April is a busy month for STEM majors, starting off with Science Day (pics here!), and ending right before exams. The weekend of April 22 was busy as well, as the College hosted the Wooster community Expanding Your Horizons workshop for fifth and sixth grade girls, run entirely by local women in STEM, including many CoW faculty and students. The workshop is composed of various science and math themed activates, each designed to encourage young women to pursue STEM. This year there were more than 20 sessions that the girls could sign up for!
All of the materials are provided in a plastic bag. The bag itself was used in many successful experiments!
Busy planning and building
Last year, I had volunteered for the Humpty Dumpty session, the physics focused session of Expanding Your Horizons. I enjoyed it so much I volunteered again! The goal of the session is to build a protective device for your egg using the limited amount of materials provided. Of course, rainbow markers are also available so you can draw a face on your egg and name it. Some names from this year include Terminator, Survivor, and Scramblable.
Dr. Oliver getting ready to drop Hairy the Egg (yes, that’s Hairy, not Harry)Off it goes!
After the teams are done building, the eggs inside their devices are brought up to the third floor of Taylor, and dropped to the ground, hopefully safe and sound. Last year was windy, and we had a new record of an egg flying up to the roof and never coming down. Though we did not have any runaway eggs this year, we did have a record number of surviving eggs.
Waiting in suspenseDr. Oliver, ready to drop an innocent egg from a tremendous heightEgg in flightAnd it’s safe!Fall of Fame for surviving eggs
As a woman in STEM, I wish I had more opportunities like this growing up. The activities themselves are so exciting that I would happily participate even now. But more important, it provides a safe and creative space for young women to experiment science. Before coming to college, all of my science teachers were men, and I have had many, many experiences where I was the only woman in the room. Too many people have had similar experiences. So hopefully, we have encouraged more women to join us in STEM fields!
Wooster March for Science Poster
The end of the Expanding Your Horizons workshop marked the beginning of Wooster’s March for Science, where a diverse group of people, including former Wooster Physics Professor Dr. Garg, gave speeches and stood to raise awareness of the importance of science. As I said at the start, April is a busy month for STEM!
As promised, I’m posting a bit more about my trip to Amsterdam and the Netherlands in general. I was able to work a little sight-seeing in during the working part of my visit. And, I was able to time my visit with my children’s spring break, so my family were able to come and join me for nearly a week of vacation as well.
Outside the Kröller-Müller Museum
One highlight of my sight-seeing was visiting the Kröller-Müller Museum. This museum is inside a national park just outside the village of Otterlo, and contains a huge number of pieces by Van Gogh and many of his contemporaries. It’s rather out of the way and little difficult to get to, but fortunately it is close to Wageningen University so I was able to see it at the end of the day of my visit there. The museum is surrounded by an extensive sculpture garden, and the experience as a whole was wonderful.
While I was in Vienna in the fall, I saw an outstanding exhibit at the Albertina Museum on the development of pointillism, and the way that the ideas of color separation influenced subsequent painters like Van Gogh, Matisse, Picasso, and (my new favorite) van Rysselberghe. As it turns out, a number of the paintings in that exhibit (for example) were on loan from the Kröller-Müller Museum, and the works still at the museum expanded on the shifts in painting style that I had seen earlier. The dynamic brush strokes and distinct blobs of color that many of the artists used are captivating to me.
You can actually view what seems to be the whole collection of the Kröller-Müller Museum online, but of course, there is no comparison to being there and standing in front of the canvas itself, looking at the individual brush strokes.
Arched passage through the great Dom Tower at Utrecht. The tower and the church are no longer connected, since a 1647 tornado!Canal in Utrecht. Note the service doors for the houses above that open directly onto the canal for deliveries.
During my first weekend there, I was invited to a family dinner by Todd Hufnagel, a professor from Johns Hopkins who was also visiting Peter Schall’s group as part of his sabbatical. This gave me the opportunity to visit Utrecht, about 30 minutes from Amsterdam by train. Despite being so close (by U.S. standards), Utrecht has a very different feel from Amsterdam. I didn’t have a lot of time to explore, but found the Dom Tower (the tallest and oldest church tower in the country) truly impressive. There is no way to capture its scale in a single photo. Walking through the arched tunnel at the base of the tower was quite an experience too, since it seems to funnel the wind, so it was almost difficult to walk!
After dinner with Todd Hufnagel and family
Todd and I had discovered just after we met at Science Park that we had a student in common — my former I.S. student Elliot Wainwright (Wooster Physics ’15) is now a graduate student in Materials Science and Engineering at Johns Hopkins, which turns out to be exactly the department that Todd is a professor in! So, after dinner, we took this photo, just to surprise Elliot. It worked.
Windmills at the Zaanse Schans
One of the most popular images of the Netherlands, of course, is the windmill. We visited an outdoor historical village called the Zaanse Schans just north of Amsterdam, which has a number of rebuilt or relocated windmills which are still operating. You can tour each mill and see how it works. My favorite was the oil mill De Bonte Hen which is the one on the right in the photo. I love seeing the ingenuity of mechanized equipment — in this case how flax seeds were ground, warmed, and eventually pressed to create linseed oil, all by harnessing the rotational motion of the windmill.
A Hague clock from about 1657, built according to Huygens’s new design
Also at the Zaanse Schans, there was a compact but absolutely packed museum on clocks and methods of measuring and displaying time. I knew some of the challenges of accurately keeping time, but I had not realized that Christiaan Huygens (of the famous Huygens construction used in optics) had invented the use of the pendulum clock! There were also older clocks that used torsional oscillations to keep time and had no display at all — they only chimed the hour, so you had to wait until the chime to find out what time it was.
Only 80,000,000 micrometers to go!
Another museum we really enjoyed was Micropia, a museum dedicated to life at the microscopic level. Given that microorganisms were first described by Dutch scientist van Leeuwenhoek, this museum seems particularly appropriate for the Netherlands. The museum was amazingly interactive and fascinating. There was wonderful basic science, where you could control the microscopes to see different organisms, and also applications to our daily life, like seeing the colony of bacteria resulting from sampling someone’s calculator or cell phone. We definitely all washed our hands when we left!
Frites! With homemade mayonnaise, satay sauce, and onion.
One of the ways I like to explore a different country is by checking out the local foods. I knew in advance that the frites (what we would call French fries) would be good, but the enormous meringues took me by surprise.
Giant meringues! Seriously giant meringues!
All the tulip varieties you might ever want, at Keukenhof Garden
Finally, I was very excited to see the famous gardens of Keukenhof, with a magnificent spring display of all types of bulbs. The daffodils were in full swing, but outside, only the very earliest tulips were blooming. Fortunately, a huge area of tulips was partially indoors and so already blooming. These displays made me desperately want to plant tulips at my house again. I’ve given up on tulips because the deer always munch them just before they bloom, but maybe I should try again.
Keukenhof Garden
Overall, we were very fortunate with the weather, and had the opportunity to see some beautiful things (art and nature!) and learn a good bit of history during our visit. There are so many things that we enjoyed during our visit that I just can’t include it all here, so feel free to ask me for more information if you are interested!
As regular blog readers know, I am currently on a research leave for the year. A good part of my leave has been spent in Wooster, but I believe it is important to spend a significant time outside of Wooster as well in order to get fresh ideas and perspectives to inform my research and ultimately my mentoring and teaching of students.
To get to Science Park, just follow the bike path.
So, as part of this time outside Wooster exploring new ideas, I spent the last half of March in Amsterdam, the capital of the Netherlands! I had not been to the Netherlands before, so this was a completely new experience for me. This trip was focused on getting a broader perspective on our beadpile research project. Specifically, I wanted to learn more about the field of soft matter, a branch of condensed matter which is not standard solid state physics. Granular materials like the bead pile fall under the broader area of soft matter. Several years ago at the March Meeting, I met Dmitry Denisov, who had been a post-doc with Rinke Wijngaarden and was then a postdoc with Peter Schall. Wijngaarden and his group were responsible for some really lovely papers about avalanches in piles of rice (and some other grains) in a quite different geometry than our conical pile of beads. At this meeting, Denisov was presenting some quite impressive work from Schall’s group with shear on a 3-d collection of beads, submerged in an index-matched fluid and imaged through the depth of the pile by using a laser sheet to illuminate the beads one slice at a time. Shortly after this meeting, I decided to create an opportunity to visit these groups!
Fortunately, Peter Schall was very happy to host me in the Soft Matter group at the University of Amsterdam for a brief visit. I have to say that this is one of the things that I appreciate so much about physics — at least in the research areas that I am active in, researchers are so open to having guests visit. The open exchange of ideas is really in practice. I know there are more competitive areas of physics, but in my experience, scientists are almost always happy to talk to me about their results and discuss what I am doing. It is all too easy to take for granted how unusual and how different from a business environment this openness is.
Science Park flags on a clear, windy day, with the Café Restaurant POLDER (in a historic farmhouse) in the background, and one of the many bike paths on the left
All of the science departments at the University of Amsterdam (UvA) have recently moved farther from the central city to a new area known as Science Park. Science Park hosts a number of research institutes and start-up space in addition to the entire science faculty from the UvA. The faculty from the UvA are in building 904, a massive building which houses all types of sciences, and an attached but decoupled building to house all of the labs. The design is intended to allow more collaboration between different scientific disciplines, and this intent does seem to be working. Overall, like most modern buildings I’ve visited in Europe, there was a great deal of natural light. And, of course, communal space with coffee machines and tea kitchens so that those working there can get together for coffee and tea breaks, or eat lunch together. This aspect is something I miss in the U.S. — I keep thinking that I should start a regular coffee and cake time, but it hasn’t seemed to work out.
Walking up to Building 904 for the first time
The lobby of building 904, home to the UvA Faculty of Science
During my visit, I spent a very productive morning talking to Dmitry Denisov comparing the rice pile results to my bead pile results. And I talked to most of the graduate students about their different projects and toured the labs, which is always the best part for me as an experimentalist. I was really struck by the variety of things that they are working on, and also by the number of ways that the Casimir effect can come into play. Since I previously only remembered the name of the Casimir effect and not the actual effect, this was good information for me to learn!
The transition from the lab building (on the left) to the office building (on the right).
In addition to visiting the University of Amsterdam, I traveled all the way across the country to the University of Twente! Located in Enschede, it’s only a few kilometers from the border with Germany, and it took me about two hours door to door from my rental apartment in Amsterdam. There are quite a number of researchers working on soft matter in the Netherlands, so I wanted to visit as many as possible. In Twente, I got to learn quite a bit more than I knew about non-Newtonian fluids (like the famous oobleck mixture of cornstarch and water) and also talked for a long time about craters and avalanches resulting from drops of liquid impacting a granular base.
The lovely, open campus of the University of Twente, on a bit of a grey day
Besides visiting Twente, I also visited the University of Wageningen. Wageningen and Twente are both much newer universities than UvA. Wageningen has been building rapidly in the last 10 or 20 years, and its campus is very modern. One thing I really liked as a visitor was that the name of each building was incorporated into the building itself, so that you could tell from a huge distance away which building is which.
I was visiting the Helix building, which was plainly this building here:
The Helix building at Wageningen UniversityAnother view of the Helix building, just because I like the picture with the reflections in the windows.
The brightness of the sun may make it a little difficult to read in the small photo (click for full size!) but in person, you could see HELIX from quite a distance. And, inside, the space inside the HELIX-marked windows was a three-story atrium with public spaces and of course, coffee and tea kitchens.
Wageningen is organized rather differently than a typical university, which I found interesting. It is focused on life sciences and the environment, and so the physicists there are working on things related to those areas. Overall, very interesting. And when I saw the room of 10 confocal microscopes just waiting to be used, I nearly swooned. I don’t use confocal microscopes yet, but I know what they cost, and if I had access to a room full of 10 of them, I’d figure out something to do with them!
De Boelelaan 1081 at the VU. Note the cool griffin on the sign — the griffin is the university’s emblem, and its wings form a V.
Finally, near the end of my visit, came my meeting with Rinke Wijngaarden at the Vrije Universiteit Amsterdam, or the VU. The VU was founded in 1880 — the fact that it is Vrije or “free” means that it was not controlled by the church or the state, so that it was free to pursue knowledge in the general interest of society.
Professor Wijngaarden has changed research areas and no longer works in granular material, but we had a very productive discussion about some of his results in rice, and how his findings might relate to our beadpile experiment. There are a number of differences in the behavior of our spherical beads and their rice grains, and there are also a number of things about the system that they were easily able to measure that we have a hard time measuring, because of the difference in our pile geometries.
Overall, the discussions with Wijngaarden and with Dmitry Denisov about the bead pile and rice pile were absolutely the scientific highlights of the trip. I came away with many new ideas about tracking the pile and analyzing the data. Very exciting!
This post is already rather long, so I will have to make another post with more of the tourist-type activities and photos. I know you need to see some tulips (I did!), so that will come shortly. But in the meanwhile, here is a lovely canal and windmill for your viewing pleasure.
Just another walk home from Science Park, with beautiful light on the canal and a windmill in the distance.
Chaotic systems are extremely sensitive to the initial conditions and parameters that define them. Minute perturbations of the parameters can even convert chaotic motion to periodic motion. This alliance between control methods and physics — cybernetical physics — opens the door to many applications, including dynamics-based computing. We recently published an article that introduces nonlinear dynamics and its rich, sometimes chaotic behavior as an engine of computation. After reviewing our previous work demonstrating how to compute using nonlinear dynamics, we describe the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.
Our article was published in the Philosophical Transactions of the Royal Society, the world’s first and oldest science journal, which previously published work by Isaac Newton, Michael Faraday, and James Clerk Maxwell. Of course, no comparison between our work and theirs is intended, except via a logarithmic scale. 🙂
Title page of volume 1 of the Philosophical Transactions of the Royal Society, the world’s first and oldest science journal
The hotel lobby. Quoting Jackie here, “Not a dump.”
When we arrived at the hotel I had a mini scream-out-of-excitement inside. Yes, because it was fancy and was my first time seeing a bathtub since winter break, but mostly because there was a sign for the times for the APS meeting shuttle in the lobby, and people were walking around with APS name tags and fancy poster holders. I was there for the first conference of my life and this was the official stamp that I was there.
The highlight of the meeting has to be presenting my summer research at the poster session. Just before the poster session started, my advisor Dr. Lindner asked me to go over my presentation for the poster, and I was so nervous that I completely froze, just standing there not saying anything. Then my phone rang so I took advantage of the excuse, and Dr. Lindner went to check out another poster while I talked. By the time he came back to check on me, the phone call was long over, and I had been explaining my summer research work to a professor from a Korean university. This was pretty awesome! Since I knew where he was from, we briefly spoke Korean, and he explained graduate programs at his school if I was interested in studying there. It was really nice to see people from all over the world come to collaborate on and discuss physics, especially since I have lived overseas for most of my life.
Dr. Lindner suggested the stadium shape when I wanted a non-traditional poster but could not make an ellipse work. I think the poster turned out great!
It is amazing how natural everything felt during the presentation. I stood by my poster for three hours but the time passed by so fast that I felt I could go on much longer. It was also amazing how the assumption was that I was pursuing at least a Masters degree, or even a PhD. Those people who realized I was an undergrad did so because they recognized The College of Wooster name. One person exclaimed, “Is this another one from Wooster?” and stood there looking astonished.
A screenshot of my schedule. Apparently I missed the “phone books” they used to give out and had to download a phone app instead.
After my presentation was over there were still so much to do. I attended a couple of smaller talks, as well as larger sessions by Nobel Laureates and the author of the Physics of Superheroes James Kakalios. Most of the physics was beyond me, and I could not even understand the questions that people were asking the presenters, but it was still great to see how the researchers in the field were interacting, and the wide range of topics open to pursuit. My favorite talk was the Physics of Superheroes, which included such sensitive questions such as which comic universe is more scientifically accurate, DC or Marvel.
A more personal memory from the conference, we picked up these lighting up toys from the Mathematica booth. My dad and grandfather used to bring back little toys like this from the conferences they attended when I was younger, so me bringing back a memento from a conference I attended makes it feel official.
A lit up stellated icosahedron AKA ‘Spikey’
I am still not 100% over the trip. A part of me is still at the conference, with the excitement, the thousands of people at one large convention center all for one purpose of exploring physics. I would encourage anyone who is interested in their field, to attend the meeting and present their work, even if they are shy like I am. Attending the March Meeting has been a great experience and I look forward to attending the meetings to come.
I think besides my presentation, my favorite experience from this year’s APS March Meeting was my interaction with the wonderful scientists from TeachSpin. They had a booth in the Exhibit Hall that was open the whole week. I remember walking up to it on Monday simply because of our school’s use of some of their advanced laboratory apparatuses. The gentleman at the booth Monday evening invited us to breakfast the following morning and gave me the flier for the breakfast. In the morning, I was the only one awake and raring to go at 6:30 AM on Tuesday morning, so I went by myself. I showed up early as I do and got to speak with the gentleman from the night before and another scientist from TeachSpin over some beignets and coffee. Others slowly leaked in and after a small amount of time, I realized that everyone else was either a scientist for TeachSpin or an instructor at a college or university.
I soon discovered that the breakfast was a meeting for the Advanced Laboratory Physics Association (ALPhA). I was asked five or six times how long I’d been teaching at The College of Wooster because I looked like a younger instructor. Each time, this was followed by me saying that I am a student and then being asked what year of my PhD program I am in. To everyone’s surprise I am an undergraduate student who was invited to the breakfast. Everyone there was very kind though, and I even met a friend of College of Wooster President Sarah Bolton from Williams College. At the meeting, TeachSpin unveiled their newest apparatus that can be used for a slew of condensed matter experiments. I was awestruck by the thought and creativity put into the new apparatus. After seeing it used for only a few experiments, I think it should be in every advanced undergraduate laboratory lineup of apparatuses.
Apart from the meeting, my conversations with the scientists from TeachSpin throughout the week were among the most pleasant and thought-provoking. They encouraged me to think about my future in different ways than I have been recently, which has lifted my spirits quite a bit. I also got to have conversations about some very intriguing physics around the new condensed matter apparatus as well as conversations about my own research interests. They also inquired if I was presenting this week and I told them I was to give an oral presentation. They were very encouraging and helped to lift a lot of my fear surrounding my talk. I felt bad that so much of the conversation seemed to be around what I think–I did listen to a lot of their thoughts as well, but I would have liked to hear more about them and what it is like to work at TeachSpin and what the rest of their careers have been like. They have just started a “Food Truck for the Physics Mind”, and I hope they get to bring this truck of experiments to Wooster in the coming year. I would very much like to speak with them again and hear more about their lives as physicists in laboratory education.
Being an undergraduate presenter in a room full of research faculty
Guest Blog by Zane Thornburg ’18
For this year’s APS March Meeting, I decided that it would be a great idea to give an oral presentation on my summer REU research with Dr. Paul Bonvallet on Osorb from this past summer. I didn’t give any thought at the time about what sort of crowd would be present in the room and would be presenting around me. On the first day of the conference, I sat down in another session and realized all the presenters were research professors mixed with an occasional graduate student or post-doc. I became very nervous for my presentation immediately and worked every night to make it better between Monday and Thursday afternoon. I thought it was done upon arrival, but I will always find ways I want to change my work.
Zane presents his work in New Orleans
There I was, Thursday afternoon. I showed up to the start of the session to get a feel for how all the other talks before me went, of which there were nine. I had gone through my presentation multiple times that morning in preparation so I was feeling pretty good. I was nervous the whole week about the presenter before me, because I had looked him up and it turned out he is a distinguished professor working on polymers and I have 10 weeks of experience. I became nervous for a different reason at the end of his presentation, though. He ended up going several minutes over his allotted 12 minutes, which seemed to me to increase the tension in the room, so I had to start my talk with that feeling in my head. I ended up finishing right before the 10 minute mark out of my 12 minutes, which was the fastest I had ever given the presentation. The others in the room seemed pleased with a concise talk. I received a single question at the end, which I was able to answer quickly since I had just reviewed Dr. Bonvallet’s specific aims for the project moving forward that morning.
Overall, I feel like it went really well and I encourage anyone who does any interesting research to present at this conference. Even if you don’t have years of work to report, presenting is still an exhilarating experience.
Momentum conservation (or Newton’s third law) ensures two-way or bidirectional coupling for typical media like guitar strings and spring mattresses. One-way or unidirectional coupling enables the propagation of solitary waves or solitons with diverse behaviors in otherwise dissipative media, but at the expense of both momentum and energy conservation. Nevertheless, one-way media are possible, provided the coupling is powered to conserve overall momentum and energy.
We recently published an article in Chaos describing the design, construction, and dynamics of low-cost mechanical arrays of 3D-printed bistable elements whose shapes interact with wind to couple them one-way. Periodic boundaries enable solitons to annihilate in pairs in arrays with an even number of elements. Solitons propagate indefinitely in odd arrays that frustrate pairing.
Topological frustration and the power of invisible wind ensure perpetual motion, as in the video below. The mechanical analogue of an electronic ring oscillator of inverting NOT gates, the one-way array is a mechanical clock whose ticks are the reversals of its bistable elements. The design, development, and construction of the array involved five undergraduate co-authors and incorporated two Wooster yearlong senior thesis projects and one NSF REU summer project.
Wind blows down, soliton move right. Each bistable element and the gears were 3D printed in nylon plastic. The parity (odd) of the array guarantees perpetual motion.
Last week I had a wonderful trip to the University of Oregon in Eugene to give a colloquium for the Department of Physics. This was my first visit to the university, and actually my first visit to Oregon at all!
Wooster Physics and Oregon Physics are connected in a number of ways — Dr. Leary did his Ph.D. there, and he recommended the department to several Wooster physics graduates. So there are now four Wooster alums doing their graduate work there! Saul Propp and Amanda Steinhebel are both second year grad students and they recommended me to the colloquium organizers and set up my schedule.
The Wooster physics crew: Nicu, Saul, me, Amanda, and Andrew.
I spent the morning talking about active matter, flocking, and granular flow with a number of different faculty. This might have been my favorite part of the day — as a curious person, I find it so wonderful to just sit down with a really smart person and have them explain their current research to you. For me, these kinds of discussions are where I really see how various areas of physics, which may seem totally different at first, really fit together and complement each other. I love seeing these connections between different fields. Over my physics career, I’ve changed areas several times (always as a condensed matter experimentalist), so I know a little about a lot of subjects, and I think that gives me a good starting point for these conversations. I saw some amazing cell behavior, learned a new video analysis tool that I can use right away in my own work, met a post-doc who I knew previously as a grad student at Illinois, talked about gender issues in physics, ate pizza and got totally quizzed by the grad students, talked about art and physics, saw an awesome new AFM and other enviable equipment, and saw some photon anti-bunching results that were only a few hours old. Sweet!
Atrium at Willamette Hall, the main physics building at the University of Oregon
The physical space at Oregon was really attractive. I know Oregon has more than its share of cloudy days, and it was raining while I was there, but the physics building is designed with large windows and a central atrium, so that despite the grayness outside, it still felt light inside.
There is a lot of art incorporated into the building as well, although it might be helpful to have some obvious signs explaining the meaning of the art. The Feynman diagrams in the floor are pretty straight-forward to recognize (if not understand!), but I didn’t find out the meaning behind the cool starry metal-work at the top of the atrium. Maybe they are just stars… Or hyperbolic surfaces? Somehow related to DNA? It’s a mystery, but great art.
Metalwork art installation at the top of the atrium
I am totally a physicist and not a biologist, but I am a gardener and I enjoy seeing how plants are different across our country and in different landscapes. For example, this tree just outside Willamette Hall was just covered in moss, so you can see this silvery green outlining the trunk and limbs. And the crocuses were in full bloom elsewhere on campus, while here in Ohio, the snowdrops (which are an earlier bulb than the crocus) have just started blooming in my yard.
Crocuses!Moss-covered tree on campus
I will say it was a lot of travel from Ohio to Oregon for a one-day visit. I was lucky to get a good flight though, so that I only had to change planes once in each direction. And, the change of planes was in Denver. I used to live in Denver, so it always feels like home when I fly through the airport. On the way out, we landed just as the sun was setting behind the Front Range, and it was beautiful. As my plane left Denver for the trip farther west to Eugene, I made full use of my window seat and played a little game of “what can I recognize”. It was fully dark by then but I recognized the patterns of the lights, and followed the trail of Interstate 70 from downtown, past our old neighborhood on Sheridan Boulevard, out to Denver West and Golden and up into the mountains.
Sunset behind the Front Range in Denver
All in all an excellent trip! I have a few more trips planned during this research leave — a research trip coming up soon and another trip to give a colloquium. Sadly, I’m going to miss the March Meeting in New Orleans, so I am relying on my colleagues (hint, hint!) and the students to blog about that always-amazing meeting!
Recent Comments
Thanks, Mark! I enjoy reading your posts as well.
Nice post, John! Thanks for writing these. I always enjoy them.
Thanks, Mark! I enjoy reading your posts as well.