Recent NEWS - Howard S. Cohl, Ph.D. - Web Log
Recent NEWS 12/28/10
Recent NEWS 6/6/08
Recent NEWS 11/20/07
- Over the past year my research has focused on computing closed form expressions for
fundamental solutions (Green's functions) for integer powers (k) of some important linear
partial differential operators. I obtain fundamental solutions for integer powers of
these operators by recursively determining an appropriate sequence of functions which when
operated k-times by the operator yields the n-dimensional Dirac delta distribution. Initially
my focus was on the fundamental solution for integer powers of the Laplacian operator in
Rn. It is well-known that the functional behaviour of the fundamental solution of
the Laplacian is given by a function of the Euclidean distance depending on the dimension (n)
of the space. The derivation has been completed and it is noted that the behaviour of these
functions are different depending on whether the dimension of the space is even or odd. The
derivation was followed-up by completely determining Fourier series expansions for the
fundamental solutions (for integer powers of the Laplacian in a set of rotationally invariant
coordinate systems in Rn). I then proceeded to compute fundamental solutions for
integer powers of the Helmholtz operator (Laplacian plus a constant) in Rn. In
both even and odd dimensions (Rn), I then computed closed form expressions for the
fundamental solution of the Helmholtz operator, and for integer powers of the Helmholtz
operator in terms of Hankel functions of the first kind.
- As a very interesting experience, I am co-chairing the
New Zealand Mathematics and
Statistics Postgraduate Conference 2008 which is going to be held from November 18-21 in
Whitianga in the Coromandel peninsula.
Recent NEWS 7/23/03
- After completing my postdoc at the University of Exeter in the UK, I decided
to chase my long-time dream of studying mathematics at a more dedicated level. I applied
for a position in a PhD program in Mathematics at a variety of Universities in the southern
hemisphere. Ultimately I was offered a position in the Department of Mathematics at the
University of Auckland and I've been here in Auckland since March, 2006. I am focusing on
matters of Mathematical interest in the area of linear partial differential equations and
for fundamental solutions (Green's functions) for certain linear partial differential equations.
I am working with Rod Gover and Tom ter Elst.
- It has now just begun summer in New Zealand and I am going to be attending three conferences;
one in Queenstown (in the southen alps on the south island) which I am departing for tomorrow --
New Zealand Mathematics and Statistics Post-Graduate's Conference, Thursday 22nd - Friday 23rd November, 2007;
one in Wellington (at the bottom of the north island) in December -- Joint Meeting of the AMS - NZMS 2007
incorporating the New Zealand Mathematics Colloquium 2007
Victoria University of Wellington, New Zealand
Wednesday 12th - Saturday 15th December, 2007, and another in Nelson
(at the top of south island) in January -- New Zealand Mathematics Research Institute,
Summer Workshop on Conformal geometry and geometric approaches to PDE, Nelson,
Sunday 6th - Saturday 12th January, 2008.
Recent NEWS 5/18/03
- I am working on lecturer Matthew Bate's smooth particle
hydrodynamics (SPH) code in the school of physics at the University of Exeter in the county
of Devon in the United Kingdom (England). I am attempting to put
radiation transport into his code so that we can do cluster star
formation with the addition of adding in radiation from newly formed stars
in his SPH simulations.
- I recently attended a conference in Kiev, Ukraine, "Symmetry
in Nonlinear Mathematical Physics" and presented a talk there entitled,
"The Proper Treatement of Linear Inhomogeneity in 3-Space and 1-Time."
- After presenting in Kiev, I went to Warsaw, Poland to meet with
Prof. Antoni Sym and his graduate student Robert Prus who have recently
found an R-separable coordinate system for the 3-variable Helmholtz
equation. This coordinate geometry is cylcidic in nature, but it is
not rotationally invariant.
Recent NEWS 11/30/02
- I am now in the process of settling in the stellar
astrophysics group in the School of Physics at the University
of Exeter, United Kingdom.
Recent NEWS 7/13/02
- I am relocating to the University of Exeter in the
United Kingdom (England). I am going to be working with their
astrophysics group in the School of Physics at the University
of Exeter. The School of Physics just started the small three
professor team in 2000! Now, I get to go to this brand new group
and help them get some good physics in their coding efforts.
I am looking forward to this trip, in the mean time, I am going
to be traveling around the country. I am headed towards Baton
Rouge, Louisiana to do some work with my collaborators over there.
Then I will spend the holidays with my fam. I then take off for
a meeting with the Domina Eberle Spencer who works at the Department
of Mathematics at the University of Connecticut, Storrs. Then,
I am headed to the University of Chicago, and finally to the
University of Minnesota. I will be able to contact people through
e-mail basically because so many people have e-mail these days.
Plus I should have access to a computer when I am at academic
institutions. My web site has continued to evolve, check out my
site at Howie's site.
If you feel like responding, feel free and e-mail me at
- Check out my most recent publication, "Portent
of Heine's Reciprocal Square Root Identity," Cohl, H.S. (2002)
which was presented in the proceedings of the 1st 3D Stellar Evolution
Workshop, in Livermore, California, 2002.
- Joel E. Tohline has recently written an annual reviews article
on the topic of binary star formation. If you are interested in this
hot topic in theoretical astrophysics, you should check it out!
Annual Review in Astronomy and Astrophysics 2002 40:349-85.
- Two new additions to my web site! Online CHAT
and online FORUM.
Join me in a global conversation with the people of this our planet earth.
Recent NEWS 2/18/02
- I am now working on postdoctoral research for the djehuty project at the
Lawrence Livermore National Laboratory.
The goal of this research is aimed at numerically simulating three-dimensional
stellar interior structure. My current focus is on algorithmicly enhancing the
solution by improving key physics packages. H. S. Cohl and Doug Peters are
producing a nonaxisymmetric Newtonian boundary solver combined and code to solve
Poisson's eqation for the Newtonian potential throughout the interior of the star.
Gravitational potential Dirchlet boundary solutions for Poisson's equation are
obtained by convolving the mass density with the Green's function for generalized
equation of axisymmetric potential theory over the dual mesh. The elliptic PDE
solve is using djehuty's preexisting radiation solve code. The solution of the
matrix problem is obtained using HYPRE preconditioners (multigrid) followed by an
iterative conjugate gradient solve.
Recent NEWS 12/30/01
- We are proud to inaugurate our new site and new look
located at http://hcohl.sdf.org.
Our new provider,http://www.shell42.com,
is an awesome UNIX shell access provider, with excellent rates for
high-quality access to the UNIX world!
Recent NEWS 8/18/01
- We have published our PRA PAPER. It has been published in
Physical Review A: Atomic and Molecular
Structure and Dynamics "Useful alternative to the
multipole expansion of 1/r potentials."
It is in the November 1st, 2001 PRA issue, vol 64, Issue 5, 052509.
Recent NEWS 8/14/01
Recent NEWS 8/10/01
- OK. Getting back in full order. Here is the original CCGF paper:
ApJ 1999 vol.527, pp. 86-101
Recent NEWS 7/25/01
- Check this out Cohl,
Tohline's original Poisson
solver paper on the web. Wow. TECHNOLOGY...,
Check it out. "Parallel Implementation of a Data-Transpose
Technique for The Solution of Poisson's Equation in Cylindrical Coordinates."
Recent NEWS 7/24/01
- The twenty fifth of July. It's hard to keep yelling Hurray all the
time, whew...., Hurray! Keep checking out
I keep making incremental progress, one day it will live up to its expectations,
I assure you. Unless the heavens erupt and Tsunamies engulf us like Lovecraftian
towering walls erasing all signs of habitation on the nearby lands and us, well,
let's just say, I'm glad this server is in Mississippi, so I live on somehow.
In fact, if I did hear that a tsunami was coming toward the east bay, I'd be
moving like hell away from here. My house would get thrown around quite a few
times, it wouldn't be a pleasant sight.
environments which both stimulate and makes curious the unsuspecting observer. In
HCE we capture the full essence of what we
are trying to describe in a such a way that even lay observers can get the full
perspective. We speak in such a language that hopefully everything can be built up
from a centralized viewpoint. I will be doing my best to keep everybody up to date.
This is e-radio, live at 8 PM PST.
New restructuring!!!! If you're familiar with the old
one, you'll love the new one!
Check it out as DAD or
ME. I put my resume stuff at the bottom! : )
Recent NEWS 7/22/01
Recent NEWS 6/9/01
- The twenty second of July. Hurray! Check out the
Francis John Welsh Whipple (1876-1943),
and superintendent of the Kew observatory (1925-1939). Well anyways, I think
that's the guy, I think he worked with
G. N. Watson and they did some neat stuff
in England together regarding hypergeometric transformations which I am going
to look onto more. His Whipple formulae
when looked at in toroidal (anchor ring) coordinates. This is a presentation I brought
forward on these interesting formulae.
- Check out an HTML version of our
Astronomische Nachrichten paper!
I did this back in 00. It's entitled,
Developments in determining
the gravitational potential using toroidal functions."
It's not perfect though and some of the equations got garbled in the
LaTeX2HTML conversion. If you are someone who understands these kinds of
think, please get help! Or help me figure out how to master the LaTeX2HTML
craft. If you are interested there is the journal AN in your local University
library, or contact me and I'll send you a copy.
- Check out
"The Potential of a Point."
These pieces are presented as an evolving work and are always welcome to
debate. Constructive criticism is always welcome. : ) Here we discuss the
various harmonic aspects of gravity and the
Coulomb -- BTW: Did you know that the man was
originally interested in Astronomy and
Charles Augustin de Coulomb (1736-1806)
interaction and the amazing properties associated with special function manifestations of the
natural variation which we observe to exist in the universe on very small
scales associated with electromagnetism or on extremely large distance scales
for gravity. We explore the very soul of
- I am going to be staying for one full week at the
University of Chicago,
Department of Mathematics,
researching Mathematical developments in the classical theory of
Chandrasekhar, ...). This effort is mainly due to the
gratitude and expertise of
and I thank him a lot for this opportunity.
- If you're interested, there are some photographs of
Eduard Heine that I came across on
University of St. Andrews "MacTutor Archive" site. There is also a *short* history given
therein. Some mathematicians suppose he might have wanted to be called Eduard
because he might be often mistook by others by, what some literary people have said might have
been "Germany's greatest poet"
who lived and was
prolific at about the same time as
- I will be giving a talk at the
University of Chicago,
Department of Mathematics,
CAMP/Nonlinear PDE's seminar on Wednesday June 27th.
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