We show that a particular choice of these parameters reproduces the undeformed algebra. The modified coproduct rules and the associated Hopf algebra are also obtained. Finally, we show that for the choice of parameters leading to the undeformed algebra, the deformations are represented by twist functions.Comment: 9 pages, LaTeX, shortened, version appearing in Phys. Rev.

Ehrenfest theorem, Galilean invariance and nonlinear Schr\"odinger equations

Galilean invariant Schr\"odinger equations possessing nonlinear terms coupling the amplitude and the phase of the wave function can violate the Ehrenfest theorem. An example of this kind is provided. The example leads to the proof of the theorem: A Galilean invariant Schr\"odinger equation derived from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for any linear or nonlinear lagrangian.Comment: Latex format, no figures, submitted to journal of physics

Structure and activity relationships for amine-based CO2 absorbents-II

A study to determine the structure and activity relationships of various amine-based CO2 absorbents was performed, in which the absorption of pure CO2 at atmospheric pressure was measured to assess the total absorption rates and capacities. Steric hindrance effect was noticed when side chain with alkyl group was present at the α-carbon to the amine group in the absorbent structure. An increase in the number of amine groups in absorbent structure, results in a higher capacity of upto 3.03 moles CO2/moles amine. Aromatic amines substituted with alkyl groups at the 2nd and 5th position show an increase in both absorption rate and capacity. © 2008 The Institution of Chemical Engineers

Efimov effect from functional renormalization

We apply a field-theoretic functional renormalization group technique to the few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with U(1) symmetry, two-component fermions with U(1)\times SU(2) symmetry and three-component fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant unitarity limit for infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed point behavior for all considered systems. Nevertheless, the numerical three-body solution in the s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be approximately s=1.006, consistent with the result of Efimov.Comment: 21 pages, 6 figures, minor changes, published versio

SO(2,1) conformal anomaly: Beyond contact interactions

The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory, within which lies the apparent singularity.Comment: 11 pages. A few typos corrected in the final versio

On the new approach to variable separation in the time-dependent Schr\"odinger equation with two space dimensions

We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit separation of variables. Besides that, we carry out separation of variables in the Schr\" odinger equation with the anisotropic harmonic oscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of coordinate systems providing its separability. Most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schr\" odinger equation ($V=0$).Comment: 21 pages, latex, to appear in the "Journal of Mathematical Physics" (1995

Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schr\"odinger equation

The non-standard quantum deformation of the (trivially) extended sl(2,R) algebra is used to construct a new quantum deformation of the two-photon algebra h_6 and its associated quantum universal R-matrix. A deformed one-boson representation for this algebra is deduced and applied to construct a first order deformation of the differential equation that generates the two-photon algebra eigenstates in Quantum Optics. On the other hand, the isomorphism between h_6 and the (1+1) Schr\"odinger algebra leads to a new quantum deformation for the latter for which a differential-difference realization is presented. From it, a time discretization of the heat-Schr\"odinger equation is obtained and the quantum Schr\"odinger generators are shown to be symmetry operators.Comment: 12 pages, LaTe