8,130 research outputs found
On the Nonquivalence of Shadow Prices and Dual Variables
The purpose of this paper is to demonstrate that in the event of degeneracy is present in an optimal basic solution to a linear programming problem, the optimal values of the dual variables doe no necessarily correspond to shadow prices. In such instances it will be shown how the actual values of the shadow prices may be determined and the nature of the relationship between shadow prices and dual variables
Contribution and Proportionate Liability under the Federal Securities Laws in Multidefendant Securities Litigation after the Private Securities Litigation Reform Act of 1995
Onset of Wave Drag due to Generation of Capillary-Gravity Waves by a Moving Object as a Critical Phenomenon
The onset of the {\em wave resistance}, via generation of capillary gravity
waves, of a small object moving with velocity , is investigated
experimentally. Due to the existence of a minimum phase velocity for
surface waves, the problem is similar to the generation of rotons in superfluid
helium near their minimum. In both cases waves or rotons are produced at
due to {\em Cherenkov radiation}. We find that the transition to the
wave drag state is continuous: in the vicinity of the bifurcation the wave
resistance force is proportional to for various fluids.Comment: 4 pages, 7 figure
Structural and Compositional Changes in Aging Bone: Osteopenia in Lumbar Vertebrae of Wistar Female Rats
Changes in vertebral bone mineral content and density during aging were quantified in female Wistar rats. This study represents a longitudinal follow up utilizing single photon absorptiometry for the measurement of bone mineral content (BMC), quantitative computed tomography (OCT) for the measurement of bone mineral density (BMD), and image analysis histomorphometry for the measurement of trabecular bone volume (TBV) and bone cortical area (BCA). The above measurements were accompanied by biochemical assays of calcium concentrations in the respective bones. All aging animals experienced significant decreases in BMC, BMD, TBV, BCA and in the calcium content of their bones. The above features have been further emphasized through the use of scanning electron micrographs showing the age-related structural changes in a three-dimentional fashion. New, advanced technologies will enable the quantitation of 3-dimensional images that are currently obtained from the scanning electron micrograph; thus will provide new consideration as related to trabecular bone compactness (density). Energy dispersive x-ray spectroscopy indicated that the nature of crystals in aging bones does not differ markedly from that encountered in young specimens. Data are also provided with regard to the health of the animals, and it became apparent that aging rats undergo changes in their kidneys yet do not show any significant change in renal functional parameters as measured in both the serum and the urine. Hence, new noninvasive methodologies are currently available for longitudinal studies related to the skeleton in laboratory animals enabling reliable monitoring of age-related and hormonally induced changes in bones (spine and hip) of well defined experimental models
Elastic turbulence in curvilinear flows of polymer solutions
Following our first report (A. Groisman and V. Steinberg, \sl Nature , 53 (2000)) we present an extended account of experimental observations of
elasticity induced turbulence in three different systems: a swirling flow
between two plates, a Couette-Taylor (CT) flow between two cylinders, and a
flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of
width of the region available for flow to radius of curvature of the
streamlines. The experiments were carried out with dilute solutions of high
molecular weight polyacrylamide in concentrated sugar syrups. High polymer
relaxation time and solution viscosity ensured prevalence of non-linear elastic
effects over inertial non-linearity, and development of purely elastic
instabilities at low Reynolds number (Re) in all three flows. Above the elastic
instability threshold, flows in all three systems exhibit features of developed
turbulence. Those include: (i)randomly fluctuating fluid motion excited in a
broad range of spatial and temporal scales; (ii) significant increase in the
rates of momentum and mass transfer (compared to those expected for a steady
flow with a smooth velocity profile). Phenomenology, driving mechanisms, and
parameter dependence of the elastic turbulence are compared with those of the
conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure
Conditional probabilities in quantum theory, and the tunneling time controversy
It is argued that there is a sensible way to define conditional probabilities
in quantum mechanics, assuming only Bayes's theorem and standard quantum
theory. These probabilities are equivalent to the ``weak measurement''
predictions due to Aharonov {\it et al.}, and hence describe the outcomes of
real measurements made on subensembles. In particular, this approach is used to
address the question of the history of a particle which has tunnelled across a
barrier. A {\it gedankenexperiment} is presented to demonstrate the physically
testable implications of the results of these calculations, along with graphs
of the time-evolution of the conditional probability distribution for a
tunneling particle and for one undergoing allowed transmission. Numerical
results are also presented for the effects of loss in a bandgap medium on
transmission and on reflection, as a function of the position of the lossy
region; such loss should provide a feasible, though indirect, test of the
present conclusions. It is argued that the effects of loss on the pulse {\it
delay time} are related to the imaginary value of the momentum of a tunneling
particle, and it is suggested that this might help explain a small discrepancy
in an earlier experiment.Comment: 11 pages, latex, 4 postscript figures separate (one w/ 3 parts
Correlation energy of an electron gas in strong magnetic fields at high densities
The high-density electron gas in a strong magnetic field B and at zero
temperature is investigated. The quantum strong-field limit is considered in
which only the lowest Landau level is occupied. It is shown that the
perturbation series of the ground-state energy can be represented in analogy to
the Gell-Mann Brueckner expression of the ground-state energy of the field-free
electron gas. The role of the expansion parameter is taken by r_B= (2/3 \pi^2)
(B/m^2) (\hbar r_s /e)^3 instead of the field-free Gell-Mann Brueckner
parameter r_s. The perturbation series is given exactly up to o(r_B) for the
case of a small filling factor for the lowest Landau level.Comment: 10 pages, Accepted for publication in Phys.Rev.
Equation of state of a strongly magnetized hydrogen plasma
The influence of a constant uniform magnetic field on the thermodynamic
properties of a partially ionized hydrogen plasma is studied. Using the method
of Green' s function various interaction contributions to the thermodynamic
functions are calculated. The equation of state of a quantum magnetized plasma
is presented within the framework of a low density expansion up to the order
e^4 n^2 and, additionally, including ladder type contributions via the bound
states in the case of strong magnetic fields (2.35*10^{5} T << B << 2.35*10^{9}
T). We show that for high densities (n=10^{27-30} m^{-3}) and temperatures
T=10^5 - 10^6 K typical for the surface of neutron stars nonideality effects
as, e.g., Debye screening must be taken into account.Comment: 12 pages, 2 Postscript figures. uses revtex, to appear in Phys. Rev.
Sub-femtosecond determination of transmission delay times for a dielectric mirror (photonic bandgap) as a function of angle of incidence
Using a two-photon interference technique, we measure the delay for
single-photon wavepackets to be transmitted through a multilayer dielectric
mirror, which functions as a ``photonic bandgap'' medium. By varying the angle
of incidence, we are able to confirm the behavior predicted by the group delay
(stationary phase approximation), including a variation of the delay time from
superluminal to subluminal as the band edge is tuned towards to the wavelength
of our photons. The agreement with theory is better than 0.5 femtoseconds (less
than one quarter of an optical period) except at large angles of incidence. The
source of the remaining discrepancy is not yet fully understood.Comment: 5 pages and 5 figure
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