50,674 research outputs found
Relativistic N-boson systems bound by pair potentials V(r_{ij}) = g(r_{ij}^2)
We study the lowest energy E of a relativistic system of N identical bosons
bound by pair potentials of the form V(r_{ij}) = g(r_{ij}^2) in three spatial
dimensions. In natural units hbar = c = 1 the system has the semirelativistic
`spinless-Salpeter' Hamiltonian H = \sum_{i=1}^N \sqrt{m^2 + p_i^2} +
\sum_{j>i=1}^N g(|r_i - r_j|^2), where g is monotone increasing and has
convexity g'' >= 0. We use `envelope theory' to derive formulas for general
lower energy bounds and we use a variational method to find complementary upper
bounds valid for all N >= 2. In particular, we determine the energy of the
N-body oscillator g(r^2) = c r^2 with error less than 0.15% for all m >= 0, N
>= 2, and c > 0.Comment: 15 pages, 4 figure
Convexity and potential sums for Salpeter-like Hamiltonians
The semirelativistic Hamiltonian H = \beta\sqrt{m^2 + p^2} + V(r), where V(r)
is a central potential in R^3, is concave in p^2 and convex in p. This fact
enables us to obtain complementary energy bounds for the discrete spectrum of
H. By extending the notion of 'kinetic potential' we are able to find general
energy bounds on the ground-state energy E corresponding to potentials with the
form V = sum_{i}a_{i}f^{(i)}(r). In the case of sums of powers and the log
potential, where V(r) = sum_{q\ne 0} a(q) sgn(q)r^q + a(0)ln(r), the bounds can
all be expressed in the semi-classical form E \approx \min_{r}{\beta\sqrt{m^2 +
1/r^2} + sum_{q\ne 0} a(q)sgn(q)(rP(q))^q + a(0)ln(rP(0))}. 'Upper' and 'lower'
P-numbers are provided for q = -1,1,2, and for the log potential q = 0. Some
specific examples are discussed, to show the quality of the bounds.Comment: 21 pages, 4 figure
Coulomb plus power-law potentials in quantum mechanics
We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the
Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q >
-2 and q \ne 0. We show by envelope theory that the discrete eigenvalues
E_{n\ell} of H may be approximated by the semiclassical expression
E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}.
Values of mu and nu are prescribed which yield upper and lower bounds.
Accurate upper bounds are also obtained by use of a trial function of the form,
psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for
V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with
comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure
Energy bounds for the spinless Salpeter equation: harmonic oscillator
We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H =
\beta\sqrt(m^2 + p^2) + vr^2, v>0, \beta > 0, in three dimensions. By using
geometrical arguments we show that, for suitable values of P, here provided,
the simple semi-classical formula E = min_{r > 0} {v(P/r)^2 + \beta\sqrt(m^2 +
r^2)} provides both upper and lower energy bounds for all the eigenvalues of
the problem.Comment: 8 pages, 1 figur
Application of satellite imagery to hydrologic modeling snowmelt runoff in the southern Sierra Nevada
There are no author-identified significant results in this report
The large area crop inventory experiment: A major demonstration of space remote sensing
Strategies are presented in agricultural technology to increase the resistance of crops to a wider range of meteorological conditions in order to reduce year-to-year variations in crop production. Uncertainties in agricultral production, together with the consumer demands of an increasing world population, have greatly intensified the need for early and accurate annual global crop production forecasts. These forecasts must predict fluctuation with an accuracy, timeliness and known reliability sufficient to permit necessary social and economic adjustments, with as much advance warning as possible
Relativistic N-Boson Systems Bound by Oscillator Pair Potentials
We study the lowest energy E of a relativistic system of N identical bosons
bound by harmonic-oscillator pair potentials in three spatial dimensions. In
natural units the system has the semirelativistic ``spinless-Salpeter''
Hamiltonian H = \sum_{i=1}^N \sqrt{m^2 + p_i^2} + \sum_{j>i=1}^N gamma |r_i -
r_j|^2, gamma > 0. We derive the following energy bounds: E(N) = min_{r>0} [N
(m^2 + 2 (N-1) P^2 / (N r^2))^1/2 + N (N-1) gamma r^2 / 2], N \ge 2, where
P=1.376 yields a lower bound and P=3/2 yields an upper bound for all N \ge 2. A
sharper lower bound is given by the function P = P(mu), where mu =
m(N/(gamma(N-1)^2))^(1/3), which makes the formula for E(2) exact: with this
choice of P, the bounds coincide for all N \ge 2 in the Schroedinger limit m
--> infinity.Comment: v2: A scale analysis of P is now included; this leads to revised
energy bounds, which coalesce in the large-m limi
Extended analytical study of the free-wing/free-trimmer concept
The free wing/free trimmer concept was analytically studied in order to: (1) compare the fore and aft trimmer configurations on the basis of equal lift capability, rather than equal area; (2) assess the influence of tip mounted aft trimmers, both free and fixed, on the lateral directional modes and turbulence responses; (3) examine the feasibility of using differential tip mounted trimmer deflection for lateral control; (4) determine the effects of independent fuselage attitude on the lateral directional behavior; and (5) estimate the influence of wing sweep on dynamic behavior and structural weight. Results indicate that the forward trimmer concept is feasible with the reduced size examined, but it remains inferior to the aft trimmer in every respect except structural weight. Differential motion of the aft trimmer is found to provide powerful lateral control; while the effect of fuselage deck angle is a reduction of the dutch roll damping ratio for nose-down attitudes
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