3,105 research outputs found
Nonadiabatic Dynamics in Open Quantum-Classical Systems: Forward-Backward Trajectory Solution
A new approximate solution to the quantum-classical Liouville equation is
derived starting from the formal solution of this equation in forward-backward
form. The time evolution of a mixed quantum-classical system described by this
equation is obtained in a coherent state basis using the mapping
representation, which expresses quantum degrees of freedom in a
2N-dimensional phase space. The solution yields a simple non-Hamiltonian
dynamics in which a set of coherent state coordinates evolve in forward and
backward trajectories while the bath coordinates evolve under the influence of
the mean potential that depends on these forward and backward trajectories. It
is shown that the solution satisfies the differential form of the
quantum-classical Liouville equation exactly. Relations to other mixed
quantum-classical and semi-classical schemes are discussed.Comment: 28 pages, 1 figur
The influence of the continental shelf on the tides of the Atlantic coast of the United States
Examination is made of the hypothesis that the tide along the eastern coast of the United States results from a co-oscillation of water over the Continental Shelf engendered by motion at the continental slope, the barrier against which the oceanic tidal wave is reflected . Using methods which are effective in analyzing tides in embayments, the range of tide and the time of high water over the continental slope have been estimated from data on the tide at the coast and from the topography of the off-lying shelf...
Interference phenomena in the tides of the Woods Hole region
The relations of mean range of tide, time of high water, and time of slack water along Vineyard and Nantucket Sounds may be attributed to the interference of tidal waves entering the sounds from their opposite ends. Interference of the semidiurnal constituents is maximal in the neighborhood of Woods Hole where the great reduction of these constituents, relative to the diurnal constituents, results in a pronounced diurnal inequality in the range of successive tides at appropriate phases of the moon...
The tides of the waters of New England and New York
From the Preface: This book is written for the many intelligent people who work or play
along the coast between Sandy Hook and the Bay of Fundy in the hope that
it will give them a better understanding of matters which greatly influence
the daily ordering of their activities. It may be of value to the serious student
of the tides, at the beginning as an introduction to tidal theory and later as a
summary of the tides on this particular coast. The stretch of coast considered
and the off-lying ocean contain examples of practically all known tidal
phenomena.
The book is based for the most part on information given in the tide
and current tables published by the U.S. Department of Commerce, National
Oceanic and Atmospheric Administration, formerly the Coast and
Geodetic Survey. It is not intended to replace these tables if one would know
what to expect at any particular place on any particular day. Rather, it attempts
to explain why the tide locally is as it is and why it varies from place
to place
The processes determining the concentration of oxygen, phosphate and other organic derivatives within the depths of the Atlantic Ocean
The great oceans of the world all contain at intermediate depths less oxygen and more
nitrate and phosphate than is found at either lesser or greater depths. This is one of the
most marked physical features of the sea which must be attributed to the action of biological agencies.
Those who have discussed this condition recently are agreed that it originates through the oxidation of organic matter derived primarily from the surface layers of the ocean, where alone the original synthesis of organic matter can occur. The condition obtaining at any depth is considered to depend upon the balance between the rate at which oxygen is removed from the water by respiratory and other metabolic processes and the renewal of oxygen in the layers in question by movements of the water. One group of investigators has emphasized the latter factor as the dominant one in determining the observed distribution of oxygen (Jacobsen, 1916; Dietrich, 1937; Wüst, 1935; Wattenberg, 1929, 1938). Oxygen content is reduced to the greatest extent at those depths in which the
water is in minimal motion and hence the renewal of oxygen is least. Seiwell (1937) and Sverdrup (1938) have pointed out that this condition is not a necessity and is indeed in certain situations contrary to the apparent facts. They have shown that the observed distribution of oxygen may be accounted for by assuming various suitable relations between the rates at which oxidation occurs as a function of the depth and the rates of renewal by the circulation of water.
These discussions appear to consider the state of the water to depend upon factors
operative more or less locally and in situ. Specifically, oxidation is assumed to follow the sinking of organic matter from the surface to the depth in question in the discussions of Wattenberg (1937) and Seiwell (1937). The renewal of oxygen is assumed to depend on the horizontal circulation. Several considerations appear to have been given insuffcient weight in discussions of
this subject. It is not at all clear why the depth of the oxygen minimum layer varies so
greatly from place to place or what its relation is to the particular nutritive conditions in
the sea's surface. Observations made in the relatively shallow water of the Gulf of Maine
indicate that organic decomposition and oxidation take place for the most part not far
from the sea surface. It seems not unreasonable to assume that the properties of the water
which depend upon organic decomposition may have been determined primarily at a
time when the water was relatively near the sea surface and that the water has subsequently
moved into its observed position. The recent evidence, reviewed by Montgomery
(1940), that mixing processes along surfaces of constant potential density may
occur with great ease, even in the absence of directional flow, provides a convenient
mechanism for establishing a distribution of oxygen and the products of organic activity
at great depths which is dependent in large part on processes taking place much nearer
the sea surface in remote regions. These considerations have suggested that the wellmarked
evidence of decomposition which is observed at great depths in the central Atlantic
Ocean may be due to the flow of water along surfaces of equal potential density
from regions near the sea surface in high northern and southern latitudes rather than to
the decay of organic matter derived directly from the overlying surface waters.
This view requires that the characteristics of the water show a marked continuity in
their distribution along layers of constant potential density, and that these layers emerge at or near to the sea surface in places suitable to produce the peculiar character of the
layers in question.
To test this possibility, data secured by the "Meteor," the "Discovery," and the
"Atlantis" have been examined. The most illuminating information was secured from
two north-south sections which together extend from Greenland to Antarctica. The South
Atlantic was traversed by a section, made by the "Discovery" in April-May, 1931, extending
along the thirtieth meridian from 57°36'S to 14°27'N ("Discovery" Reports,
1932). This is Section 2 of Clowes (1938). A section of the North Atlantic was constructed
from the data secured by the "Atlantis" extending from 1°N to 34°N west of the fortieth
meridian in March, 1932 (Stations 1158-1179), and from 39°N to 49°N near the fortieth
meridian in September, 1935 (Stations 2485-2491), and by the "Meteor" (Stations
120-125) extending from 50°N to 58°N near the forty-fourth meridian, occupied in
March, 1935 (Bull. Hydrographique, 1933, 1936).
The data have been converted into suitable common units. Phosphate has been expressed
as milligram-a toms phosphorus per cubic meter (γ-atoms P per liter) uncorrected
for salt error. The function of the oxygen content which is of importance is the quantity
which has disappeared from the water owing to metabolic processes. This has been approximated
by assuming the water to have been saturated with air at the time it acquired
its temperature and salinity at the sea surface and subtracting the recorded oxygen content
from the value calculated on this assumption. The "apparent oxygen utilization" so
obtained has been expressed as cubic centimeters per liter.
In plotting the data for the sections, a rectangular grid on which latitude is represented horizon tally and sigma-Ï„ is represented vertically has been chosen. Mon tgomery
(1938) has shown that surfaces of equal sigma-Ï„ are approximately of constant potential
density. Consequently, on such a diagram the path of free movement by lateral mixing
or flow is along horizontal lines. Any correlation of the distribution of a component of the
sea water with potential density becomes at once apparent, if present. The surface of the
sea and surfaces of any particular depth are represented by curved lines on the diagram.
A grid of this type has been used by Spilhaus (1941) to distinguish different water types
in the complex situation which exists at the margin of the Gulf Stream
The exchange of oxygen across the sea surface
In temperate latitudes the oxygen content of sea water near the surface varies with the season. This results because the solubility of oxygen in the water changes with its temperature and because of the unequal production and utilization of oxygen by organisms at different seasons. Both factors cause an exchange of oxygen across the sea\u27s surface. The present paper is an attempt to determine the magnitude of this exchange as it occurs in the Gulf of Maine and to evaluate the factors responsible
The tide in coastal waters
The tide in many straits and embayments between New York and the Bay of Fundy may be described by theoretical equations based on the interference of a progressive wave entering at one end of the reach with, in the case of straits, a second wave entering at the opposite end or, in the case of embayments, a second wave arising from the reflection of this wave from a barrier at the head of the embayment...
The analysis of tidal phenomena in narrow embayments
The tides of coastal embayments derive their energy from the ocean tides rather
than from the direct action of lunar and solar gravitational forces. They are considered
to be part of co-oscilating systems in which the period is determined by the tide in the
outer sea, while the detailed character of the motion depends on the size and form of
the enclosed basin (Defant, 1925; Doodson and Warburg, 1941).
In narrow basins of simple form in which the influence of the earth's rotation is small,
the motions resemble standing waves. Ideally, such waves are characterized by the
simultaneous rise and fall of level on either side of a nodal line at which no change in
elevation takes place. The elevation at high water increases with distance from the
nodal line and slack water coincides with high and low water.
The properties of tides due to standing waves may be deduced by assuming the
motion to result from a primary progressive wave moving up the channel which undergoes
complete reflection at a barrier. Mathematically, this situation may be treated as the
interference of two identical progressive waves moving in opposite directions and so
related that both waves are in phase at the barrier. This treatment of standing waves
assumes the presence of total reflection, the absence of damping and the absence of
effects of the earth's rotation. Since these conditions are not realized in natural tidal
basins, the standing wave concept leads to oversimplification.
In coastal embayments the most striking departure from the expectations of the
standing wave concept is the discrepancy between times of high water and slack water,
which may be great near the mouths of the larger bays and sounds. High water does not
occur simultaneously within such enclosures but is earlier near the sea. Commonly, the
nodal line is represented merely by a region in which the tidal range is small. These are
effects which can be explained if damping of the primary and reflected waves by frictional
or other effects is taken into account.
According to these concepts, the problem of tidal behavior in embayments is to
determine numerically the properties of the primary and reflected waves so as to account
for the observed relations of amplitude and stream velocity of the actual tide and to
correlate these numerical properties with the geographical form of the embayment.
In the present paper an attempt is made to treat the tidal behavior in such a way that
the observed changes in elevation and motion of the water along the path of the wave
may be used to determine the distribution of phase of the primary and reflected waves
along the channel and to measure the damping.
The relations between the several aspects of a wave as it advances along a channel
of uniform depth and width have been developed theoretically so as to show the times
of high water and slack water, the range of the tide, and the phase relations of the
primary and reflected waves along the channel for any degree of damping. By expressing
the relationship of the several aspects of a reflected wave in a form in which the wave
period is taken as the unit of time and distance is given in terms of the related phase
changes, it is possible to eliminate the purely geographical dimensions and to obtain a
wholly general description of the tide which may be used to indicate how any given
channel distorts the behavior of the wave as it advances.
In the case of irregular channels, in order to justify the application of relations
deduced for uniform channels, in which the change in phase of the primary and reflected
waves and their damping is proportional to the distance traveled and in which the
velocity of the waves is constant, it is necessary to make the following assumptions:
1. That the effect of irregularities in cross section is to alter the velocity of the
primary and reflected waves; i.e., to distort the geographical distribution of phase
differences.
2.That damping is proportional to the phase change in the waves rather than to
the distance traveled.
3. That the damping coeffcient, as defined, is constant along the length of the
channel
Advanced manned space flight simulation and training: An investigation of simulation host computer system concepts
The findings of a preliminary investigation by Southwest Research Institute (SwRI) in simulation host computer concepts is presented. It is designed to aid NASA in evaluating simulation technologies for use in spaceflight training. The focus of the investigation is on the next generation of space simulation systems that will be utilized in training personnel for Space Station Freedom operations. SwRI concludes that NASA should pursue a distributed simulation host computer system architecture for the Space Station Training Facility (SSTF) rather than a centralized mainframe based arrangement. A distributed system offers many advantages and is seen by SwRI as the only architecture that will allow NASA to achieve established functional goals and operational objectives over the life of the Space Station Freedom program. Several distributed, parallel computing systems are available today that offer real-time capabilities for time critical, man-in-the-loop simulation. These systems are flexible in terms of connectivity and configurability, and are easily scaled to meet increasing demands for more computing power
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