12,031 research outputs found
Solving simple quaternionic differential equations
The renewed interest in investigating quaternionic quantum mechanics, in
particular tunneling effects, and the recent results on quaternionic
differential operators motivate the study of resolution methods for
quaternionic differential equations. In this paper, by using the real matrix
representation of left/right acting quaternionic operators, we prove existence
and uniqueness for quaternionic initial value problems, discuss the reduction
of order for quaternionic homogeneous differential equations and extend to the
non-commutative case the method of variation of parameters. We also show that
the standard Wronskian cannot uniquely be extended to the quaternionic case.
Nevertheless, the absolute value of the complex Wronskian admits a
non-commutative extension for quaternionic functions of one real variable.
Linear dependence and independence of solutions of homogeneous (right) H-linear
differential equations is then related to this new functional. Our discussion
is, for simplicity, presented for quaternionic second order differential
equations. This involves no loss of generality. Definitions and results can be
readily extended to the n-order case.Comment: 9 pages, AMS-Te
Supersonic through-flow fan engine and aircraft mission performance
A study was made to evaluate potential improvement to a commercial supersonic transport by powering it with supersonic through-flow fan turbofan engines. A Mach 3.2 mission was considered. The three supersonic fan engines considered were designed to operate at bypass ratios of 0.25, 0.5, and 0.75 at supersonic cruise. For comparison a turbine bypass turbojet was included in the study. The engines were evaluated on the basis of aircraft takeoff gross weight with a payload of 250 passengers for a fixed range of 5000 N.MI. The installed specific fuel consumption of the supersonic fan engines was 7 to 8 percent lower than that of the turbine bypass engine. The aircraft powered by the supersonic fan engines had takeoff gross weights 9 to 13 percent lower than aircraft powered by turbine bypass engines
Quaternionic Electroweak Theory and CKM Matrix
We find in our quaternionic version of the electroweak theory an apparently
hopeless problem: In going from complex to quaternions, the calculation of the
real-valued parameters of the CKM matrix drastically changes. We aim to explain
this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published
The octonionic eigenvalue problem
By using a real matrix translation, we propose a coupled eigenvalue problem
for octonionic operators. In view of possible applications in quantum
mechanics, we also discuss the hermiticity of such operators. Previous
difficulties in formulating a consistent octonionic Hilbert space are solved by
using the new coupled eigenvalue problem and introducing an appropriate scalar
product for the probability amplitudes.Comment: 21 page
Steady state and transient temperature distributions in the human thigh covered with a cooling pad
An analytical and experimental study was done on the performance of cooling pads attached to a human thigh. Each cooling pad consisted of a long, water cooled tube formed into a serpentine shape with uniform spacing between the parallel sections. The analytical work developed a cylindrical model for the human thigh. The transient times predicted by this model ranged from 25 to 80 minutes, which is reasonably close to the experimental results. Calculated and measured steady state temperature profiles were in fair agreement. The transient times associated with a change from a high metabolic rate of 1800 Btu/hr (528 w) to a low level of 300 Btu/hr (88 w), were found to be about 120 minutes. A change from 300 Btu/hr (264 w) to 300 Btu/hr (88 w) resulted in 90 to 100 minute transients. However, the transient times for a change in metabolic rate in the opposite direction from 300 Btu/hr (88 w) to 1800 Btu/hr (528 w) were 40 to 60 minutes
Right eigenvalue equation in quaternionic quantum mechanics
We study the right eigenvalue equation for quaternionic and complex linear
matrix operators defined in n-dimensional quaternionic vector spaces. For
quaternionic linear operators the eigenvalue spectrum consists of n complex
values. For these operators we give a necessary and sufficient condition for
the diagonalization of their quaternionic matrix representations. Our
discussion is also extended to complex linear operators, whose spectrum is
characterized by 2n complex eigenvalues. We show that a consistent analysis of
the eigenvalue problem for complex linear operators requires the choice of a
complex geometry in defining inner products. Finally, we introduce some
examples of the left eigenvalue equations and highlight the main difficulties
in their solution.Comment: 24 pages, AMS-Te
Alien Registration- Godin, Leo C J. (Westbrook, Cumberland County)
https://digitalmaine.com/alien_docs/20051/thumbnail.jp
Quaternionic potentials in non-relativistic quantum mechanics
We discuss the Schrodinger equation in presence of quaternionic potentials.
The study is performed analytically as long as it proves possible, when not, we
resort to numerical calculations. The results obtained could be useful to
investigate an underlying quaternionic quantum dynamics in particle physics.
Experimental tests and proposals to observe quaternionic quantum effects by
neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te
The Asymptotic Giant Branch and the Tip of the Red Giant Branch as Probes of Star Formation History: The Nearby Dwarf Irregular Galaxy KKH 98
We investigate the utility of the asymptotic giant branch (AGB) and the red
giant branch (RGB) as probes of the star formation history (SFH) of the nearby
(D=2.5 Mpc) dwarf irregular galaxy, KKH 98. Near-infrared (IR) Keck Laser Guide
Star Adaptive Optics (AO) images resolve 592 IR bright stars reaching over 1
magnitude below the Tip of the Red Giant Branch. Significantly deeper optical
(F475W and F814W) Hubble Space Telescope images of the same field contain over
2500 stars, reaching to the Red Clump and the Main Sequence turn-off for 0.5
Gyr old populations. Compared to the optical color magnitude diagram (CMD), the
near-IR CMD shows significantly tighter AGB sequences, providing a good probe
of the intermediate age (0.5 - 5 Gyr) populations. We match observed CMDs with
stellar evolution models to recover the SFH of KKH 98. On average, the galaxy
has experienced relatively constant low-level star formation (5 x 10^-4 Mo
yr^-1) for much of cosmic time. Except for the youngest main sequence
populations (age < 0.1 Gyr), which are typically fainter than the AO data flux
limit, the SFH estimated from the the 592 IR bright stars is a reasonable match
to that derived from the much larger optical data set. Differences between the
optical and IR derived SFHs for 0.1 - 1 Gyr populations suggest that current
stellar evolution models may be over-producing the AGB by as much as a factor
of three in this galaxy. At the depth of the AO data, the IR luminous stars are
not crowded. Therefore these techniques can potentially be used to determine
the stellar populations of galaxies at significantly further distances.Comment: 15 pages, 14 figs, accepted for publication in Ap
Mutual Inductance Route to Paramagnetic Meissner Effect in 2D Josephson Junction Arrays
We simulate two-dimensional Josephson junction arrays, including full mutual-
inductance effects, as they are cooled below the transition temperature in a
magnetic field. We show numerical simulations of the array magnetization as a
function of position, as detected by a scanning SQUID which is placed at a
fixed height above the array. The calculated magnetization images show striking
agreement with the experimental images obtained by A. Nielsen et al. The
average array magnetization is found to be paramagnetic for many values of the
applied field, confirming that paramagnetism can arise from magnetic screening
in multiply-connected superconductors without the presence of d-wave
superconductivity.Comment: REVTeX 3.1, 5 pages, 5 figure
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