text:
Beyond the blingski
As the opening of a $1,000-a-night hotel seals Moscow's reputation as the world's most decadent city, Peter Moore goes in search of remnants of Soviet Russia among all the glitz
Just Soviet stories ... Stalin's Moscow Metro. Photograph: Alamy
Fri 6 Jul 2007 20.03 EDT
Red Square was closed to the public. The stark granite mausoleum holding Lenin's remains was covered by scaffolding and surrounded by rows of blue chairs. A gang of workmen were putting the final touches on a stage that ran the length of the old GUM department store. At the far end of the square, a team from a local advertising agency hoisted up banners promoting the latest Nokia mobile phone on poles in front of St Basil's cathedral.
I asked a bored military officer manning one of the barricades when the square would be open again and he shrugged. "Maybe after the Victory Day Parade," he said. "Maybe not."
The soldier's surly response made me smile. With news that both Ritz Carlton, where basic rooms start at $1,000 a night, and Mamaison were about to bring their particular brand of five-star sophistication to the city, I had come to Moscow to see how much of the Soviet spirit remained. In a city now obsessed with sushi, designer handbags and partying with Ukrainian models, the soldier's brusque reply was redolent with the images I had in my head of babushkas in head scarves, grey apartment blocks and old men clutching vodka bottles.
The mood was lost when a camp choreographer breezed on to the stage and led a group of children through a practice run of a very bad rap routine. The Victory Day parade used to be an annual display of Soviet muscle, the chance to show off the latest bit of nuclear weaponry to the nervous west. Now, it seemed, it was a surreal version of Russia's Got Talent.
At least getting a Russian visa had been a Kafka-esque ordeal. A quick call to the embassy in London revealed that I needed a letter of invitation, hotel vouchers and a ticket stub from a Chelsea home game. I made a half-hearted attempt to organise it myself before getting a company called Russia Direct to do it all for me. They are based in Edinburgh, bizarrely, and for £90 I got a visa, a mysterious letter in Cyrillic and a list of contact numbers in Moscow should I need to speak to anyone. I was joking about the Chelsea ticket, but if it ever becomes a requirement I'm sure these guys would happily sit through a goalless draw at Stamford Bridge to get it for you.
With the visa sorted, my next task was to find an old Soviet-style hotel on the web. I wanted something boxy and dour, set over at least 12 floors with a babushka looking after each one. In a perfect world, my babushka would chain-smoke, neglect her cleaning duties and sell the toilet paper to Georgian gangsters. Unfortunately, most of these establishments have now been turned into business hotels and charge upwards of £200 a night.
Not so the Hotel Asia. It was set in a 15-storey tower block opposite the metro station on Ryazansky Prospekt and boasted a hunting-style pub and a Ukrainian folk restaurant within easy walking distance. Its website offered the choice between renovated and unrenovated rooms. I chose the unrenovated option and got a time capsule of Soviet hospitality circa 1973. There was a rug on the floor, a divan as my bed, peeling wallpaper and a metal tray with two cut-glass tumblers. My floor had its own babushka too, but she let the side down badly by greeting me each morning with a cheery "Zdrasvooytyeh!" (hello) and changing the sheets on my bed daily.
Getting around Moscow the Soviet way was easy. I just took the Metro. It has 165 stations and carries nine million passengers a day. Moscow is supposed to be the most expensive city in the world, but a single ride to anywhere on the network only costs 17 roubles. A card of 20 rides will set you back 250 roubles.
When Stalin ordered the construction of the Metro, he envisaged it as a showcase of his particular brand of socialism. HG Wells told him to save the cash and buy 1,000 London buses instead. Stalin ignored him and peasants and workers were shipped in from all over the country to build it. The Communist Youth League pitched in as well. And the Soviet Union's finest artists were recruited to decorate the stations. It is not an exaggeration to say that each platform is a work of art.
The Metro caters to every taste. Want a bit of pompous classicism mixed in with Empire style and Moscow baroque? Then head for Komsomolskaya on the circle line. Bronze statues of revolutionary heroes? Try Ploshchad Revolyutsii. Art deco stained glass? Novoslobodskaya. Vulgar gilt? Kievskaja. A mosaic of workers admiring the red tractor they have just built? The central hall at Novokuznetskaya.
You can't escape New Russia entirely. The speakers installed along the escalators to play hymns to Soviet productivity now pump out ads for mobile phones. And I'm sure the 24-sheet billboard of a girl in her underwear on the wall in Proletarskaya wasn't what the Communist Youth League had in mind when they decorated the platform with hammers and sickles.
But Stalin would be pleased to see that even today the turnstiles are manned by babushkas as uncompromising as he was. One old drunk guy tried to sneak through without paying and was immediately confronted by a small stocky woman who blocked his way yelling "Nyet! Nyet!" I was terrified even though I had a valid ticket.
My quest for a typically Soviet dining experience was slightly more difficult. When I asked my hotel babushka where she had dined during Soviet times, she said she ate dumplings at home. Now she and her husband eat at My-My. Pronounced Moo-Moo, it's a chain of self-service restaurants where you can stuff yourself for a couple of quid. My babushka liked the black-and-white bovine theme, especially the one in Arbat with a fibreglass cow out front.
A friend gave me the number of Nathan Toohey, the restaurant reviewer for the Moscow Times. He took me to Glavpivtorg, a faithful recreation of the beer restaurants popular with Apparatchiks during the Soviet era. It is authentic right down to the pretty girls in homey green skirts and lace blouses who meet you at the door. Upstairs the thick leather chairs are reminiscent of a gentleman's club. There's a wall-sized map of Russia and a huge desk topped by three Bakelite phones should you wish to conduct a thermo-nuclear war. Dried Caspian roach fish is served on a wooden rack with a stick used to remove the scales. You can drink beer, eat prawns, whack a fish with a stick and pretend it's the Cuban missile crisis all over again. Maybe that's why it's so popular with high-ranking officers of the FSB, the new security service, whose headquarters is conveniently located in Lubyanka Square, just down the road.
Another popular spot with the boys from the FSB is the Sword and the Shield. It is known locally as the KGB Club. CCCP badges adorn the poles outside and the emblem of the former secret service department is proudly displayed in the window. I thought it was supposed to be ironic like Maxim's, the Soviet-themed pizza parlour in Budapest which serves Stalin and Lenin pizzas. But when I tried to take a photo of the life-size portrait of President Putin in a karate outfit hanging over the stairs I was brusquely informed that this was not a good idea. The decor isn't satirical. It's homage.
There is certainly no shortage of Soviet paraphernalia on the streets of Moscow. The souvenir stalls in front of Red Square and on Arbat overflow with reproduction badges, hats and posters from the Soviet era. But you'll find the real thing in unexpected places, too. I spotted a relief of Lenin on Tverskaya ul, a popular shopping street. The cinema on Novy Arbat is decorated with wonderful mosaic celebrating worker solidarity. Unfortunately, the mosaic's socialist message was overwhelmed by a garish poster advertising Shrek the Third directly underneath it.
A few statues and sculptures from the Soviet era have found a home in Park Iskusstv, an unassuming garden that sits beside the Moscow river. Here you'll find eulogies to Soviet women carved in stone, metallic celebrations of the space race, a bronze Soviet adviser pointing the way forward to his noticeably shorter African and Asian comrades. There are a couple of Lenin, the Felix Dzerzhinsky that was torn down after the failed 1991 coup, and a three-metre-high Stalin. The statue of Stalin is backed by rows of faceless stone heads behind barbed wire. It's a reminder of the millions who lost their lives in Gulags and a sobering reminder that my Soviet nostalgia is an indulgence afforded to someone who has not lived through those times.
I tried to get into Red Square for the Victory Day parade but my way was barred by barrel-chested Omon guards dressed in battle fatigues. They are the special forces trained to fight in Chechnya, so I did what they said. Instead, I retired to a bar and watched the parade on television like every other Muscovite. Soldiers marched. Putin rattled his sabre at the Estonians for moving a Soviet war memorial. And the rappers rapped. They were only a small part of a programme that was heavy on girls twirling around in traditional costumes.
Once the parade was over I rode the Metro to Park Pobedy, the station that serves Victory Park, a huge memorial complex that celebrates the Great Patriotic War. Here war veterans with chests full of medals accepted flowers and well-wishes from thousands of Muscovites. Then I followed the crowds to Sparrow Hills, where every person in Moscow had gathered to watch fireworks explode over the city below. At my back was the daunting Moscow State University, one of the seven brutal skyscrapers Stalin ordered to compete with the Americans.
In the end, I never got to see the waxy body of Lenin. Workmen were still pulling down the scaffolding when I dropped by his mausoleum on my last day in Moscow. The only queue I saw was one outside the ubiquitous portaloos at Izmailovo markets. And although there was a man in uniform on every street corner I was only asked for my papers once, on my last day, as I left my hotel.
In one final salute to the proletariat I caught a commuter train from Paveletskaya out to Domodedovo airport. At 63 roubles it's the cheapest option. It was old rolling stock painted blue with a stark grey interior and, because it was the end of the day, it was filled with commuters going home. Old babushkas sat with plastic bags bursting at the seams. A guy dressed in black listened to a Russian MP3 player. Once we got past the golden ring to the apartment blocks and grey factories, the train filled with men wearing overalls and a side-parting in their hair. Then, as the train rumbled past the wooden dachas and through the beech forest on the edge of the airport, a woman wandered through the carriage selling turtle-shaped fridge magnets that lit up when you flapped its flippers.
I had found the Moscow I had come to see.
BA (ba.com) flies Heathrow-Moscow direct from £125 each way. Russia Direct (russiadirect.net) arranges 30-day Russian visas for £80.
Hostel Asia (hostels.ru/en/hostel-asia) doubles from €60.
Country Code: 007.
Flight time London-Moscow: 4hrs.
£1 = 45.46 roubles.
· Peter Moore's The Wrong Way Home is published by Bantam, £7.99.
Moscow holidays
Russia holidays


text:
\section{Introduction}

In simplest terms, spiral galaxy disks can be described as geometrically
thin, flat, and circular.  We understand that spiral disks are
geometrically thin because the gas of which they are composed is cold
(the sound speed of the gas is much smaller than its circular orbital velocity);
and they are both circular and flat because, being dissipative, the
gas is fairly efficient at both minimizing out-of-the-plane motions and
radial excursions that would lead to departures from circular orbits.

Describing spiral disks as {\it perfectly} circular and flat is clearly
an oversimplification, however.  In addition to the nonaxisymmetric
structures that are obvious in optical photographs of many spiral disks,
21-cm maps of the projected velocity fields of spiral disks often reveal
isovelocity contours that are significantly twisted
(\cite{RLW}; \cite{RN78}; \cite{RCC79}; \cite{N80a}, 1980b; \cite{B81};
 \cite{S85}).   Kinematical tilted-ring models have been constructed in
an effort to explain the presence of such twists in the velocity maps
of \ion{H}{1} disks.  The models indicate that the outer
regions of many normal spiral disks are significantly warped out of the
principal plane that is defined by the optically visible, central portion of
each galaxy.  The line of nodes that defines the intersection of adjacent
rings of gas in these kinematical models also usually must be twisted significantly
as a function of radius in order to explain the observed contour maps
(for recent reviews, see \cite{Briggs90}; \cite{Bosma91};
\cite{CTSC93}, hereafter CTSC).

It is not particularly surprising that many galaxies are observed to
possess extended, rotationally flattened disks because such structures
appear to be fairly ubiquitous in gravitationally bound, astrophysical
systems.  (There is strong evidence, for example, that rotationally
flattened disks either exist now or have existed in the past
around our sun, individual planets within our solar system,
numerous protostars, the primary star of many mass--exchanging binary
star systems, and active galactic nuclei.)
What is peculiar about the \ion{H}{1} disks
of many galaxies is that the disks are significantly warped.
It is not clear why natural dissipative processes similar to those
which work effectively to minimize
out-of-the-plane motions in stellar or protostellar
``accretion'' disks are unable to suppress warps in the gaseous disks of galaxies.
As Binney (1992) has reviewed, there still is no generally accepted
dynamical model of spiral galaxies
that satisfactorily explains either the origin or the current structure of
warped \ion{H}{1} disks.

Almost thirty years ago, Hunter \& Toomre (1969) examined whether
normal, infinitesimal bending oscillations might be exhibited by
thin, rotating disks of self-gravitating material, permitting them
to sustain coherent warps for more than a Hubble time.
They concluded that ``for any disk whose density tapers sufficiently
gradually to zero near its edge,'' the frequency spectrum of such
oscillations is at least partly continuous and, as a result, coherent
warps cannot be sustained.
Over the subsequent decade,
a number of other ideas surfaced to explain the persistence of warps in
galaxies, each one taking advantage of the demonstrated existence of
dark matter halos around galaxies.  As Toomre (1983) has reviewed,
however, models proposing to use the halo as an active agent to
excite warps in otherwise flat disks -- for example, via the Mathieu
instability (Binney 1981) or via a flapping instability (Bertin
\& Mark 1980) -- each present significant difficulties.
Toomre (1983) and Dekel \& Shlosman (1983) proposed, instead, that
untwisted steady-state warps may be sustained as a result of steady
forcing by a nonspherical, tilted halo.
Building on the early work of Hunter \& Toomre (1969) and
the idea that forcing by a nonspherical dark halo can influence the dynamics
of the visible disks of galaxies, Sparke (1986) and
Sparke \& Casertano (1988) have shown that
a discrete warping mode can persist
if the disk is sufficiently self-gravitating and if it is embedded
in a nonspherical halo whose equatorial plane is tilted with
respect to the centralmost regions of the disk.

Adopting this model of galaxy warps, the following evolutionary
picture emerges.  During the galaxy formation process, gas
which falls into a spheroidal dark matter halo generally will
find that its angular momentum vector is tipped at some nonzero
angle, $i$, away from the symmetry axis of the halo.  If the
gas is cold, it will settle into a rotationally flattened disk that
is tilted at the same angle $i$ with respect to the
equatorial plane of the halo.  In the centralmost regions of
the galaxy, where the self-gravity of the gas (or, ultimately,
the combined gas/star system) dominates over the gravitational
influence of the halo, the gas will be content to remain in
orbits that preserve this original tilt.  In the outermost
regions of the galaxy where the gravitational field of the
halo dominates, however, the gas should settle into the
halo's equatorial plane.  As Toomre (1983) and Dekel \& Shlosman
(1983) both sketched in their original concept papers, there
also should be an intermediate region where the gas will
be influenced significantly by the nonspherical gravitational
fields of both the halo and the central gas (or gas/star) disk.

Through their modeling efforts,
Sparke (1986) and Sparke \& Casertano (1988) confirmed this
earlier suspicion that in the intermediate region, the gas
can reside in a steady-state,
``warped disk'' structure that provides a smooth radial
transition between the separate ``flat disk'' orientations of
the inner and outer regions of the galaxy.  Concentrating on
the dynamics of the centralmost and intermediate regions
-- that is, by building models in which there was effectively
no gas in the outermost regions -- Sparke \& Casertano (1988)
showed that, in steady-state, the warped disk exhibits a
straight line of nodes which precesses slowly and coherently
in a direction retrograde to the orbital motion of the gas.
In a time-dependent simulation, furthermore, Hofner \& Sparke
(1994) showed that settling to this steady-state warped disk
structure occurs from the inside, out, and is driven
not by dissipative processes that are similar to those which
are thought to drive settling in most stellar or protostellar
accretion disks but, rather,
because ``bending waves carry energy associated with transient
disturbances out toward the disk edge.''
They also showed that, during an evolution as the bending waves
propagate outward through the intermediate region of the disk,
a twisted structure can develop and persist until the gas
has had sufficient time to settle into the steady-state
(constant line of nodes) configuration.
Sparke \& Casertano (1988) and Hofner \& Sparke (1994) have demonstrated
that, with an appropriate choice of parameters, this
model of disk warping matches well the observed properties of
several galaxies with warped disks. (See also Kuijken 1991 and
Dubinski \& Kuijken 1995.)

As Hofner \& Sparke (1994) have pointed out, in galaxies
with extended \ion{H}{1} disks ``the outermost gas cannot be expected
to form part of a coherent warping mode.''  They did not include
normal dissipative forces in their simulations and therefore
were unable to comment on how such forces might influence the
settling process.  In this paper, we examine the disk-settling
process from the other extreme, ignoring the self-gravity of the
gas but introducing an effective kinematical viscosity into the
dynamical equations in order to simulate the effects of dissipative
forces.  Hence, our effort is complementary to the work of Hofner
\& Sparke (1994) and is most relevant to galaxies with
extended \ion{H}{1} disks -- although there is one
galaxy used for model comparisons (NGC 2841) that is shared by both works.
We adopt the view that warps in extended \ion{H}{1} disks
which exhibit substantial twists are transient features.
Independent of precisely what physical process
was responsible for initially placing the gas in an orbit
that is inclined to the halo's equatorial plane ({\it e.g.}, gas infall
at the time of formation or a recent tidal encounter with another
galaxy), the twisted structure
can be understood as the result of differential precession in the gaseous disk
as it dissipatively settles toward that ``preferred plane.''

In the past, there has been considerable concern (first enunciated by
Kahn \& Woltjer [1959], but reiterated in the
reviews by both Toomre [1983] and Binney [1991]) that
differential precession will destroy any warped disk structure
on a time scale that is short compared to a Hubble time
and, therefore, that the mechanism we are examining cannot reasonably be
used to explain the persistence of such structures.
In the outermost regions of \ion{H}{1} disks, however, precession times are
relatively long and, as was first pointed out by
Tubbs \& Sanders (1979), a warped gas layer can persist
for a Hubble time if the dark halo in which the
disk is embedded deviates only slightly from spherical symmetry.
By modeling carefully the process of disk settling that is driven
by normal dissipative forces and comparing the models to the observed
kinematical properties of galaxies with extended, warped \ion{H}{1} layers,
we hope to be able to more carefully examine the viability of such models.

Steiman-Cameron \& Durisen (1988, hereafter SCD88) have developed
this idea rather extensively.
They have adopted a numerical, cloud-fluid
model to simulate the time-dependent evolution of a galaxy
disk that intially is tilted out of the equatorial plane of an underlying,
spheroidal dark halo.  The disk is assumed to be composed of a
set of annular mass elements, or ``clouds,'' which act like atoms in a viscous
fluid.  The SCD88 model has offered some valuable physical
insight into the time-dependent settling process
that is driven by normal dissipative forces and their dynamically generated
model of a twisted galaxy disk has been surprisingly successful at matching
the peculiar optical image of one particular galaxy, NGC 4753 (\cite{SCKD92}).

Our model is analogous to the one developed
by SCD88 but it derives from an analytical prescription of the
viscous settling process.  More specifically, we employ
the ``twisted-disk'' equation formalism first
developed by Bardeen \& Petterson (1975) and Petterson (1977, 1978)
to describe the time-dependent settling of a thin, viscous disk in a
nonspherical dark halo potential.  This is a rather natural formalism to adopt
because, as numerous kinematical ``tilted-ring'' models have demonstrated,
warped \ion{H}{1} galaxy disks display a structure that resembles,
at least qualitatively, the twisted geometry that had once been thought
to be important in accretion disks which surround certain compact
stellar objects (Bardeen \& Petterson 1975; see a recent rejuvenation
of this idea put forward by Maloney \& Begelman 1997).  In adapting the model
to galaxy disks, we have replaced the approximate Keplerian gravitational
potential used in earlier accretion disk work with a logarithmic potential
appropriate to galaxy halos.
(Pringle [1992] also recently described how the twisted--disk formalism
may be adapted to galaxies.)
In the limit of
stress-free precession, our model reproduces the analytical prescription of
disk settling first presented by SCD88, but our model is not constrained to
this limit.  A more general solution to the governing equations
predicts an exponential settling rate that depends on time to the first
power, rather than on time to the third power as has been derived in the
limit of stress-free precession.  Furthermore, an analytical, steady-state solution
to the governing equations produces a twisted-disk structure that
is very similar to previously constructed, kinematical models.
We demonstrate that projected surface density maps and radial
velocity maps derived from our analytical model match
published \ion{H}{1} maps of five well-studied warped disk galaxies
(M83, NGC 300, NGC 2841, NGC 5033, and NGC 5055) very well.

\section{The Generalized Twist-Equation}

Bardeen \& Petterson (1975) and Petterson (1978) have written the
hydrodynamic equations determining the structure
and evolution of nonplanar, thin accretion disks in a ``twisted-coordinate
system.''  In this system, the position $P$ on each ring of radius $r$
is referenced to a local cylindrical coordinate frame $(r, \psi, z^\prime)$
which has been rotated with respect to the cartesian coordinate system of
the central reference ring by the two orientation angles $\gamma$ and $\beta$
(see Fig.\ 1).  For an appropriate choice of the two functions $\gamma\bigl(r
\bigr)$ and $\beta\bigl(r\bigr)$, including specifically the assumption that
$\beta\bigl(r\bigr) \ll 1$, the equations
separate into a set of the usual hydrodynamic equations for a flat disk
and a pair of coupled ``twist-equations'' governing the orientation of
the disk.  Because of its ability to describe an apparently complicated,
fully three-dimensional dynamical problem with a relatively simple and elegant
mathematical model, a number of different groups have subsequently also
adopted this formalism.  However, until recently there has been some
disagreement over what terms may be dropped from the fully three-dimensional,
nonlinear partial differential equations (due to their ``smallness'' relative to other
terms) when deriving the governing twist-equations.
(For a complete discussion of the various simplifications and
assumptions made in deriving this formalism see
Petterson [1978, 1979]; Hatchett, Begelman, \& Sarazin [1981]; and
Papaloizou \& Pringle [1983].)   As the following brief review points out, the
disagreements have not been over the general {\it form} of the equations but, rather,
over the precise value of certain order-unity coefficients.  Ultimately, as explained
below, we have adopted the derivation presented by Papaloizou \& Pringle (1983).

According to Petterson (1978), the twist-equations take the
following form:
\begin{eqnarray}
\dot \beta+v_{r}\beta^\prime&=
&\frac{\nu}{2}C_0 \biggl[\beta^{\prime\prime}+
C_1\frac{\beta^\prime}{r}-\gamma^{\prime2}\beta\biggr]\;
+\;\frac{1}{2\pi
 v_{\psi}}\int_0^{2\pi} F_{T}\cos\psi\,d\psi ,\nonumber  \\ \\
\dot \gamma+v_{r}\gamma^\prime&=&
\frac{\nu}{2}C_0 \biggl[\gamma^{\prime\prime}+
C_1\frac{\gamma^\prime}{r}+
\frac{2\gamma^\prime\beta^\prime}{\beta}\biggr]
\;+\;\frac{1}{2\pi\beta
v_{\psi}}\int_0^{2\pi} F_{T}\sin\psi\,d\psi,\nonumber
\label{P78teqs}
\end{eqnarray}
with $C_0 = 2$ and $C_1 = 1/2$. In these expressions,
dots and primes denote differentiation with respect to time and space,
respectively, $v_{r}$ and $v_{\psi}$ are the radial and azimuthal
components of the fluid velocity, $\nu$ is the vertically averaged kinematical
viscosity, and $F_{T}$ is an externally supplied ``twisting force''.

Hatchett, Begelman, \& Sarazin (1981, hereafter HBS) pointed out some
inconsistencies between Petterson's (1978)
derivation and the earlier presentation by Bardeen \& Petterson (1975).
Through an independent derivation, they determined that the twist-equations
do take the form of equation (1), but they concluded that the two coefficients
should have the values $C_0 = 1$ and $C_1 = -1$.  Most significantly,
HBS showed that the pair of twist-equations can be written as a single,
{\it complex} twist-equation of the form
\begin{equation}
\dot w + v_r w^\prime = \frac{\nu}{2}C_0
\biggl(w^{\prime\prime} + C_1\frac{w^\prime}{r}\biggr)
+i{\it L}\;,
\label{HBSteq}
\end{equation}
where the complex variable {\it w} is defined in terms of the angles $\beta$ and
$\gamma$ as
\begin{equation}
w\equiv \bigl(\beta\sin\gamma\bigr)-i\bigl(\beta\cos\gamma\bigr)\;,
\end{equation}
and
\begin{equation}
{\it L}\equiv -\frac{1}{2\pi v_{\psi}}\int_0^{2\pi} F_{T}\exp{\Bigl[i\bigl(\gamma+
\psi\bigr)\Bigr]}\,d\psi\;.
\label{Ldef}
\end{equation}
Written in this form, the twist-equation readily submits to analytical solution
for certain driving forces.

Papaloizou and Pringle (1983, hereafter PP) have
suggested that the HBS derivation also has shortcomings (for example,
as viscous evolution occurs according to the HBS equations, angular
momentum does not appear to be conserved globally).
They have derived a set of twist-equations that more consistently
ties in with traditional $\alpha$-disk models and have demonstrated
explicitly that their derived equations conserve angular momentum.
As can most easily be deduced from the presentations of Kumar \&
Pringle (1985) and Pringle (1992), for a disk whose
inner radius goes to zero and whose surface density is independent of
radius, the PP derivation also leads to a complex twist-equation
that takes the form of equation (\ref{HBSteq}).  However, adopting
PP's ``naive approach'' in order to gain physical insight into the
nature of the problem (i.e., setting Kumar and Pringle's function
$f(\alpha)=\alpha$), one concludes from these three papers that the
proper coefficients are:
\begin{equation}
C_0 = 1, \eqnum{5a}
\end{equation}
\begin{equation}
C_1 = \biggl[
2\frac{d\ln (v_{\psi}/r)}{d\ln r} + \frac{d\ln Z}{d\ln r} \biggr],
 \eqnum{5b}
\label{PPcoefs}
\end{equation}
where
\begin{equation}
Z \equiv r^2v_{\psi}.\eqnum{5c}
\end{equation}
\noindent
For a Keplerian disk $v_{\psi} \propto r^{-1/2}$; therefore,
$C_0 = +1$ and $C_1 = -3/2$.
Interestingly, these are the same coefficients that appear in Bardeen \&
Petterson's (1975) earliest presentation of the twist equations.
Henceforth, we will adopt and build upon the twist-equations derived
by PP because it is clear that in a viscous disk
evolution that is governed by the PP twist-equations,
angular momentum is conserved.

Petterson (1978), HBS, and PP each used an approximately
Keplerian potential to represent the underlying gravitational potential
well that governs disk dynamics.  While the Keplerian potential correctly
describes the gravitational field in which a thin accretion disk surrounding
a compact object sits, it is inappropriate for a thin galaxy disk sitting in
the potential well of a nonspherical dark-matter halo.
Utilizing Kumar \& Pringle's (1985) and Pringle's (1992) extensions of
the PP derivation, it is possible to generalize the complex twist-equation
to incorporate an arbitrary power-law form for the gravitational potential.
Specifically, adopting a rotation law of the form
\setcounter{equation}{5}
\begin{equation}
v_\psi\propto r^{(1-q)},
\label{rotlaw}
\end{equation}
expression (\ref{PPcoefs}) becomes
\begin{equation}
C_1 = \biggl[- 2q + (3-q)\biggr].
\end{equation}
Furthermore, as Petterson (1978) has pointed out,
the radial velocity can be expressed in terms of the vertically averaged
kinematical viscosity as

\begin{equation}
v_{r}=\nu\frac{r}{v_{\psi}}\frac{\partial}{\partial r}\biggl(\frac{v_{\psi}}
{r}\biggr)\;.
\label{radial velocity}
\end{equation}
Employing our generalized rotation law, we therefore can write
\begin{equation}
v_{r}=-q\frac{\nu}{r}\;.
\label{radvsub}
\end{equation}
Using this expression in conjunction with equations (5a) and (7),
the complex twist-equation (2) takes the form:
\begin{equation}
\dot w=\frac{\nu}{2}
\biggl[ w^{\prime\prime}+(3-q)\frac{w^\prime}{r}\biggr]
+i{\it L}\;.
\label{BTFteq1}
\end{equation}

\section{Twisted Disks in a Scale-Free Logarithmic Potential}

As outlined in $\S$ 1, our objective is to examine the evolution of a cold
gaseous disk that is embedded in a spheroidal, dark halo potential.  In
general, we assume that when the gas is initially introduced into the
halo potential well, the orientation of its angular momentum vector
is not aligned with the symmetry axis of the halo.  Because the halo is not
spherically symmetric, the halo's gravitational field will exert a finite
``twisting force'' on the gaseous disk; in simplest terms, this field
forces rings
of gas at different radii to precess about the symmetry axis (or symmetry
plane) of the halo.

In the present context, a spheroidal dark-matter halo
can be satisfactorily represented by a scale-free logarithmic
potential (cf. \cite{R80}; \cite{SCD88}, 1990).
This potential is a useful approximation because
a circular disk orbiting inside such a potential will exhibit a flat rotation
curve (i.e., $q = 1$ and $v_{\psi}$ is independent
of radius), as seen in real galaxies.
In a halo potential of this type,  the precession frequency
about the symmetry axis of the potential $\omega_{p}$ is
\begin{equation}
\omega_{p}=\pm \frac{3}{4}\eta\frac{v_{\psi}}{r}\;,
\end{equation}
where $\eta$ is a constant which measures the strength of the quadrupole
distortion of the halo and the minus (plus) sign indicates that the spheriodal
halo is oblate (prolate).

For a twisted disk embedded in a spheroidal potential well, the twisting
force that enters the derived twist equation assumes precisely the same
algebraic form as the twisting force that Bardeen \& Petterson (1975)
used when modeling the evolution of a disk orbiting a nonspherical,
compact stellar object, namely,
\begin{equation}
F_{T}=2\omega_{p}v_{\psi}\beta\sin\psi\;.
\label{twisting force}
\end{equation}
Hence, from equation (\ref{Ldef}),
\begin{equation}
{\it L}=\omega_{p}w\;,
\end{equation}
and we deduce that the evolution of a thin galaxy disk in a scale-free logarithmic halo
potential can be described by the expression
\begin{equation}
\dot w=\frac{\nu}{2}
\bigl[w^{\prime\prime}+2\frac{w^\prime}{r}\bigr]
\pm i\biggl(\frac{3}{4}\eta v_{\psi}\biggr)\frac{w}{r}\;.
\label{BTFteq3}
\end{equation}
Unless explicitly stated otherwise, we henceforth will adopt the minus
sign in front of the last term of this expression, thereby assuming that
the halo is {\it oblate} in shape.

Before the character of {\it general} solutions to this complex
ordinary differential equation is examined, it is worthwhile to demonstrate that when
certain limiting physical conditions are imposed, familiar analytical
expressions for the time variation of the inclination angle $\beta(t)$ and
the ``twist'' angle $\gamma(t)$ are derivable from (\ref{BTFteq3}).
This will give us additional confidence that (\ref{BTFteq3}) offers a
valid description of the dynamics of a twisted galaxy disk.  We present,
first, the limit of viscous-free precession, then the limit of stress-free
precession.

\subsection{Viscous-free Precession}

In the limit where viscous effects are completely negligible, $\nu\rightarrow 0$
and equation (\ref{BTFteq3}) reduces to the case of free
precession,
\begin{equation}
\dot\gamma=-\frac{3}{4}\eta\frac{v_{\psi}}{r}\eqnum{15a}
\end{equation}
with no associated evolutionary damping of orbit inclinations, that is,
\begin{equation}
\dot\beta =0\;.\eqnum{15b}
\end{equation}
\noindent
Equation (15a) can be integrated to give
\setcounter{equation}{15}
\begin{equation}
\gamma\bigl(r,t\bigr)=\gamma_{0}\bigl(r\bigr)-\biggl(\frac{3}{4}\eta
\frac{v_{\psi}}{r}\biggr)t\;,
\end{equation}
where $\gamma_{0}\bigl(r\bigr)$ prescribes the twisting of the disk at time
$t=0$.

\subsection{Stress-free Precession}

If the viscous stresses due to twisting have negligible effect on
differential precession during the settling process -- a condition
that SCD88 refer to as ``stress-free precession'' -- one may set
$\beta^{\prime\prime}=\gamma^
{\prime\prime}=\beta^\prime=0$ in the governing, complex
twist-equation.  Under this condition, equation (\ref{BTFteq3})
predicts the following evolutionary behavior:
\begin{equation}
\dot \gamma = \nu\frac{\gamma^\prime}{r}-
\frac{3}{4}\eta\frac{v_\psi}{r}\\ \eqnum{17a}
\end{equation}
\begin{equation}
\dot \beta = -\frac{1}{2}\nu\bigl(\gamma^\prime
\bigr)^{2}\beta. \eqnum{17b}
\end{equation}
\noindent
This pair of equations matches equations [37a] and [37b] of SCD88
except that the first term on the RHS of equation [17a] is a factor
of 2 larger than the equivalent term in equation [37b] of SCD88.
We suspect that the SCD88 result is in error, but we have been
unable to identify where SCD88 dropped the factor of 2 because their
published derivation was not sufficiently clear.

If we furthermore adopt the ``stress-free'' precession condition introduced
by SCD88, the first term in equation (17a) is set to zero (hence the
discrepant factor of 2 is not an issue) and the equation reduces to the
form of equation (15a) --- hence,
\setcounter{equation}{17}
\begin{equation}
\gamma^\prime=\gamma_{0}^\prime+\biggl(\frac{3}{4}\eta\frac{v_{\psi}}{r^{2}}
\biggr)t\;.
\end{equation}
With $\gamma_{0}^\prime=0$, equation (17b) specifically integrates to give
\begin{equation}
\beta=\beta_0\exp\biggl[-\bigl(t/\tau_{e}\bigr)^3\biggr]\;,
\end{equation}
where
\begin{equation}
\tau_{e}\equiv \biggl[\biggl(\nu/6\biggr)\biggl(\frac{3}{4}\eta\frac
{v_{\psi}}{r^{2}}\biggr)^{2}\biggr]^{-\frac{1}{3}}\;,
\end{equation}
and $\beta_{0}$ is the value of the inclination at $t=0$.  Hence the
analytical settling model presented by SCD88 (see also Steiman-Cameron,
Kormendy, \& Durisen 1992) can be
straightforwardly derived from our generalized twist-equation.

It is not at all clear how widely applicable the SCD88 analytical
settling model is to the warped \ion{H}{1} disks of normal spiral galaxies
because the simplifying assumptions (e.g., $\beta^{\prime\prime}=
\gamma^{\prime\prime}=\beta^\prime=0$) are quite limiting.  However, with the
analytical twist-equation in hand, we can perform a less restrictive
examination of such systems.

\subsection{General Separable Treatment}

We begin by rewriting equation (\ref{BTFteq3}) in the form
\begin{equation}
\dot w=w^{\prime\prime}+2\frac{w^\prime}{x}-i\frac{w}{x}\;,
\label{BTFteq4}
\end{equation}
where derivatives are now taken with respect to the dimensionless
time and space variables
\begin{eqnarray}
\tau&\equiv & t/t_0\nonumber\\
\;x&\equiv & r/r_0\nonumber,
\end{eqnarray}
and
\begin{eqnarray}
t_{0}&\equiv & \frac{8}{9}\nu\bigl(\eta v_{\psi}\bigr)^{-2}\;\label{dimt}\\
\;
r_{0}&\equiv & \frac{2}{3}\nu\bigl(\eta v_{\psi}\bigr)^{-1}\;.
\label{dimr}
\end{eqnarray}
\noindent
If we assume that the spatial
and temporal parts of the complex angle $w$ are separable, i.e.,
\begin{equation}
w=T\bigl(\tau\bigr)\cdot\zeta\bigl(x\bigr)\;,
\end{equation}
then
\begin{equation}
T=T_0\exp\bigl[-k^2\tau\bigr],
\end{equation}
where $k$ is in general complex, and $\zeta(x)$ must be a solution of
\begin{equation}
\zeta'' + 2 \frac{\zeta'}{x} + \bigl(k^2 - \frac{i}{x}\bigr)\zeta = 0.
\end{equation}
The above equation can be transformed by the substitutions $\xi^2 = -4ix$ and
 $\zeta(x) = Z(\sqrt{-4ix})/\sqrt{x}$,
into a form which shows its relationship to Bessel's equation
\def{\rm d}{{\rm d}}
\begin{equation}
\frac{{\rm d}^2 Z(\xi)}{{\rm d}\xi^2} + \frac{1}{\xi}\frac{{\rm d} Z(\xi)}{{\rm d}\xi} +
\biggl(1 - \frac{1}{\xi^2} - \frac{1}{4} k^2\xi^2 \biggr) Z(\xi) = 0 \; .
\label{zeq}
\end{equation}
The character of the solutions and the
spectrum of $k$ are determined by boundary conditions, but some general comments
can be made without reference to specific boundary conditions or initial state.
The fact that one can do so is important here since we do not have a
well-posed problem in which we know the initial state and the relevant boundary
conditions.  For each $k$ there is a radius $x$ inside which the third term
inside the parantheses in equation (27) may be neglected.
In this region the solution behaves as $J_1(\xi)$.
We rule out $Y_1$ because it is not finite at the origin (Abramowicz
\& Stegun 1972) whereas for plausible initial states $w$ must be finite
everywhere.  In general, the spectrum of $k$ may contain both growing
and decaying modes.  We do not consider growing modes since their
presence would indicate instability.  The fact that one can fit
a number of observational cases with the simpler solution in which only
decaying modes are present may be considered a justification {\it
a posteriori} of this assumption.
In any case, it is clear that if an arbitrary initial state can be written
as a superposition containing many values of $k$ satisfying appropriate
boundary conditions, the behaviour in the central region will approach the solution
with $k=0$. This tendency manifests itself as a function of time first near the
center and later further out as any contribution with large $Re(k^2)$ dies away
rapidly. Since the solution with $k=0$ is formally the steady--state solution,
we would expect it to apply more or less universally to the interior regions of
twisted disks, no matter what the initial conditions were. The memory of the
initial conditions is erased inside--out leaving at most an exponentially
decaying twist in the innermost regions.

Because the functions of primary interest to us ultimately are $\beta\bigl(x\bigr)$
and $\gamma\bigl(x\bigr)$, we note that
\begin{eqnarray}
\beta&=&T_0\biggl[{\zeta_R}^2+{\zeta_I}^2\biggr]^{\frac{1}{2}}\exp
\biggl[-Re\bigl(k^2)\tau\biggr],
\label{beta}\\
\gamma&=&\bigl(\theta + \phi\bigr)+\frac{\pi}{2},
\end{eqnarray}
where:
\begin{eqnarray}
\zeta&=&\zeta_R+i\zeta_I,\\
\theta&\equiv & -Im\bigl(k^2\bigr)\tau,\\
\phi &\equiv &\tan^{-1}\bigl(\zeta_I/\zeta_R\bigr).
\label{phi}
\end{eqnarray}

Because $\dot \gamma = \dot \theta = -Im\bigl(k^2\bigr)/t_0$, we recognize also
that for a given $k$, the time--dependent solution of equation (21) presents a
wave (with a ``twisted'' spiral character) that propagates azimuthally through the
disk with a pattern speed
\begin{equation}
{\Omega}_p = -Im\bigl(k^2\bigr)/t_0 = -\frac{8}{9} Im\bigl(k^2\bigr)
\frac{\bigl(\eta v_{\psi}\bigr)^2}{\nu}\;.
\label{omeq}
\end{equation}

\subsection{Steady-State Solution}

Drawing on the HBS discussion, we realize that an analytical solution to the
steady-state problem can be derived.  Specifically, setting
$\dot w=0$ in equation (\ref{BTFteq4}) or $k^2=0$ in equation (\ref{zeq}), we obtain
formally
\begin{equation}
w=\frac{1}{\sqrt{x}}Z_{1}\bigl[\sqrt{-4ix}\bigr]\;,
\label{BTFteq5}
\end{equation}
where $Z_{1}$ is any first-order Bessel function of the first kind
(see Gradshteyn \& Ryzhik 1965, \S 8.491, equation 3).
The physically most
relevant solution appears to be $Z_{1}=J_{1}$ because in this case
$\beta$ is finite as $x\rightarrow 0$
and as $x$ increases, $\beta$ increases
monotonically (Abramowicz \& Stegun 1972).
As a point of reference for all subsequent models, then,
we define the steady-state twisted-disk function
\begin{equation}
w_{ss}\equiv \frac{1}{\sqrt{x}}J_{1}\bigl[\sqrt{-4ix}\bigr] =
\frac{1}{\sqrt{x}}[{\rm ber}_1(2\sqrt{x}) + i {\rm bei}_1(2\sqrt{x})]\; ;
\label{wss}
\end{equation}
where ${\rm ber}_1$ and ${\rm bei}_1$ are the Bessel--real and Bessel-imaginary or
Kelvin
functions (see e.g. McLachlan 1941; Abramowicz \& Stegun 1972).
This solution leads to the functions $\beta_{ss}(x)$
and $\gamma_{ss}(x)$ shown in Fig.\ 2. From (\ref{wss}) one can obtain $\beta_{ss}$
and $\gamma_{ss}$ in closed form as follows:
\begin{mathletters}
\begin{eqnarray}
\beta_{ss}  &= \frac{1}{\sqrt{x}} M_1(2\sqrt{x}), \\
\gamma_{ss} &= \theta_1(2\sqrt{x}) + \frac{\pi}{2} ;
\end{eqnarray}
\end{mathletters}
\noindent
where $M_1(x)$ and $\theta_1(x)$ are the modulus and phase functions for
${\rm ber}_1(x)$ and ${\rm bei}_1(x)$.
Over the interval $1 \lesssim x \lesssim 20$, $\beta_{ss}$ and $\gamma_{ss}$ are
approximated well by the expressions:
\begin{mathletters}
\begin{eqnarray}
\beta_{ss} &\approx & 1 + 1.20\biggl(\frac{x}{10}\biggr)
+ 0.75\biggl(\frac{x}{10}\biggr)^2
+ 1.22\biggl(\frac{x}{10}\biggr)^3,\\
\gamma_{ss} &\approx & \frac{\pi}{4}\biggl[1 + 6.8\biggl(\frac{x}{10}\biggr)
- 3.9\biggl(\frac{x}{10}\biggr)^2
+ 1.63\biggl(\frac{x}{10}\biggr)^3
- 0.28\biggl(\frac{x}{10}\biggr)^4\biggr].
\end{eqnarray}
\end{mathletters}
\noindent
As we shall illustrate presently,
the {\it form} of the function $w_{ss}$ over the interval
$1 \lesssim x \lesssim 20$ defines
a warped disk model whose features match the observed
properties of a number of individual \ion{H}{1} disks.

\section{Application to Galaxies}
\subsection{Standard Model}

The steady-state solution just derived is formally inappropriate for real galaxies
especially because the outermost regions of real galaxy disks are unlikely to be
described well by time-independent conditions.  However, over the (innermost) regions
of a galaxy disk where differential precession and viscous dissipation have been able
to effect appreciable settling in a Hubble time, we expect the spatial structure of the
disk to assume a form that is very similar to the one portrayed by the function
$w_{ss}\bigl(x\bigr)$.  More specifically, the discussion in \S 3.3
and equations
(\ref{beta})-(\ref{phi}) suggest a general time-dependent behavior of the form:
\begin{mathletters}
\begin{eqnarray}
\beta&\sim&g\vert w_{ss}\vert,
\label{betass}\\
\gamma&\sim&\tan^{-1}\bigl[-Re(w_{ss})/Im(w_{ss})\bigr],
\label{gammass}
\end{eqnarray}
\end{mathletters}
\noindent
where
\begin{equation}
g\sim\beta_0e^{-\sigma\tau}\;,
\eqnum{38c}
\label{f}
\end{equation}
is a spatial constant that describes the amplitude of the warp at a given
time and whose time-evolution follows the above form with $\sigma$ being the
lowest $Re(k^2)$ compatible with boundary conditions.  Again, since we do
not have a well-posed problem, all we can say is that whatever restrictions
the boundary conditions impose on the spectrum of $k$,
only the lowest $Re(k^2)$ will survive after some time.  When comparing our model
to the properties of real galaxy disks, we will treat $g$ as a free parameter
that measures the overall amplitude of a galaxy's warp
and not be immediately concerned about the values of $\beta_{0}$, $\sigma$,
or the age of each disk.

The other free parameter that may be adjusted before our twisted disk model
is compared to real galaxy disks is  $x_{max}\equiv r_{max}/r_{0}$, the
radial cutoff to the function $w_{ss}\bigl(x\bigr)$ that will correspond to
the maximum radial extent $r_{max}$ of a galaxy's \ion{H}{1} disk.
Although $r_{max}$ can be specified for individual galaxies
(see Table 1), the length scale $r_{0}$ as defined in equation (\ref{dimr}) cannot be
specified {\it a priori} because neither of the physical parameters
$\nu$ or $\eta$ is known for individual galaxies.
Hence, initially it was unclear to us what cutoff radius $x_{max}$
({\it i.e.}, what range $0 \leq x \leq x_{max}$) should be adopted
for our model.  Fortunately, from previously published tilted--ring models of
warped \ion{H}{1} disks we were able to determine how rapidly
the warp angle $\beta$ and the twist angle $\gamma$ vary with radius in
real galaxies.  More specifically, we measured the ``pitch--angles"
$d\ln \beta (x)/d\ln x$ and $d\ln \gamma(x)/d\ln x$ in several systems,
then looked for the range(s) of $x$ in our steady--state model over which
both pitch--angle values occurred simultaneously.  We found good matches only
when $x_{max} \sim 10$, that is, galaxy models which match the observations
cannot be produced with values of $x_{max}$ that are orders of magnitude less than
or greater than $10$.
Previously constructed tilted--ring
models also directed the choices of the maximum warping angles
$g$ in our models.

\subsection{Comparison with Specific Galaxies}
By selecting a single value of $x_{max}$ (specifically, $x_{max} = 13$)
and a rather narrow range of warp amplitudes $g$, we have been able to
match many of the qualitative features that are frequently seen in
the published \ion{H}{1} maps of galaxies.
For example, using the model parameters identified in Table 1, we have
produced the surface brightness maps and radial velocity maps
depicted in Fig.\ 3 for comparison with published maps of the galaxies
M83, NGC300, NGC2841, NGC5033 and NGC5055.

Figure 3 actually has been pieced together from five separate
frames of a $>$ 600-frame digital animation sequence in which the viewer
``flies around'' our model disk, examining it
from a variety of different lines of sight.  The two angles $i_o$ and $t_o$
uniquely define the orientation of the
observer's line of sight with respect to the $(x,y,z)$ Cartesian coordinate system (see Fig.\
1) that is fixed in the body of the galaxy.
(When the inclination angle $i_{o} = 0^\circ$ or
$360 ^\circ,$ the galaxy is being viewed face-on with its angular momentum
vector pointing
directly at the observer; when $i_{o} = 90^\circ,$ the galaxy is seen edge-on with its
angular momentum vector pointing down.  When the azimuthal orientation angle $t_{o} =
0,$ the $+x$ axis is pointing to the right in each image; when $t_{o} = 90^\circ,$
the $-y$ axis is pointing to the right.)  In each frame of Fig.\ 3, the disk is displayed in
three
different ways:  the righthand image is the disk's projected 2D velocity contour map;
the central image is the disk's projected 2D surface brightness map; and the
lefthand image presents a 3D rendering of an isodensity surface that encloses virtually the
entire disk.  Each of the velocity contour maps and surface brightness maps in Fig.\ 3 were
produced with the 3D radiative transfer routine developed by V\"ath (1994); each 3D
isodensity
surface was generated using the IDL imaging package.  In the lefthand image of each
frame,
the light source reflecting from the disk's
surface originates from the same position as the viewer's eye.  The five frames displayed in
Fig.\ 3 were selected from our animation sequence because they identify observer lines of
sight
from which our model's
projected 2D maps match well the published maps of the five indicated galaxies.

NGC 2841:  To produce the frame of Fig.\ 3 that is identified as NGC 2841, we set
$g=1.2\times 10^{-2}$
in our model disk which corresponds to a maximum warp at the edge of the disk
of $4.5^\circ$.  In Fig.\ 3, the galaxy's angular momentum vector is pointed almost
directly
straight up (the disk is tipped slightly so that the viewer is seeing the ``top'' side of the
galaxy), so velocity contours to the right of the kinematic minor axis are red-shifted and
contours to the left are blue-shifted.  Our 2D projected surface-brightness and velocity
maps should be compared, respectively, with the \ion{H}{1} maps published as Figs.\ 7a
and 7b in Bosma (1981).  Bosma's maps have been reprinted here in Fig.\ 4a.
In order to make the relevant comparisons, the observational maps
have been rotated counterclockwise approximately $125^\circ$ in order to properly
orient them with
respect to our model images.  After this rotation has been made, as our 3D
rendering
illustrates, the southern edge of our model disk is farther away from the observer than is its
northern edge; this is consistent with the tilt interpretation one derives from an optical
photograph of NGC 2841 and dust obscuration arguments (cf. Plate 14 in Sandage 1961
and Table 3 of CTSC).

The velocity contour map of our model of NGC 2841 displays the same gentle,
counter--clockwise twist as the observed \ion{H}{1} velocity map.  Furthermore,
the north-south extensions seen in Bosma's
surface-brightness map of NGC 2841 can be identified with the ``leading arm''
features that appear in the projected surface-brightness image of our twisted disk
model.

M83:  To produce the frame of Fig.\ 3 that is identified as M83, we set
$g=2.2\times 10^{-2}$ in our
model disk, which corresponds to a maximum warp at the edge of the disk of
$8.3^\circ$.
The model is oriented so that, in Fig.\ 3, the galaxy's angular momentum vector is pointed
into the page, almost directly away from the observer. (With this orientation, M83's
optically
visible spiral arms -- cf. Plate 28 in Sandage 1961 -- are ``trailing'' spiral features.)
The disk is not being viewed
precisely face-on; as displayed in Fig.\ 3, it is oriented such that, even if the disk were
perfectly flat, its upper half would be tipped slightly away from the observer and its lower
half toward the observer.  As a result of this orientation, velocity contours to the right of
the kinematic minor axis are blue-shifted and contours to the left are red-shifted.  Our 2D
projected surface-brightness and velocity maps should be compared, respectively, with the
\ion{H}{1} maps published as Figs.\ 2 and 3 in Rogstad, Lockhart, \& Wright (1974;
hereafter RLW).  RLW's maps have been reprinted here in Fig.\ 4b.
In order to make the relevant comparisons, the observational maps have been
rotated counterclockwise approximately $180^\circ$ in order to properly orient
them with respect to our model images.

The velocity contour map produced by our twisted disk model of M83
displays most of the broad features that appear in the \ion{H}{1} velocity map published
by RLW.
The surface-brightness map published by RLW displays a pair of
faint, ``leading spiral'' arms that are not noticeable in the image we have produced in Fig.\ 3
from our model.  (The features are actually present in our model at a very low amplitude
level  and can be enhanced somewhat by adjusting the model parameter $g$.  See, for
example, the tilted--ring model developed by RLW and the model published by CTSC.)
Analogous features {\it are} present in our surface-brightness image
of NGC 300, presented below. As the 3D isodensity surface of our model of M83
suggests, these spiral--arm features probably appear in projected surface-brightness
maps of M83 because the galaxy's twisted \ion{H}{1} disk is bending toward
the observer in the northwestern quadrant and away from the observer in the
southwestern quadrant.

NGC 5033:  To produce the frame of Fig.\ 3 that is identified as NGC 5033, we set
$g=3.2\times 10^{-2}$
in our model disk which corresponds to a maximum warp at the edge of the disk of
$12^\circ$.  In Fig.\ 3, (see also Fig.\ 5 and the related discussion in \S 4.3,
below),
the galaxy's angular momentum vector is pointed down and away
from the observer, so velocity contours to the right of the kinematic minor axis are
blue-shifted and contours to the left are red-shifted.  Our 2D projected
surface-brightness and velocity maps should be compared, respectively, with the
\ion{H}{1} maps
published as Figs.\ 4a and 4b in Bosma (1981).  Bosma's maps have been
reprinted here in Fig.\ 4c.  In order to make the relevant comparisons,
the observational maps have been rotated counterclockwise approximately
$100^\circ$ in order to properly
orient them with respect to our model images.

Both the velocity contour image and the surface-brightness image produced by
our model of NGC 5033 bear a striking resemblance to Bosma's published maps.
The relatively steep density gradients that
are visible at the northeast and southwest edges of Bosma's surface-brightness maps are,
according to our model, clearly due to the disk bending toward the observer at one edge
and away from the observer at the other.

NGC 5055:  To produce the frame of Fig.\ 3 that is identified as NGC 5055, we set
$g=5.7\times 10^{-2}$
in our model disk which corresponds to a maximum warp at the edge of the disk
of $21.3^\circ$.  This galaxy's angular momentum vector, like that of NGC 5033 (notice
that $i_{o}$ is the same in these two systems), is pointed down and away from the
observer, so velocity contours to the right of the kinematic minor axis are blue-shifted and
contours to the left are red-shifted.  Our 2D projected surface-brightness and velocity maps
should be compared, respectively, with the \ion{H}{1} maps published as
Figs.\ 6a and 6b
in Bosma (1981).  These maps are reprinted in Fig.\ 4d of this manuscript.
In this case, the observational maps did not need to be rotated more than
$\sim 10^\circ$ clockwise in order to make the relevant comparisons.

Again, the velocity contour image and the surface-brightness image produced by our model
bear a strong resemblance to Bosma's published maps.
Notice, in particular, that from this line-of-sight,
thin arcs are displayed in the upper lefthand and lower righthand regions of our
model's projected surface-brightness map.  Bosma's \ion{H}{1}
surface-brightness map definitely displays similar features.

NGC300:	To produce the frame of Fig.\ 3 that is identified as NGC300, we set
$g=5.7\times 10^{-2}$
in our model disk, which corresponds to a maximum warp at the edge of the
disk of $21.3^\circ$.  The model is oriented so that the galaxy's angular momentum
vector
is pointed out of the page, almost directly at the observer. The disk is not being viewed
precisely face-on; as displayed in Fig.\ 3, it is oriented such that, even if the disk were
perfectly flat, its upper half would be tipped slightly toward the observer and its lower half
away from the observer.  As a result of this orientation, velocity contours to the right of the
kinematic minor axis are blue-shifted and contours to the left are red-shifted.  Our 2D
projected surface-brightness and velocity maps should be compared, respectively, with the
\ion{H}{1} maps published as Figs.\ 1 and 2 in Rogstad, Crutcher, \& Chu
(1979; hereafter RCC).  RCC's maps have been reprinted here in Fig.\ 4e.
In order to make the relevant comparisons, the observational maps have been
rotated counterclockwise approximately $160^\circ$ in order to properly orient them
with respect to our model images.
Notice that after this rotation has been made, our 3D rendered image of
NGC300 closely resembles the perspective drawing of RCC's tilted-ring model
(see their Fig.\ 6).

Notice, first, that the velocity contour image of our model of NGC 300 closely
resembles RCC's published velocity map.  In addition, our
surface-brightness map displays a pair of faint, ``leading
spiral'' arms that touch the left and right edges of the image shown in Fig.\ 3.  We believe
that these arms provide an explanation for the faint features that extend to the northwest
and, particularly, southeast regions of the RCC map.

\subsection{Prograde versus Retrograde Precession}
The model that was used to generate images for Fig.\ 3 was constructed assuming that the
precessional frequency $\omega_{p}$ was negative (see eq. 11).  That is, the underlying
halo was assumed to be {\it oblate} in shape and accordingly, the precessional motions
retrograde with respect to the orbital motion of the gas.  Because the magnitude of the
precessional frequency {\it decreases} with increasing radius in each disk, retrograde
precession results in a physical twist that has a ``leading'' appearance in the 3D,
rendered image of each system.  (In contrast, optically visible spiral arms are generally
thought to be ``trailing'' features.)  Knowing this, one can discern whether the angular
momentum vector of each galaxy is pointing into (out of) the page by simply
noticing whether
the warped structure exhibits an overall clockwise (counterclockwise) twist.

As CTSC pointed out, an identically good fit to the \ion{H}{1} maps can be obtained with
a disk that exhibits a retrograde twist (i.e., one that settles into a prolate
spheroidal
halo) as with a disk that exhibits a prograde twist.  After switching the sign of $\omega_p$
in eq. (11) to reverse the sense of the twisting in the 3D model, one need only adjust one's
line-of-sight viewing angle according to the prescription
\begin{eqnarray}
{i_{o}}^\prime&\equiv & \pi-i_o\;\\ \;
{t_{o}}^\prime&\equiv & \pi-t_o\;
\end{eqnarray}
in order to generate projected velocity and surface-density maps
from a ``prolate'' model that are identical to the maps generated from
and ``oblate'' model.  Fig.\ 5b illustrates
what the ``prolate'' model for NGC 5033 looks like once this transformation is employed.

If two quite different 3D disk structures (one with a prograde twist and one
with a retrograde twist) can generate identical 2D maps when projected onto the
sky, how can one decipher which offers the physically more realistic model?
As CTSC pointed out, information gleaned from optical photographs can often
provide the supplementary
information that is needed to identify which model is more realistic.  For example, one
must
insist that the angular momentum vector of M83 points away from the observer ({\it into}
the
page on Fig.\ 3) if its optical spiral arms are to be interpreted as {\it trailing} features;
hence a warped disk model with a prograde twist (and settling in an {\it oblate} spheriodal
halo) as illustrated in Fig.\ 3 is the preferred solution.  Similar arguments (or ones based
on dust obscuration) lead one to conclude that the disks of NGC 2841, NGC 5055
\footnote{In our judgement, CTSC misidentified NGC 5055 as requiring a
prolate halo.}, and NGC 300
are also settling in oblate spheriodal halos.  However, for NGC 5033, the retrograde
twisting
(prolate spheriodal halo) model is clearly preferrable to the prograde twisting model.  This
statement is supported by two arguments:  first, dust obscuration in an
optical photograph of NGC 5033
(cf. Fig.\ 4a of CTSC and Panel 127 of Sandage \& Bedke 1994) identifies
the western edge of the galaxy as nearer to the observer than its
eastern edge; second, model 5b must be chosen over 5a if the optical
spiral arms are to be interpreted as trailing features.  Hence, the 3D
image of NGC 5033 shown in Fig.\ 5b is the correct depiction
of the galaxy as inferred from our model fitting.

\subsection{Interpretation}

\subsubsection{Limited Range of Model Parameters}
It should be noted that the animation sequence from which the frames shown in Fig.\ 3
were
selected was originally constructed with the expressed intention of flying through lines of
sight that we previously had determined would produce good fits to M83, NGC 5033 and
NGC 300; the only intrinsic model parameter that was adjusted during the fly-by sequence
was the overall warp amplitude $g$.  During our viewing of the fly-by sequence,
we also spotted images that matched the published observational maps of NGC
2841
and NGC
5055.  The frames presented in Fig.\ 3 have been taken directly from the original animation
sequence; absolutely no attempt has been made to fine-tune the model parameters to fit
these two additional galaxies separately.  Clearly, then, it is primarily the line-of-sight
viewing angle to each disk and not the parameters defining the underlying structural
properties of each disk that had to be adjusted from galaxy to galaxy
in order to match the observations.  Considering its simplicity --
in particular, the significantly reduced number of free parameters as compared to
previous tilted-ring models -- the agreement between the projected maps of our
model and observed \ion{H}{1} maps is excellent.  We conclude, therefore, that the
function $w_{ss}\bigl(x\bigr)$
and the corresponding expressions for $\beta_{ss}$
and $\gamma_{ss}$ given by Eqs. (36a) and (36b)
provide a good template for matching the observed kinematical structure of
\ion{H}{1} disks.
Because a single value of the parameter $x_{max}$ and little variation
in the parameter $g$
are required to achieve a good model fit to five separate galaxies,
we conclude that these five systems intrinsically have very similar warped disk
structures.

\subsubsection{Physical Interpretation}
Most importantly, however, since the function $w_{ss}\bigl(x\bigr)$ derives from
a physically reasonable dynamical picture of disk settling, there is an expectation
that our model provides insight into the underlying physical properties of
these systems.  For example, since $x_{max} = 13$ for each galaxy, we conclude
from definition (\ref{dimr}) that in each galaxy, the ratio
\begin{displaymath}
\frac{\nu}{\eta}\approx 0.12v_{\psi}r_{max}\sim 600\,\rm{km\,s}^{-1}
\,\rm{kpc}=2\times10^{29} \rm{cm}^2 \rm{s}^{-1}\;,
\end{displaymath}
where $r_{max}$ is the outer radius of the observed \ion{H}{1} disk.
(Table 1 shows the values of $\nu/\eta$ calculated individually for
each modeled system.)  Also, if our model is relevant at all, the existence
of each warped layer indicates that viscous settling has been effective in a
Hubble time ($t\sim {H_0}^{-1}$) and $\tau\sim 1/\sigma$.
Without a proper understanding of the boundary conditions, we are unable to
determine the correct physical value of $\sigma$.
Assuming for the moment that $\sigma \sim 1$ and setting
$H_0 = 75\,\rm{km\,s}^{-1}\,\rm{Mpc}^{-1}$,
we conclude from definition
(\ref{dimt}) that
\begin{displaymath}
\frac{\nu}{\eta^2}\sim{v_{\psi}}^2{H_0}^{-1}\sim 600\,\rm{km\,s}^{-1} \rm{Mpc}\;.
\end{displaymath}
These two ratios can only hold if, in each system,
\begin{displaymath}
\nu\sim0.6\,\rm{km\,s}^{-1} \rm{kpc}=2\times10^{26} {\rm{cm}}^2 \rm{s}^{-1}\;
\end{displaymath}
and
\begin{displaymath}
\eta\sim{10}^{-3}\;.
\end{displaymath}
It is worth noting that the values obtained for $\nu$ in all cases
(see Table 1) are
consistent with a rough estimate of the viscosity due to
dissipational cloud--cloud collisions in the solar neighborhood where
$\nu \sim 0.25$  km/s kpc (Lynden-Bell \& Pringle 1974). Very modest
variations in cloud dimensions, r.m.s. velocity and filling factor
from galaxy to galaxy are sufficient to reproduce the range of values
shown on Table 1.  The fact that reasonable viscosity estimates are obtained
by assuming $\sigma\sim 1$ may be considered as a posteriori justification for
our choice.

\section{Discussion and Conclusions}

Utilizing the formalism originally introduced by Petterson to describe
warped and twisted accretion disk structures in Keplerian potentials, we
have derived a single, complex ODE to describe time dependent settling of
an \ion{H}{1} disk in the logarithmic potential that appears to be typical of normal
spiral galaxies.  Over the interval $1 \lesssim x \lesssim 20$, the analytical function
$w_{ss}\bigl(x\bigr)$ -- derived from an analysis of the steady-state limit
of the general twisted-disk equation -- appears to describe quite accurately the
general warped and twisted structure that is exhibited by a number of galaxy
disks.  It should be noted again that our analysis is based on the assumption
that the warping angle $\beta$ is $\ll 1$.
For galaxies with larger warps (including
some that we have modeled) this is a simplifying assumption and should be
disregarded in more proper treatments (see Pringle [1992]).

From our model fits we conclude that, quite generally, the effective kinematical
viscosity in these neutral hydrogen disks is $\nu\sim0.6$ km s$^{-1}$ kpc.
That is, the effective Reynolds number in these systems is
\begin{displaymath}
R_e\sim\frac{r_{max} v_{\psi}}{\nu} \sim \frac{x_{max}^2 v_\psi}{r_{max}}
\sim6000\;.
\end{displaymath}
According to equation (\ref{radvsub}), this also implies that the ratio of
the radial inflow velocity of the gas to its orbital velocity is
\begin{displaymath}
\frac{v_r}{v_{\psi}}\approx\frac{1}{R_e}\sim\times{10}^{-4}\;.
\end{displaymath}

This model also provides a mechanism by which the parameter $\eta$ -- the
quadrupole moment of the underlying dark halo potential well -- can be
measured in spiral galaxies.  Our fits to five normal spirals with well-studied
warped \ion{H}{1} disks specifically indicate that $\eta\sim{10}^{-3}$.  (This value
can be increased to $\eta\sim{10}^{-2}$, with a corresponding factor of ten
increase in viscosity, only if the age of these disks is
assumed to be 0.1$\,{H_0}^{-1}$ -- which seems unlikely -- or
$\sigma$ in expression 38c is found to be $\sim 0.1$.)  Hence, we conclude
that the dark halos in which these warped disks sit are, to quite high
accuracy, spherically symmetric.  This particular conclusion should not
come as a surprise because some time ago Tubbs and Sanders (1979) pointed out
that if warped disks are identified as transient structures,
the warp can only be sustained for
a Hubble time if the underlying halo potential is very nearly spherical.
Although we have examined in detail here only the steady-state solution, the
derived time-dependent twisted-disk equation provides a tool that can be
utilized to model the time-evolution of warped \ion{H}{1} disks without resorting to
elaborate numerical techniques.

The twisted-disk formalism in general -- and the analytical function $w_{ss}\bigl(x\bigr)$
in particular -- provides an avenue through which models of warped \ion{H}{1} disks can
advance from purely kinematical fits (e.g. tilted-ring models) to dynamical models
based on a reasonable physical model.  In the future, we also expect to use the
time-dependent form of the twisted-disk equations as a point of comparison for fully
three-dimensional gas dynamic simulations of \ion{H}{1} disks settling into distorted
halo potentials.
\acknowledgments

We appreciate the assistance that H. Cohl provided us in rendering the
3D galaxy images shown in Figs.\ 3 and 5, and also would like to thank
Dr. A. Bosma and Dr. D. Rogstad for granting permission to reprint figures from
their earlier papers. We also would like to thank the anonymous referee
for suggestions that resulted in substantial improvements in this
manuscript.
This work has been supported in part by NASA through grants NAGW-2447
and NAG5-2777, and in part by the U.S. National Science Foundation
through AST-9528424.

redpajama_set_name: RedPajamaArXiv


Alexander McLernon was born in the parish of Derryloran, Cookstown, the husband of Sarah Jane McLernon (nee Nelson). He was employed at Gunning's Factory, Milburn, Cookstown, before he enlisted with the 9th Battalion Royal Inniskilling Fusiliers. On 1st July 1916, when the 9th Inniskillings made their advance toward the Schwaben Redoudt, Alexander McLernon was seen to have been severely wounded. At the end of July, Mrs. Sarah Jane McLernon received a letter stating that all efforts to find her husband had failed and he hoped that he may still be alive and a prisoner of war.
3 National Archives UK Medal card can be purchased here - Alexander McLennon !!


text:
Q: Import a symbol from the Fourier font family
Possible Duplicate:
Importing a Single Symbol From a Different Font

I would like to use a single symbol from the fourier family in mathmode in one of my formulae in my document. In the comprehensive symbol archive,
ftp://tug.ctan.org/pub/tex-archive/info/symbols/comprehensive/symbols-a4.pdf
on page 53, the \partial symbol in table 147 is what I am after. How can I manage this?

A: I can't remember where I got this from, but here's what I have in my custom .sty file:
\DeclareFontEncoding{FML}{}{}%
\DeclareFontSubstitution{FML}{futm}{m}{it}%
\DeclareSymbolFont{fourier}{FML}{futm}{m}{it}%
\DeclareMathSymbol{\partialup}{\mathord}{fourier}{130} % Upright partial derivative symbol

I think that's the one you're looking for.

A: Minute differences, but the symbol \partial in table 147 is actually the italic non-variant version (kahen's solution is the roman \varpartial symbol):
\DeclareFontEncoding{FML}{}{}
\DeclareFontSubstitution{FML}{futm}{m}{it}
\DeclareSymbolFont{fourieritalic}{FML}{futmi}{m}{it}
\DeclareMathSymbol{\fpartial}{\mathord}{fourieritalic}{64}

redpajama_set_name: RedPajamaStackExchange


The New American Bible is the most widely used Catholic Bible version in the U. S. today. The Weekday and Sunday Mass readings are taken from the NAB version, and the U. S. Bishops have endorsed it for use in Catholic Church and school religious education programs across the country. With over 60 hours of narration and almost 7,000 unique scripture screens, the NAB Old Testament on DVD features Emmy-Award winning narrator Stephen Johnston. His crystal clear, mellow baritone voice provides distinct pronunciation, in and easy-to-understand style.


text:
MSCT and MR compete for intraoperative imaging
Intraoperative guidance with multislice CT could prove advantageous where intraoperative MR imaging falters. Researchers might benefit from applying each modality's capabilities where they prove most useful, according to Florida researchers.
Intraoperative guidance with 1.5T and 3T MR scanners overcomes most limitations of low-field systems and has already proved its worth in neurosurgical settings. But these scanners are complex, expensive to run, and require MR-compatible operation rooms. In contrast, MSCT adapts easily to the OR environment and provides significant speed and visualization. With MSCT guidance, surgeons can perform thoracoabdominal interventions in minutes without compromising image quality, said Dr. Gary M. Onik, an interventional radiologist and director of surgical imaging at the Center for Surgical Advancement's Celebration Health/Florida Hospital.
In an ongoing study, Onik and colleagues have thus far prospectively enrolled 30 patients who have undergone abdominal, chest, and brain surgeries under intraoperative guidance and monitoring with a 16-slice scanner. The fully OR-integrated system includes a mechanized arm that guides several surgical instruments, a table specially designed to serve as a patient-immobilization device and respiratory-gating platform, and fluoroscopy and ultrasound equipment for simultaneous multimodality scanning and monitoring.
The Center for Surgical Advancement's system can guide laparoscopic and thoracoscopic procedures to remove occult pathology and to displace organs to protect them from thermal injury or bleeding during cryo- or radiofrequency ablation procedures. It also allows simultaneous monitoring and control of outcomes and complications. The CSA team presented their preliminary findings at the American Roentgen Ray Society meeting last month.
The researchers have developed ways to minimize the system's shortcomings. Alternative guidance and monitoring with ultrasound reduces the need for CT. They have also developed patient-protective pads to cut radiation exposure and are designing a special device that will allow manipulation of surgical instruments outside the scan's gantry. Several institutions have already expressed interest in the CSA's intraoperative MSCT setup, and plans are under way to implement it in a mobile operating room for smaller hospitals, Onik said.
"We have been able to monitor lesions and guide the laparoscopic surgeon down to the pathology to remove it minimally invasively. Intraoperative MSCT has had a major impact on the ability of our surgeons to take patients who otherwise would have been candidates for open surgery," he said.
Harvard researchers plan to install a PET/CT scanner in their OR for similar purposes and expect to benefit from PET's specificity to detect tumors, said Dr. Ferenc A. Jolesz, director of the MRI and image-guided therapy program at Brigham and Women's Hospital.
In spite of MSCT's perceived advantages, only MR can provide intraoperative imaging without interrupting surgery, Jolesz said.

redpajama_set_name: RedPajamaCommonCrawl


Creating a spinoff to a popular TV show is never an easy task, which is evidenced when one looks at the long list of failed attempts at doing so. Even harder is creating a spinoff of a critically acclaimed series like Vince Gilligan's crime epic Breaking Bad, which many hold up as one of the best dramas to grace TV in recent memory. Thankfully, Better Call Saul proved more than up to the task, quickly establishing itself as another critical darling.
Of course, it's not just critics who have responded well to Saul, with the series drawing consistently good - if not Walking Dead-level - ratings for AMC. As evidence, Saul's future has never really been in doubt so far, with its renewals for both season 2 and this year's season 3 seen by most as foregone conclusions. In the land of fiction though, one man not pleased with the current direction of Better Call Saul is likely main character Jimmy McGill (Bob Odenkirk) himself, whose life just seems to get more complicated with each passing episode.
As fans will recall, Better Call Saul season 2 ended with a crafty Chuck (Michael McKean) tricking Jimmy into admitting to a serious crime while being unwittingly recorded. It remains to be seen what exactly Chuck will do with this proverbial smoking gun of evidence, but there's no way it leads anywhere good for Jimmy. Thankfully, as reported by Variety, AMC has revealed the date on which Jimmy's story will further begin to unfold: Monday, April 10. Additionally, TVLine officially confirms the addition of Breaking Bad villain Gus Fring (Giancarlo Esposito), which was teased earlier this week in an amusing parody commercial for Fring's Los Pollos Hermanos chicken restaurant.
Better Call Saul season 3's April premiere date is noticeably later than that of seasons 1 and 2, which premiered in February. Season 3 will once again consist of 10 episodes though, so it seems that Jimmy's 2017 run will extend nearly into the summer. In addition to the premiere date and Gus Fring reveals, AMC has also released an official sneak peek clip from season 3's premiere, featuring what looks to be a fairly large change in Jimmy and Kim's working relationship at their joint practice. The full clip can be seen above.
During a TCA press event earlier today Esposito made it known that when Gus makes his debut on Better Call Saul, he won't quite be the cold and calculating meth kingpin he was on Breaking Bad, and that he's "still finding his way." For Jimmy's sake, here's hoping he doesn't find his way too quickly. At the moment, Walter White's future "criminal lawyer" has more than enough on his plate.
Better Call Saul season 3 premieres Monday, April 10 on AMC.


Yes, you can now pay your bills with a classic Untuxable design, the Annoyed Cat. Yes, it's legal! You can get a variety of denominations – the stamps come 20 to a sheet. You can even get postcards with the Annoyed Cat postage already printed on them, in a variety of sizes!


One of the wonderful things about Italy was the paper. Yes, for the bookbinder in me, this was a paper paradise. I have always enjoyed working with Italian papers and so you can imagine how excited I got when I saw several art stores that had sheet after sheet of wonderful styles.
They had gorgeous marbled papers, lovely stationery that made you want to write long letters, and silky soft leather bound books.
Aren't they gorgeous? I look forward to working with these for new creations. Now, I have to get going and start packing. We start our journey back home tomorrow and as always it'll be super hard to say good-bye to Germany but we'll be back.
Hope you've all been having a wonderful summer so far and I look forward to catching up with your blogs once I've settled back home.
I love seeing all the photos from your travels around Germany & Italy. I am glad you enjoyed your time in Italy and found some wonderful places for inspiration! Those papers and handmade and lovely books. The Italian papers are just gorgeous – can't wait to see what you create with them.
I think you are on your way back – safe travels and look forward to hearing more news soon!
Bliss! 🙂 I see you have a package (I think that is you?). What did you buy??
Those are soooo lovely! Thanks for sharing the pics!
So pretty! I hope you enjoyed your trip!


I know there are a heap more. I know more will be submitted. This is just what I found when scanning the first few pages of a search for "xhtml".
I've encountered 5144 directly on this blog with my clip art. I've found that I have to start the paragraph right after the <object> tag without a newline. A little annoying, but workaround-able.
Shelley just created Bug 5998 right now. This is a bug for WP accepting illegal Unicode code points like U+FFFE, which Jacques so kindly demonstrated.


text:
Alan Bain
Aspro, Aspro
Emailabaincsu.eduau
2 Research report not released to public
Academics' perceptions of collaboration in higher education course design
Newell, C. & Bain, A., 2020, In: Higher Education Research and Development. 39, 4, p. 748-763 16 p.
organizational structure 40%
empirical research 33%
Addressing the challenges of program and course design in higher education with design technologies
Bain, A., 10 Jul 2020, In: Journal of Applied Instructional Design. 9, 2, p. 1-9 9 p.
best practice 86%
A longitudinal study of the practice fidelity of a site-based school reform
Bain, A., Apr 2010, In: Australian Educational Researcher. 37, 1, p. 107-123 17 p.
school reform 100%
longitudinal study 68%
teacher 27%
A systems view of terminology
Bain, A., 2005, In: International Journal of Speech-Language Pathology. 7, 2, p. 94-97 4 p.
Bridging the Research-to-Practice Gap: A Review of the Literature Focusing on Inclusive Education
Grima-Farrell, C., Bain, A. & McDonagh, S., Dec 2011, In: Australasian Journal of Special Education. 35, 2, p. 117-136 20 p.
literature 100%
educational practice 57%
Bridging the research-to-practice gap in education: A software-mediated approach for improving classroom instruction
Weston, M. E. & Bain, A., May 2015, In: British Journal of Educational Technology. 46, 3, p. 608-618 11 p.
instruction 90%
Can schools realize the potential of knowledge management?
Bain, A. & Parkes, R., 2006, In: Canadian Journal of Learning and Technology. 32, 2, p. 1-8 8 p.
knowledge management 100%
transaction 18%
learning process 14%
Collaborative course design and mapping: A team approach to course development and review
Bain, A., Zundans-Fraser, L., Lancaster, J. & Hollitt, J., 2004, Making Spaces: Regenerating the Profession, Proceedings of the 2004 ATEA Conference,. Bathurst, Australia: Australian Teacher Education Association
Curriculum authoring tools and inclusive classroom teaching practice: a longitudinal study
Bain, A. & Parkes, R., 2006, In: British Journal of Educational Technology. 37, 2, p. 177-190 14 p.
teaching practice 100%
integrity 58%
Designing Emergent Feedback Systems: Lessons Learned from a 10-Year School Reform Initiative
Bain, A., 2005, In: International Journal of Educational Reform. 14, 1, p. 89-111 23 p.
comprehensive school 34%
reform model 14%
scaling 10%
narrative 5%
Designing university courses to improve pre-service teachers' pedagogical content knowledge of evidence-based inclusive practice
Lancaster, J. & Bain, A., Feb 2019, In: Australian Journal of Teacher Education. 44, 2, p. 51-65 14 p., 4.
university 100%
self-organization 86%
Does the ATAR predict pre-service teacher capacity for inclusive classroom practice?
Auhl, G. & Bain, A., Apr 2021, In: Australian Journal of Teacher Education. 46, 4, p. 81-91 11 p.
classroom 100%
semester 37%
Do judgements about pre-service teachers' self-efficacy covary with their capacity to design and deliver evidence-based practice?
Lancaster, J. & Bain, A., 2021, In: International Journal of Inclusive Education. 25, 7, p. 827-842 16 p.
Pre-service Teachers 100%
Evidence-based Practice 83%
Course Design 46%
Do pre-service teachers develop a schema for inclusive classroom practice?
Auhl, G. & Bain, A., 20 Jul 2020, (E-pub ahead of print) In: Asia-Pacific Journal of Teacher Education. p. 1-17 17 p.
Early Adopting Courses Evaluation Report 1
Zundans-Fraser, L. & Bain, A., 2014, Charles Sturt University. 51 p.
Research output: Book/Report › Research report not released to public
Embedding evidence -based practice in pre-service teacher preparation.
Bain, A., Lancaster, J., Zundans-Fraser, L. & Parkes, R., 2009, In: Teacher Education and Special Education. 32, 3, p. 215-225 11 p.
evidence 100%
self-study 91%
cooperative learning 86%
level of knowledge 85%
Engaging with change: a model for adopting and evaluating school-based innovation
Weston, M. E. & Bain, A., 2009, In: Journal of Educational Administration. 47, 2, p. 156-175 20 p.
innovation 100%
methodology 61%
paradigm change 24%
school reform 19%
technical innovation 18%
How do institutional practices for course design and review address areas of need in higher education
Zundans-Fraser, L. & Bain, A., Feb 2016, In: Higher Education Research and Development. 35, 4, p. 841-853 13 p.
organizational structure 100%
regulation policy 68%
coherence 46%
If all you have is a hammer, everything begins to look like a nail: How wicked is the problem of measuring productivity in higher education?
Drengenberg, N. & Bain, A., 2017, In: Higher Education Research and Development. 36, 4, p. 660-673 14 p.
productivity 100%
organization 42%
Inclusion and Comprehensive School Reform: Lessons from the Field
Bain, A. & Lancaster, J., 2006, In: Australasian Journal of Special Education. 30, 1, p. 39-50 12 p.
comprehensive school 100%
inclusion 56%
secondary school 49%
Knowledge Discovery and Management; Streamlining Communication to Address Individual Student Needs
Bain, A., 2004, Looking Ahead: Independent School Issues & Answers. 2nd ed / n/a ed. Gilsum, United States of America: Avocus Publishing, Inc, p. 187-195 9 p.
Making a difference to the student experience through purposeful course design
Zundans-Fraser, L. & Bain, A., Aug 2020, In: Australian Journal of Teacher Education. 45, 8, p. 58-74 17 p., 4.
experience 100%
Meeting the needs of diverse learners in the mainstream: Does ATAR forecast the capacity to meet graduate teaching standards?
Auhl, G. & Bain, A., 2015, Coast to coast: Locations and directions in educational research. Baguley, M. (ed.). ACT, Australia: AARE, 1 p.
Research output: Book chapter/Published conference paper › Conference paper
graduate 100%
deficit 26%
Pattern language development in the preparation of inclusive educators.
Bain, A., Lancaster, J. & Zundans-Fraser, L., 2009, In: International Journal of Teaching and Learning in Higher Education. 20, 3, p. 336-349 14 p.
educator 100%
educational setting 32%
Rising to the challenge of transforming higher education: Designing universities for learning and teaching
Bain, A. & Zundans-Fraser, L., 2016, Singapore: Springer. 85 p. (SpringerBriefs in Education Ser.)
implementation process 59%
Secondary school reform and technology planning: Lessons learned from a ten year school reform initiative
Bain, A., 2004, In: Australasian Journal of Educational Technology. 20, 2, p. 149-170 22 p.
Self-organisation and capacity building: Sustaining the change
Bain, A., Walker, A. & Chan, A., 2011, In: Journal of Educational Administration. 49, 6, p. 701-719 19 p.
self-organization 100%
principal 13%
system theory 12%
Hong Kong 9%
secondary school 8%
Smart learning: Theory and research to practice
Bain, A. & Zundans-Fraser, L., 2014, Bathurst, NSW: Charles Sturt University. 39 p.
learning theory 100%
teaching research 13%
Strong foundations, stronger futures: Using theory-based design to embed indigenous Australian education content in a teacher education programme
Zundans-Fraser, L., Hill, B. & Bain, A., 2018, Promising pactices in indigenous teacher education. Whitinui, P., del Carmen Rodriguez de France, M. & McIvor, O. (eds.). 1st ed. Singapore: Springer, p. 265-277 13 p.
Teacher preparation and the inclusive practice of pre-service teachers: A comparative follow-up study
Lancaster, J. & Bain, A., 2020, In: International Journal of Inclusive Education. 24, 12, p. 1311-1325 15 p.
Teacher Preparation 100%
Pre-service Teachers 96%
Professional Learning 26%
Team-based collaboration in higher education learning and teaching: A review of the Literature
Newell, C. & Bain, A., 2018, Singapore: Springer. 70 p. (SpringerBriefs in Education)
Technology enhanced feedback tools as a knowledge management mechanism for supporting professional growth and school reform
Bain, A. & Swan, G., Oct 2011, In: Educational Technology Research and Development. 59, 5, p. 673-685 13 p.
knowledge management 88%
grouping 16%
level of education 16%
The design of inclusive education courses and the self-efficacy of preservice teacher education students.
Lancaster, J. & Bain, A., Jun 2007, In: International Journal of Disability, Development and Education. 54, 2, p. 245-256 12 p.
Teacher Training 100%
The design of pre-service teacher education courses and their effects on Self-Efficacy: A comparative study.
Lancaster, J. & Bain, A., 2010, In: Asia-Pacific Journal of Teacher Education. 38, 2, p. 117-128 12 p.
self-efficacy 100%
elementary education 36%
The End of Techno-Critique: The Naked Truth about 1:1 Laptop Initiatives and Educational Change
Weston, M. E. & Bain, A., Jan 2010, In: Journal of Technology Learning and Assessment. 9, 6, p. 5-25 21 p.
Laptop computers 100%
criticism 61%
conversation 57%
Reforming reactions 42%
critic 35%
The learning edge: what technology can do to educate all children
Bain, A. & Weston, M. E., 2012, 1st ed. New York: New York Teachers College Press. 235 p.
The measurement of pre-service teachers' schema for teaching students with diverse learning needs: Methodological considerations
Auhl, G. & Bain, A., 2014.
The role of collaboration in a comprehensive programme design process in inclusive education
Zundans-Fraser, L. & Bain, A., 2016, In: International Journal of Inclusive Education. 20, 2, p. 136-148 13 p.
Inclusive Education 100%
Designer 9%
examination 7%
The Self Organizing School: Next Generation Comprehensive School Reforms
Bain, A., 2007, Lanham MD, USA: Rowman and Littlefield Education. 280 p.
The self-organizing school theory: leading change for learning
Bain, A., 2011, International handbook of leadership for learning . Townsend, T. & MacBeath, J. (eds.). Germany: Springer-Verlag London Ltd., p. 953-974 21 p. 52
school theory 100%
metaphor 18%
The self-organizing university: Designing the higher education organization for quality learning and teaching
Bain, A. & Zundans-Fraser, L., 07 Jul 2017, Singapore: Springer. 192 p.
organization 100%
Transforming the measurement of learning and teaching in higher education
Bain, A. & Drengenberg, N., 01 Mar 2016, New York, United States: Routledge. 172 p.
Understanding learning and communication difficulties
Bain, A., 2010, Teaching and communicating: Rethinking professional experiences. Higgs, J. H. J. (ed.). 20 ed. South Melbourne: Oxford University Press, p. 217-225 9 p.
Using technology to bridge the research to practice gap in schools
Bain, A., Weston, M. E. & Lancaster, J., Jul 2019, Progress in Education. Nata, R. V. (ed.). New York: Nova Science Publishers, Vol. 60. p. 19-52 33 p.
counselor 100%
substance abuse 69%
coeducation 56%


After searching for several months for that perfect backdate project car, we came across a 1975 Carrera that had been converted to a Slantnose by a SoCal dealership in the late 80's. Being a California car, this chassis was rust free and a great starting point for what was to come. In addition to the rust free chassis the car also had the entire drivetrain from a 79 930. After a few more questions we learned the car had been serviced by our friends at Poudre Sports Cars in Denver, Colorado. A phone call yielded the details; the engine had been built two years prior and the parts list included JE pistons, LN cylinders, ARP head studs, topped with a K27 Turbo. Between the chassis and engine build we settled on this car as being the perfect candidate for our project and had the car dropped back off at Poudre Sports Cars so that it could be shipped over to us in Vermont.
Upon arrival at the Rennline shop, we spent some time sorting a few small issues and putting some miles on the engine to ensure everything was running correctly and up to snuff. Thanks to Poudre's top notch work, this was a short process and within no time the car was shedding its sheet metal in preparation for a complete restoration. A full array of early body panels were sourced and the slantnose parts were removed in preparation for the long hood conversion.
We are never ones to miss the opportunity to develop fresh parts for the Rennline catalog, and this project was the perfect chance to so some applied product development. First up was an RSR Style Strut brace which features dimple-died strut tower reinforcements to all but eliminate flex between the strut towers and caused by the forces transferred though the shocks themselves to the top mounts. Next up we jigged the new long hood on one of our water jets and wrote a CNC program to cut a hole for our new Center Hood Gas Filler. This piece is machined from billet aluminum right here in Vermont and is the perfect compliment to this or any 911 project.
With the extensive amount of body work needed for the backdate, we employed a hydraulic rotisserie that was custom built by one of our close friends with assistance from our CNC tooling centers. As anyone who has restored a car can tell you, removing factory undercoating is one of the worst tasks. This was made worlds easier with the rotisserie, and we tapped our catalog for some of Wurth's OEM quality SKS Stoneguard to coat the entire under body. This included the engine bay and entire floor which was body-matched after the Wurth products were applied.
Next up was the rolling gear- the suspension was all in decent shape, but a combination of old rubber and the fact that we can never leave well enough alone meant that a complete overhaul was in store. The entire suspension and steering systems were stripped down bare nuts and bolts status, and every last nut, washer and bracket were media blasted and sent for OEM equilivant yellow Zinc plating. Since Aluminum can't be zinc plated, and those parts weren't coated from the factory anyway they were media blasted and clear coated both to maintain the clean look of the raw aluminum and to make cleaning easier in the future.
With all the suspension looking brand new, we threw the book at it: Rennline HD parts everywhere, including de-cambered ball joints for increased camber, strut mounts, trailing arm bushings, spring plate bushings, and control arm bushings to name a few. With their rubber construction and higher than factory durometer composition these parts are perfect for significantly increasing the handling capabilities of these old cars without drawbacks associated with typical aftermarket bushings.
Below are a few pictures of #Project50ShadesOfGrey as it began to take shape outside of the Rennline factory. After years of working on such a big project it's nice to finally see things coming together. We can't wait to see how the final build turns out! Follow us @Rennline on Instagram to see updates of the car as the build comes to an end.
It's now February of 2018 and #Project50ShadesOfGrey is finally done and we are so excited to share the final photos with you guys. What better time to release the build than right after the release of the newest 50 Shades of Grey movie. If you have any questions about the build, or the Rennline products used in the build, send us an email at orders@rennline.com. Cheers!