We offer a Preschool program in a long day care setting and we recognise the Early Learning Years as a critical period in a child's development. University trained early childhood teachers will work closely in partnership with you throughout the year in guiding educational learning outcomes for your child in preparation for their school readiness.
Each child will have an individual program and portfolio devised specifically for them with the educators monitoring and supporting all areas of their development which is inclusive of language, physical, social and emotional aspects. They will ensure any supports for development required by your child will become the focus of their program. The program will also be guided by your child's interests and abilities and be supportive of their right to learn through spontaneous and guided play.
As part of our preschool plan, early in the year, we arrange a visit by the school nurse to our Centre. Her role is to check the sight, hearing, language and physical development of any child that we or the parent have some concerns about and she will refer them to support services if required.
Our centre will also assist, wherever necessary, in a cooperative approach with the school and yourself in development of a plan to aid a smooth transition of your child from our preschool to big school. We welcome your inspection of our Preschool and can provide time to meet with you and individually address your questions regarding our Preschool programs.


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With the season having kicked off in every major league across the planet, this winter is serving as a breath of fresh air for the entire German hockey scene.
With widespread changes being experienced at all levels nationwide, the German Ice Hockey Association has also hired a new general manager and head coach of the men's national team. The key personnel is none other than former long-time NHLer Marco Sturm, clearly one of the most recognizable international ice hockey names coming out of Germany.
Having never coached at the pro level to date, Sturm is nonetheless one of the most internationally experienced former players hailing from Germany, having represented his country at no less than 13 international tournaments in a career spanning 19 seasons.
Of those 19 seasons, 14 were spent in the NHL, seven and a half of which with the San Jose Sharks, the franchise that drafted him 21st overall in the 1996 NHL Entry Draft.
With seven seasons of 20 or more goals, and 11 overall seasons of 10 or more goals, Sturm is Germany's all-time leading NHL scorer.
Being looked at to bring and pass along that treasure of experience to the German national team program, Sturm has been a busy man since August of this year and continues to prepare for his tasks throughout this winter and heading into a critical phase of Olympic qualification.
He took a few moments out of his busy schedule to answer a few questions for IIHF.com.
Coach Sturm, for the past few months you've been serving as the head coach and general manager of the German men's national team in unison. There's no doubt about how recognized you were internationally as the face of German ice hockey while you were an active player. But that's not exactly the case when it comes to being the 'coach'. How did your being named as head coach and general manager come about?
To be honest, it's my son's fault that I'm a coach. He plays ice hockey in Florida and he once said, "Dad, can't you coach the practice?!" Well, I did and then I got around to doing it more and more and then went about getting all the coaching licences you can in the USA. That's when I realized that I wanted to take this route. So once the call came from Franz Reindl, it all came about very quickly.
You and your family appear to still be living in the USA. What's your travel schedule going to be looking like as you go about conducting your new duties?
That's right, my family and I continue to live in Florida. Both of our kids go to school there. I'll be heading back and forth to Germany. In September, I spent two weeks in Germany and I'm back for the phase leading up to the Deutschland Cup. The plan is that I'll be in Germany every four to five weeks.
In recent years, the German Ice Hockey Association had noticed that there are certain difficulties that come with having one person be both the head coach and general manager. Nonetheless, you'll be asked to face those difficulties by doing just that. What will your biggest challenges be in combining the tasks of these two positions?
I am the head coach and general manager of the men's national team, but I view myself first and foremost as the coach of the men's national team. That's what I wanted to. I'm on the ice and in the locker room. That's also what really intrigues me about the work at hand. As a general manager, it's my job to maintain contact with for example the players so as to guide the team and its roster together and running discussions "off" the ice.
From an international vantage point, many ice hockey pundits were very excited about your being named Germany's head coach. Still, there are those asking just how wise it is to name someone to such an important position when it's his first ever official head coaching job in professional hockey. What is your opinion on this?
It is correct that I don't have a whole lot of experience as a head coach, but there are few in Germany who have as much ice hockey experience as I do. I know my way around the hockey world and spent a long time playing in the world's best league – that's something no-one can take away from me. In addition, I've had the pleasure and fortune to have played under the guise and leadership of many good coaches. I'd now like to pass along everything they gave me to the players I'll now be coaching.
Last season saw the men's U20, U18, and women's national teams all get relegated out of the world's top classes. The men's team enjoyed a subtly successful World Championship in Prague, at least safely retaining the class. How do you view the state of the nation in German ice hockey?
This past season naturally wasn't very successful when you look at the results of the various national teams. But there's generally a spirit of optimism that can be felt in the German ice hockey landscape. The new steering committee surrounding President Franz Reindl has initiated a whole bunch of things right from the grassroots and we're noticing that the various clubs around the country are joining in and are ready to make fundamental changes to better develop our current and future players. It's all about looking forward. What's been in the past is now a thing of the past.
Different results than those collected by your predecessor need to be achieved. What will and needs to change and improve under 'Head Coach Marco Sturm'?
To begin, the players have to be ready to play with pride again. They need to be extremely proud to have the honour of putting on the national team jersey. This condition has become a bit lost in recent years and it's my absolute goal to bring this back.
What expectations do you have of the players who are now going to come into question for your desired national team? Can the international ice hockey world look forward to players who are currently active outside of Europe, primarily in North America, wearing a German jersey, most especially at the World Championship?
As I stated before, I'd like to bring back that pride of playing for the national team. I'm naturally also in regular contact with the candidates who are playing abroad. I've received positive feedback from each and every one of them. The clear-cut message is that they are all ready to play for Germany.
In players such as Tobias Rieder, Leon Draisaitl, and Frederik Tiffels, it's looking like it's time to be incorporating a new generation of young, internationally successful players. How important and realistic do you find this bridge-over from older to younger players for a positive progression within the national team?
I feel this is enormously important. Players like Rieder and Draisaitl are hungry and want to give their best no matter what the cost. That kind of thing becomes very contagious. And on the other hand, these young guys can learn quite a bit from the experienced players as well.
What is the federation's 'POWERPLAY 26' program and what benefits will German ice hockey reap from it over the long run?
The POWERPLAY 26 concept has the goal of ensuring that the German national team is capable of competing by 2026. In the past, we've been sluggish when it's come to working on the right things and in the right areas. We've somewhat neglected our developing kids. With the POWERPLAY 26 concept and the direct work at the youngest levels right in the many clubs, we're doing our part in doing more to teach our kids the correct things right from the beginning. The concept is geared towards working on fundamentals and that's something we are in desperate need of in the German ice hockey landscape.
Your brother-in-law Christian Künast is simultaneously taking over the reigns as the coach of the U20 national team. Does your position as the general manager include you being in regular touch with Künast and will you, in general, be having any influence on the plans for Germany's U20 and U18 teams?
Christian and I are in touch daily. He'll be a part of the coaching staff for the national team as well, just as I'll be part of the coaching staff for the U20 team. Although I'll be supporting Christian in an administrative sense, he'll be absolutely in charge as the federation's youth coach. Our common work together and constant contact are extremely important.
What are your realistic short-term and long-term goals with the national team, which is not currently ranked amongst the 12 best in the world?
We want to achieve the best possible position at the World Championship in Russia next spring and use that to improve our world ranking in the standings. An enormously important milestone is qualifying for the Winter Olympics in 2018.
Have you been thinking much about becoming a coach once your active career was over? Are there certain coaches in the world of ice hockey who serve as your coaching role model?
Not really. I've always thought that I didn't really want to be a coach, just like Uwe Krupp didn't want to be back in the day. But now I'm happy that it's come to this. In Germany, I must point out Hans Zach and Uwe Krupp as my coaching idols, although they are naturally very different in many ways. In America, both Claude Julien and Darryl Sutter definitely come to mind. Particularly Sutter, who's honesty showed me how you're really supposed to play ice hockey and how you're supposed to deal with and treat players, even if it was sometimes very direct and not always pretty. He was direct and always expressed his true opinion. He was probably the best coach I've ever had.
To conclude, we're looking for a bit of a 'bold prognosis': Will the international ice hockey community have the opportunity to see the German national team at the next winter Olympics?
Yes! That is our clear-cut goal.


New Year, New Challenge, New Blog!
I started this blog at the beginning of my running journey 3 years ago.
In 2015 I have new challenges planned and I thought a new challenge warranted a new blog.
Therefore I am retiring from this blog and would like to thank all my readers and followers for the support and encouragement given during that time!
I really need all the support I can get as this is going be a hard challenge to pull off!
Happy New Year! Out with the old in with the new!
I have just ran my last run of 2014. I managed 6.07 miles but I think the excesses of the last few weeks are starting to show as todays run felt hard and slow!
However, it's that time of year to review my fitness resolutions of 2014 and set new ones for 2015.
2014 has been a good year for me fitness wise as I have achieved most of the goals I set myself for the year!
• Conquering my fears and swimming in Open Water for the first time.
• Getting a PB AND a sub 1:50 time at The Liverpool Rock n Roll Half Marathon finishing in 1:48:52.
• Running in my first overseas race! Barcelona Half Marathon.
• Not getting in on the Ballot for the London Marathon 2015.
• Not achieving my goal for a sub 4 marathon or getting a marathon PB.
• Suffering a "panic attack" during the swim of a sprint triathlon resulting in a slow swim time.
These were my goals for 2014, and the outcome of my efforts!
My main aim was to stay injury free and I am delighted to report that after last years injuries I have managed to listen to my body and remain fit and healthy!
I completed my first sprint triathlon and despite having a panic attack during the swim I thoroughly enjoyed the experience finishing in 1:33:59.
I took part in an Introduction to Open Water Swimming Training session in Lake Windermere on 24th May then completed the 1 mile Great North Swim on 14th June finishing in 40:44. I continued to Swim in Windermere throughout the Summer and completed a total of 10 Open Water Swims swimming a total of 7.46 miles. I have never been as terrified in my life as when OW swimming so although the mileage may seem a little on the low side I am delighted that I managed to conquer my fears and swim!
This year I took part in 2 Marathons. The first was in April in Manchester and I finished in 4:22:05 and the second was in October in Dublin and I finished in 4:32:41. Unfortunately I didn't get a Marathon PB this year. My Manchester time was 35 seconds slower than my Chester Marathon time. I was very disappointed with both these races as I put in the training hours and I don't feel I got the results to justify my hard work.
This year I have completed 2 trail races. One 11K and a 10K. In the process of training for these races I have fallen in love with trail running and now enjoy it much more than staying on the roads. Altogether I have run 180.35 miles off road, including several evening runs where I needed a head torch!
I have run at least one race every month during 2014, and have completed 19 races in total spread over the year as follows:.
This excludes the parkruns I have also done!
Get PB's in all distances!
I have managed to get a PB in all distances except the marathon.
All in all a very successful year!
I have exceeded this total by 201.56 miles and have run a total of 1258.56 miles this year!
Having regular sports massages and using a foam roller when necessary to avoid injuries. Stretching after running. Listening to my body!
Going to Yoga to stretch properly.
Attending the tri club road and trail run sessions and swimming sessions.
Follow training plans and set goals.
Keep attending The Tri Club swim and run sessions.
Stretch well after exercise and go to Yoga!
Have a sports massage regularly.
Become involved with The Tri Club Cycling group.
Train using Heart Rate Monitor.
Stop Doing: Running junk miles with no purpose! Make the session important not the mileage.
Being negative and thinking I can't!
Make 2015 my Triathlon year! Do an Open Water Triathlon and an Olympic Distance Triathlon.
Enter OW swimming events and swim in different lakes.
Do a Trail Half Marathon.
Enter Cycle Sportives and generally cycle more!
Set up a new blog and continue blogging.
Interim Goals to help me to achieve my main goals!
Cycle an average speed of 15MPH.
Run 1 mile @ 7.04 minute mile pace!
Run 5K in 24.32 which is 7.54 minute mile pace!
Swim 100m in 2 minutes which is 30 seconds per 25m pace!
Swim 400m (16 lengths) in 9 minutes. which is 34.15 seconds per 25m pace!
I've struggled to blog recently, life has just been getting in the way but here's my race report from last Sundays race at Guys 10 - eventually!
Please click here to read!
Since the last time I blogged I have done a parkrun, ran speed intervals to determine my maximum heart rate, swam 1700 metres on my own, enjoyed a tri club running session running with EGGS and finally last night I went to the tri club swimming session.
That takes us to today - Adventure Thursday! Tri Club Trail run in the dark! I love these runs!
Last night I got some very exciting news!
I have been picked to be a KMF blogger to blog about my training trails and tribulations as I work towards Keswick Triathlon! I will post the link as soon as the blog is up and running!
Exciting and stressful all at the same time!
Time just seems to pass me by without me having the time to blog!
So what have I been doing in the last 9 days?
On Monday last week I decided it was time to get some cycling miles in and got on my turbo trainer set up in the garage. I decided to go for it big time and put my Spinervals DVD into my laptop. I had wiped out the memories of have difficult this was but the title "Have Mercy" should have given me a clue!
However I did manage the first 2 workouts equalling 30 minutes out of the 2 hours programme! This was a total of 8 very difficult but thoroughly enjoyable miles which definitely saw my heart rate rise!
My plan is to continue doing 2 workouts each session until I have completed the full programme and then when I am feeling stronger I will start it again and try to do more each session! I don't want to push too hard and get injured at this point in the year!
On Tuesday it was the Tri Club Road Running session and the focus was on technique and breathing. We experimented with lots of different body positions and breathing techniques to highlight to us which actually makes running easier! I really struggled to do belly breathing which apparently is the way forward! Looks like I'm going to have many a session lying on the floor practising the art before trying to add running into the mix! We did 3.77 miles including a few sprint intervals.
On Wednesday it was the Tri Club Swimming session where the focus was on body position and kick and this was a eureka moment for me! I finally understood where my body was supposed to be! I'm not saying I will be able to maintain it but at least I now know what I am aiming for! Altogether we covered a total distance of 1100 metres or 0.68 mile.
Thursday was Adventure Thursday with the Tri Club which equals a trail run in the dark! Our adventure took us up and around Arnside Knott and I loved this adventure! It was a lovely clear evening and it was great running with 12 like minded people! We ran a slow but enjoyable 5.55 miles.
I can't wait for next week's adventure!
I've not had a good week exercise wise!
I think the cold dark evenings and busy days at work have dampened my enthusiasm for getting out there!
It was raining on Monday so I decided to go swimming instead of braving the elements. I didn't do very much compared with my usual swim session as I really couldn't be bothered! I managed 3 sets of 20 lengths and just in case your maths is no good that totals 60 lengths or 0.75 mile.
Thankfully I had already signed up for the Tri Club Running Session on Tuesday or I wouldn't of made it out the door as I wasn't feeling it at all!
We ran a easy 2 miles then did 8 x 200 metres sprints with jogging 200 metres in between before finishing off with a cool down jog! I really enjoyed this session despite the idiot teenager's who tried to spoil it for us by being abusive! I was really pleased I was in a group with a couple of sturdy fellas! Altogether we ran 5 miles.
Wednesday was another swim session with the Tri Club this time focusing on breathing and exhalation. I did 1500 metres or 0.93 mile made up of drills and swimming front crawl!
Thursday got the better of me and I did absolutely nothing then regretted it later!
On Friday I was determined to do something as I was feeling l I had let myself down the day before! However, it was cold, dark and rainy so I opted to go to the Gym! A big mistake! I'm not a gym sort of girl and I hate to see all the smelly sweaty men prancing around thinking they are hero's! Anyhow I managed to survive for an hour and 10 minutes and did 6 miles on the bike, 2 miles on the treadmill, a mile rowing, a mile arm pedalling as well as some weights.I came out feeling thoroughly fed up and wishing I had braved the elements instead!
The only exercise I managed on Saturday was walking around the Trafford Centre Christmas Shopping!
That brings us to today! I woke up determined that whatever the weather I was going go for a run!
When I got up it was dry but very foggy! I had set my heart on going for a trail run and a little bit of fog wasn't going to stop me! As I got in the car and drove to my chosen destination the fog got denser and I started to rethink my plan! I wasn't going to risk running off the side of a hill in the fog!
However, miraculously the fog suddenly disappeared! It was like driving into another world! My planned route was safe after all!
I managed 6.38 very hilly, muddy, chilly miles but loved it! It reminded me why I run! I wish I could bottle this feeling for the next time I am doubting whether I will ever run again!
Another Race ... another PB!
Yesterday I ran in the Brampton to Carlisle 10 Mile Road Race!
You can read how I got on here!
I finally got my race report done from last week's 10K at Lytham!
Tomorrow I am running the Brampton to Carlisle 10 mile road race!
Here's hoping I get another PB in the bag!
Tonight I went for my first DARK TRAIL run.
I felt a little apprehensive about it as I'm not confident with my footing off road in the daytime without adding the extra hindrance of darkness but the tri club were going so I thought I would give it a go - safety in numbers and all that!
We met at around 6.50pm just as the torrential rain started, but luckily by the time everyone had arrived and we set off at 7pm the rain had stopped but the trails were nice and wet, muddy and slippery, just to add to the adventure!
With having a fairly bright head torch and being surrounded by numerous other head torches the dark wasn't an issue at all!
My path was lit quite well!
The only heart stopping moment was when I jumped over a stile and my head torch caught sight of loads of luminous eyes looking at me - we had entered a field of cows! Panic rose up my body but no one else in the group seemed fazed by it at all and nestled safely in the middle of the pack I bravely ran through them! Never in a month of Sundays would I have done that alone!
However, a little further along our journey we came across another field of cows and these ones were a little more frisky! Scared doesn't even describe how I felt as they started to gallop (do cows gallop?!) alongside us! Thankfully we made it to the gate safely - its amazing how we all turned into Mo Farrah when required. The field was very churned up with the mix of rain and cows and I was fearful I would get my trainer stuck in the mud! If it had there is no way I would have stopped to retrieve it - I would have had to run home shoeless!
Anyhow, despite this I loved this adventure and running on the trails in the dark! I am sure it will make me a more confident trail runner in the long run!
We ran 6.5 very muddy but enjoyable miles!
I can't wait for my next off-road night time adventure!
After a very busy day at work I went to laughter yoga for the very first time!
I was a little apprehensive as I had absolutely no idea what I was letting myself in for - except a laugh!
Anyhow, there was 8 of us in total and we were all nervous beginners!
At beginner of the session our tutor explained the history and benefits of laughter yoga and explained that a lot of the practise was about eye contact! At first I felt very self-conscious and uncomfortable forcing myself to laugh but I was amazed how quickly the forced laughter became real! Before long it became difficult NOT to laugh! It was both hilarious and stupid rolled into one! I would definitely recommend it as a way of team building and de-stressing. After the relaxation part at the end we all felt revived and relaxed! I would definitely recommend!
Straight after this I felt so energised that I went swimming! The pool was amazingly quiet and I had a swimming lane all to myself! I managed to swim 2050 metres (1.27 miles) and felt like I could have kept going! Perhaps there is something in this laughter lark after all!
One of the lads at my Tri Club is working towards his coaching qualification and needed 6 willing volunteers to do some swim, bike and run coaching with!
Luckily (I think) I was selected and tonight was the first swim session.
However, he wasn't coaching us this evening but observing to see what our technique was like and what we needed to work on over the coming weeks to improve our speed and technique.
We did a 400 metre warm up followed by various drills which I hate and struggle with but I know I must persevere! Unfortunately I am the slowest swimmer he has selected to coach so it's going be hard work for me each week but hopefully that means I will improve the most! I hope he realises what he has taken on!
Towards the end of the session we did a 400 metres timed swim followed by a 200 metre timed swim in order to get our CSS time so we can see if we improve with the extra coaching!
My 400m (16 lengths) time was 8.31.1.
My 200m (8 lengths) time was 4.11.6.
The coach is going do the Maths and tell us next week what this equates to in terms of a CSS time!
Altogether I did 1450 metres or 0.90 miles!
Looking forward to getting feedback on how to improve!
Tonight it was raining ... tonight it was cold ... tonight it was dark ... but I had agreed to go to the Tri Club running session and there was no getting out of it...Arghhhhh!
However, once I got over the thought of it and got out there wrapped up in my jacket and gloves (for the first time this year) I really enjoyed myself!
We started off with a warm up jog before doing some technique drills and then went on to some hill repeats. It's a while since I have made myself do hill repeats and despite it feeling like my lungs were going to explode I really enjoyed the challenge!
Then on the first descent I was taken totally by surprise by a photographer who popped out of nowhere! Apparently he was taking some photographs for some promotional material for the Tri Club. He kept making us go back up the hill to get more shots! Eventually after 4.6 miles he was happy with his lot!
This is one of the photo's taken which I am quite happy with as I look like a proper runner with both feet off the ground!
Today I was back at work after the half term holidays and back to routine!
With no training plan to follow I need to sort out some sort of routine. My goal for the Winter is to try and dedicate equal time to swimming, cycling and running so that come the Summer I hope to be fairly fit in all disciplines ready to smash the Triathlons planned!
This evening I went to the Tri Club Swim Training session and the focus was on speed intervals! Whether it's swimming or running I'm really no good at speed, but I must persevere and one day I might just surprise myself and everyone else around!
We started off the session with drills - another thing I am particularly bad at but if I can nail the drills my swimming WILL improve!
It was a tiring session and I was disappointed to see that I had done less than a mile in total - it felt far further! I had swum 1475 metres or 0.92 mile!
OK I've wallowed around eating and drinking far too much for far too long so today I gave myself a shake actually went for a run!
It was such a beautiful Autumnal morning that it would have been criminal not to take advantage!
I decided that I would go off road and have a gentle jog up Scout Scar. I didn't worry about pace or mileage and I really enjoyed it!
It was a lovely sunny morning although once I got up on the top it was a little breezy and chilly but on a positive note I only saw one cow! I kept expecting them to be hiding somewhere but thankfully if they were they were hiding well!
I ran 3.9 miles and loved it!
When you see the photo's what's not to love about running here!
Now that I am back on the programme I have even set up my turbo trainer in the garage! No excuses now!
I should be feeling relief that all the hard training miles are over but in reality I am sat here twiddling my thumbs thinking ... What now?
4 days post marathon I am still professing to be recovering but in reality my legs feel great - it's just my head isn't in the game!
Will I ever want to run again?
The end of my marathon career!
On Monday I ran in my third and final marathon! EVER!
I had a fantastic few days in Dublin and love the city and it's people!
You can read my race report here!
Dublin - We are coming to get you!
Tomorrow morning we will be leaving Kendal and heading off to Manchester airport to catch our flight to Dublin!
Then on Monday morning I shall be starting on the 26.2 mile journey to the marathon finish line!
I am feeling a mix of nerves and excitement, and trying to think positive thoughts!
Marathon Number 3 - Lets make it a good one!!
OMG What have I done?
I truly think I have finally lost the plot!
The question is will I survive 2015?
The way I'm going I will have an ironman booked by the end of the year!
With just a week to go to Dublin Marathon my motivation and enthusiasm for running has been running low in recent weeks hence the lack of blogging!
However, yesterday I got some enthusiasm back after I did my first ever park run at Fell Foot Park, Newby Bridge which was also it's first park run!
When I woke up it was a wet and dreary morning and I very nearly decided not to bother! My thoughts were along the lines of "What's the point in getting wet for 3 miles".
However, I gave myself a good talking to and got in the car before I could change my mind.
Newby Bridge is about a 25 minute drive from where I live. I arrived early at around 8.25am but I am pleased I did as already the car park was very nearly full. If I had left it much later I would have struggled to park.
Luckily by the time I got there the rain had stopped and I had a wander down to the start line feeling stupidly nervous for what was supposed to be a fun 5K run.
I was surprised how many "serious" runners were about and also surprised how many avid park run fans were there - those who travel around doing different park runs each week! Locals were definitely in the minority but what a fantastic turn-out for the first park run here!
I managed to locate some friends from the tri club and we stood and passed the time of day until 9am.
Just as the start of the race was announced the heavens opened! It was too late to put my waterproof on, so off I set in my T shirt!
There was a bit of a bottleneck initially as over 200 runners tried to negotiate narrow tracks and paths but the field soon opened out making it easier!
The route was well marked out and was mainly on grass with a couple of hills thrown in for good measure! With being wet the grass was slippery and by the second lap slightly muddy!
The route was very scenic going along the shores of the lake and around a field.
I thoroughly enjoyed the friendliness and camaraderie that surrounded the event and felt quite emotional cheering in other runners once I had finished. I witnessed varying emotions coming from a range of runners from very young children, to the elderly and larger runners! What a fantastic inclusive event which encourages everyone to get out of bed on a Saturday morning and enjoy running!
I finished in 27:43. As this is my first officially time 5K event I have nothing to compare this with but considering the weather and the undulations on the course I am happy with this and because it is my first it is also a PB.
"You finished in 105th place and were the 32nd female out of a field of 247 parkrunners and you came 5th in your age category VW45-49"
This has really spurred me on to do more Park Runs in the future!
Just the small matter of getting a marathon out the way first!
Despite the cough I survived!
Today I ran The Great Cumbrian Run in Carlisle!
Read how I got on here!
Where did the last 2 weeks go?
Although I haven't had the energy or inclination to blog in the last 2 weeks I have still been running!
During my absence I have had some good runs and some disastrous runs! I just have to keep reminding myself that I have more good runs than bad so they don't loom large in my head and become the tormentor! Dublin marathon is only 3 weeks away so its important to remain positive!
I have also been rejected yet again by the London Marathon which I have mixed emotions about! Part of me is happy as I really want to concentrate on triathlons during 2015, but part of me is disappointed as I really want to run the National Marathon!
instead I did something even dafter and booked Windermere Tri, an Olympic Distance Triathlon consisting of a 1500 metre (0.93 mile) Open Water swim, a 43K (26.7 miles) bike route and a 10K (6.2 miles) run!
I also booked The Great North Swim - the one mile route as a training swim for the triathlon. I am also looking to book some sprint triathlons and cycle sportives as training events!
Tomorrow I have my last race before the marathon! I am running The Cumbrian Run (Half Marathon) starting at Carlisle Castle! It could be a chilly one looking at the forecast!
Yesterday I ran in the English Half Marathon. You can read how I got on here!
with a busy day at work followed by some running speed intervals finishing off with some swim speed intervals, and I wonder why I feel tired!
Straight after work tonight I went for my run! The plan stated a 4 mile easy run followed by 6 x 30 seconds at 8.00 to 8.20 minute mile pace with 2 minutes slow recovery in between.
My legs felt heavy initially but after the first mile or so they loosened up and I felt OK. It was nice to run at an easy pace and I completed the 4 miles at a 9.34 minute mile pace. Then came the speed intervals and today the 30 seconds seemed to go by in a flash and I was delighted that I managed to maintain the pace (or faster) for all 6 intervals completing them in a 7.19, 7.04, 7.04. 8.17, 8.05, 8.14 minute mile pace!
I was delighted with this especially since it was on tired legs! I ran a total of 5.50 miles at an average 9.45 minute mile pace!
My Heart rate monitor showed my average heart rate as 84% of max. I still haven't worked out training by heart rate yet but I'm getting used to the numbers at the moment!
After my run and a shower I had a quick bite to eat before heading out again to the Tri Club swimming training session where the focus was on speed intervals!
Considering I had already done a run I managed to keep up with the others in my lane and swam a total of 2000 metres or 1.24 miles!
I am pleased with both my performances this evening!
Yesterday, I booked to go to Madrid for a weekend break in March with a couple of friends to run the Madrid Half Marathon!
I am very excited about it!
I loved Barcelona Half Marathon so hoping Madrid is as enjoyable!
End of week 10 Marathon Training!
Running: 42.11 miles in 4 runs (6.87 in 1 trail run and 35.23 miles in 3 road runs).
Running : 321.44 miles (47.11m trail and 274.33m road).
Swimming: 10.21 miles (2.74 m open water and 7.47m pool).
Week 10 long run ... Done!
Today the marathon plan said I was to do a 20 mile LSR!
After going out last night with friends which resulted in overeating and downing copious amounts of Sangria I wasn't feeling the love for running when I got up this morning - particularly not the love for a 20 miler!
Anyhow, determination won and my husband offered to keep me company by traveling alongside me on his bike carrying all the necessary drinks etc.
I am bored with running the same routes locally so we decided to go to Preston and do the Guild Wheel circuit. This also meant it would be safer for my husband on his bike too!
So we set off at around 10.15am for the 40 mile journey to Preston to "do" the Guild Wheel.
It was a glorious morning when we got there and started running/cycling at around 11am.
David alternated between cycling alongside me chatting and going off ahead and waiting for me to catch up.
It was very hot, probably too hot to be running but thankfully we had plenty of fluids with us to keep me going! One benefit of taking a chaperone with me!
It was a great route, and despite passing many cyclists I was surprised that we didn't come across very many runners! To me it is an ideal running route! Picturesque and traffic free!
I felt great until mile 18 when I think I hit the wall! Despite fuelling up with gels and energy drinks I was sadly lacking in energy and did contemplate making my husband run so I could have the bike!
However, I didn't want to fail so pushed on and made it back to the car weary, hot but pleased to have persevered! I think having company helped when the going got tough!
The plan had said to keep to a 9.20 to 9.40 pace and my average minute mile pace for the 20.81 miles was 9.41, so not too far off the mark!
I also wore my Heart Rate Monitor which confirmed I had worked hard with a average HR of 87% of max.
I am pleased that I have another long run behind me!
The start of week 10 began on tired legs after running in The Great North Run on Sunday.
However, I was determined to stick to the plan and the plan for Monday said speed intervals!
This consisted of 1 mile slow, before moving on to intervals of 0.62 mile keeping at a 8.05 to 8.15 minute mile pace followed by 1.5 minutes slow repeated 5 times finishing before finishing off with 1 mile slow.
It was another warm and muggy evening and I was feeling rather lacking in energy after a busy day at work but I gave myself a good talking to and managed to persuade myself to go!
I managed my one mile slow and did the first interval @ a 8.09 minute mile pace, followed by a too slow 8.24 minute mile pace. I managed to speed up for my third interval which was @ a 8.11 pace but then slowed down for the 4th and 5th interval only managing a 8.27 and a 8.23 minute mile pace!
The total run was 5.81 miles at an average 9.17 minute mile pace.
Even though I didn't hit the correct pace goal I pushed as hard as I could and felt like I had worked exceptionally hard so all in all I am pleased with how it went - considering!
On Tuesday I had another interval run to do which I really, really struggled with! My legs were objecting big time by now and they weren't going to be forced into running fast again!
The plan had been to run 3 x 2 mile speed intervals with 3 minutes slow run recovery in between. Basically, after maintaining the first 2 mile split at a 8.46 minute mile pace it all ended up slow thereon afterwards! The 2nd 2 mile split was at a 9.35 minute mile pace and the 3rd was at 9.25 minute mile pace!
The total run was 8.62 miles at an average 9.26 minute mile pace!
I found this extremely hard work and didn't enjoy it at all!
I was delighted to finally get a rest day on Wednesday - although I did get to have a good stretch at yoga! This is the first yoga I have been to for a couple of months and it felt great to be back!
On Thursday night the plan was for a 7 mile easy run so I opted to go off road for a change! With it being an easy run and with being off road I didn't look at my pace at all and it felt GOOD!
I just ran how my body and the terrain dictated and thoroughly enjoyed not having the pressure of hitting a certain pace!
I even braved running through cows - all in all I had to go through 4 fields with cows in them! Thankfully there was only on occasion where I had to go through the middle of the herd the other times I managed to scoot around them giving a very wide berth! I can't believe how brave I was!
The run ended up being 6.87 very enjoyable miles at a slow 10.36 minute mile pace!
My ankles and Achilles felt slightly uncomfortable when I got home but I think (I hope) that that is just the change in running terrain!
Fingers crossed its not the start of anything sinister!


Dayton was the son of Comfort Newbury and Nancy Collins. No further ancestry is known at this time.
Elizabeth's ancestry is unknown at this time.
Caroline first married Caleb Perry of Troy NH. Their daughter Caroline Abigail Perry married Orrin Clark Jillson, brother of settler Sylvester Weeks Jillson.
Lydia was the daughter of William Parkes and Catherine _______. No further ancestry is known at this time.
Descendants of Dayton Bill Newbury.
1. DAYTON BILL2 NEWBURY (COMFORT1) was born 07 Apr 1803 in Mansfield CT, and died 25 Mar 1871 in Waterford WI. He married (1) ELIZABETH FOSTER 22 Dec 1829 in Springfield MA. She was born Abt. 1808 in CT, and died 17 Jun 1842 in Gardner MA. He married (2) CAROLINE BENNETT 15 Sep 1843 in Hubbardston MA, daughter of WILLIAM BENNETT and CATY FOLLET. She was born 07 May 1807 in Hubbardston MA, and died 21 Apr 1881 in Hubbardston MA. He married (3) LYDIA PARKES 06 Oct 1855 in Salem WI, daughter of WILLIAM PARKES and CATHERINE ?. She died Aft. 1855.
2. i. ALBERT3 NEWBURY, b. 25 Oct 1831, Springfield MA; d. 09 Feb 1873, Worcester MA.
ii. HARRIET E NEWBURY, b. 09 Oct 1833, Uxbridge MA.
iii. GILBERT B NEWBURY, b. 05 Aug 1835, Gardner MA; d. 07 May 1848, Gardner MA.
iv. DWIGHT NEWBURY, b. 11 Mar 1838, Gardner MA; d. Bet. 1861 - 1865; m. LYDIA ALEXANDER, 18 Apr 1861, Worcester MA; b. 16 Apr 1829, Warwick MA; d. 19 Sep 1915, Worcester MA.
v. BENJAMIN FRANKLIN NEWBURY, b. 02 Jun 1840, Gardner MA; d. 22 Sep 1843, Gardner MA.
3. vi. MARIA AMELIA NEWBURY, b. 12 Jun 1842, [6/7/1842??] Gardner MA; d. Aft. 1920.
vii. SON3 NEWBURY, b. 23 Jul 1844, Gardner MA; d. 28 Jul 1844, Gardner MA.
viii. ADELAIDE M NEWBURY, b. Jun 1846, Gardner MA; d. 19 Aug 1846, Gardner MA.
ix. LUCIUS E NEWBURY, b. 24 Oct 1847, Gardner MA; d. 27 Sep 1848, Gardner MA.
2. ALBERT3 NEWBURY (DAYTON BILL2, COMFORT1) was born 25 Oct 1831 in Springfield MA, and died 09 Feb 1873 in Worcester MA. He married SYBIL S JOHNSON 14 Sep 1853 in Northfield MA. She was born Dec 1829 in Northfield MA, and died 11 Sep 1901 in Worcester MA.
4. i. MARY E4 NEWBURY, b. Jun 1854, MA; d. Aft. 1920.
5. ii. CORA ALMIRA NEWBURY, b. 16 Jul 1858, Worcester MA; d. Aft. 1940.
6. iii. CLARA LOUISA NEWBURY, b. Apr 1864, MA; d. Aft. 1940.
iv. DELIA ISABEL NEWBURY, b. 22 Oct 1865, Worcester MA; d. 15 Jul 1903, Shrewsbury MA; m. WILLIS EVERETT KNOWLTON, 29 Nov 1888, Worcester MA; b. 18 Sep 1857, Dorchester MA; d. Aft. 1920.
v. SON NEWBURY, b. 22 Oct 1865, Worcester MA.
3. MARIA AMELIA3 NEWBURY (DAYTON BILL2, COMFORT1) was born 12 Jun 1842 in [6/7/1842??] Gardner MA, and died Aft. 1920. She married GEORGE A GROAT 18 Mar 1862 in Rochester WI. He was born Abt. 1841 in NY, and died Aft. 1880.
i. ELLA4 GROAT, b. Abt. 1863, WI; d. Aft. 1870.
ii. MARY GROAT, b. Dec 1873, WI; d. Aft. 1900.
4. MARY E4 NEWBURY (ALBERT3, DAYTON BILL2, COMFORT1) was born Jun 1854 in MA, and died Aft. 1920. She married HENRY FRANCIS STEDMAN 21 Apr 1875 in Worcester MA. He was born 05 Aug 1842 in Worcester MA, and died 25 Aug 1911 in Worcester MA.
i. ALBERT HENRY5 STEDMAN, b. 22 Mar 1876, Worcester MA; d. Aft. 1900.
ii. AMY G STEDMAN, b. Dec 1882, Boston MA; d. Aft. 1920; m. WILLIAM J POLLARD, 09 Nov 1911, Worcester MA; b. Abt. 1882, MA; d. Aft. 1920.
5. CORA ALMIRA4 NEWBURY (ALBERT3, DAYTON BILL2, COMFORT1) was born 16 Jul 1858 in Worcester MA, and died Aft. 1940. She married FRED E ADAMS Abt. 1882. He was born Feb 1856 in MA, and died Aft. 1940.
i. DAUGHTER5 ADAMS, b. 11 Oct 1882, Worcester MA.
7. ii. ERNEST NEWBURY ADAMS, b. 19 May 1889, Worcester MA; d. Aft. 1940.
6. CLARA LOUISA4 NEWBURY (ALBERT3, DAYTON BILL2, COMFORT1) was born Apr 1864 in MA, and died Aft. 1940. She married FRANK E OSBORNE 07 Nov 1883 in Worcester MA. He was born Oct 1859 in NY, and died Aft. 1940.
8. i. RALPH ALBERT5 OSBORNE, b. 21 May 1886, Worcester MA; d. Aft. 1917.
ii. SYBIL PAMELIA OSBORNE, b. 22 Mar 1895, Brooklyn NY; d. Aft. 1920.
9. iii. FRANK RONALD OSBORNE, b. 29 Jan 1898, NJ; d. Aft. 1940.
7. ERNEST NEWBURY5 ADAMS (CORA ALMIRA4 NEWBURY, ALBERT3, DAYTON BILL2, COMFORT1) was born 19 May 1889 in Worcester MA, and died Aft. 1940. He married AMY L TOWNSEND 06 Nov 1912 in Worcester MA. She was born Abt. 1890 in MA, and died Aft. 1940.
i. PHILLIP TOWNSEND6 ADAMS, b. 15 Oct 1913, Worcester MA; d. 20 Oct 1913, Worcester MA.
ii. PRISCILLA ADAMS, b. Abt. 1916, MA; d. Aft. 1940.
8. RALPH ALBERT5 OSBORNE (CLARA LOUISA4 NEWBURY, ALBERT3, DAYTON BILL2, COMFORT1) was born 21 May 1886 in Worcester MA, and died Aft. 1917. He married ? ?. She died Aft. 1917.
9. FRANK RONALD5 OSBORNE (CLARA LOUISA4 NEWBURY, ALBERT3, DAYTON BILL2, COMFORT1) was born 29 Jan 1898 in NJ, and died Aft. 1940. He married JEAN E ?. She was born Abt. 1897 in Canada, and died Aft. 1940.
i. MARJORIE LOUISE6 OSBORNE, b. Abt. 1921, Canada; d. Aft. 1940.
ii. HARRISON S OSBORNE, b. Abt. 1923, NY; d. Aft. 1940.
iii. FRANK R OSBORNE, b. Abt. 1925, NY; d. Aft. 1940.


By Thomas V. Lyons, Jr.
Pequannock Fire Company Two recently hosted a training session conducted by retired Newark Deputy Fire Chief John Riker. With the use of a forcible entry door simulator, Chief Riker demonstrated the proper techniques for forcing doors utilizing firefighting tools. All in attendance were given the opportunity to participate and practice their skills.


The Mennonite Church of Lacombe began services about 1928, and formally organized in 1941. The congregation originated through immigration from the Soviet Union. Abraham Epp was minister from 1941 to 1944, the only ordained person which served this congregation during its history. The group dissolved due to internal strife and decline in membership, as those farmers who only rented their land left the area for more suitable communities. The congregation dissolved in 1945. It had been affiliated with the Conference of Mennonites in Canada (1942-1945).
The records were transferred to the Conference of Mennonites in Alberta.
The fonds consists of the congregational register, minutes, stamp, and correspondence.


text:
\section{INTRODUCTION}

Thermal photons emitted from the hot fireball created in relativistic heavy-ion
collisions is a promising tool for providing a signature of quark-gluon plasma
\cite{kapu91,baier92,Ruus92,thoma95,traxler95,arnoldJHEP}
(see \cite{Alam01R,Peitz-Thoma:02R,Gale:03R} for recent reviews).
Since they participate only in electromagnetic
interactions, they
have a larger mean free path compared to the transverse size of the hot and dense matter created
in nuclear collisions
\cite{kapusta}.
Therefore  these photons were proposed to verify the existence of the QGP phase
\cite{Feinberg76,Shyryak78}.
Spectra of thermal photons depend upon the
fireball temperature and they can be calculated from the scattering cross-section of
the processes like $q\bar q\rightarrow g\gamma$, \textit{bremsstrahlung} etc. Time evolution
of the temperature can be calculated using hydrodynamics with appropriate
initial conditions.
Thus the spectra depend upon the equation of state (EoS) of the medium and they
may be useful in finding a signature of the quark-gluon plasma\cite{dk99:EPJC,thoma07,dkdir08,Liu09}.
Recently thermal photons are proposed as a tool to measure the shear viscosity
of the strongly interacting matter produced in the collisions\cite{skv-photon,dusling09}.

 Understanding the shear viscosity of QGP is one of the most
intriguing aspects of the experiments at Relativistic Heavy Ion Collider (RHIC).
Analysis of the experimental data collected from RHIC shows
that the strongly coupled matter produced in the collisions is not too much above
the phase transition temperature $T_c$ and it may have extremely small value of shear viscosity
$\eta$. The ratio of the shear viscosity
$\eta$ to the entropy density $s$ i.e. $\eta/s$ is around $1/4\pi$ which is the smallest for
any known liquid in the nature\cite{Schf-Teaney-09R}.
In fact the arguments based on AdS-CFT suggest that
the values of $\eta/s$ can not become lower than $1/4\pi$. This is now
known as  Kovtun-Son-Starinets or 'KSS- bound' \cite{kss05}. Thus the quark-gluon plasma
produced in RHIC experiments is believed to be in a form of the most perfect liquid\cite{Hirano:2005wx}.
No wonder ideal hydrodynamic appears to be the best description of such matter as suggested by
comparison between the experimental data\cite{RHIC} and the calculations done using
second-order relativistic hydrodynamics
\cite{BR07,rom:PRL,DT08,hs08,LR08,Molnar08,Song:2008hj,LR09}.

However there remain uncertainties in understanding the application and validity
of the hydrodynamical procedure in relativistic heavy-ion collision experiments.
It is only very recently realized that the effect of bulk viscosity can bring complications
in the hydrodynamical description of the heavy-ion collisions.
Generally it was believed that the bulk viscosity, $\zeta$ does not play a significant
role in the hydrodynamics of relativistic heavy-ion collisions.
It was argued that that since $\zeta$ scaled like  $\varepsilon -3P$
at very high energy the bulk viscosity may not play a significant role because
the matter might be following the ideal gas type equation of state\cite{wein}. But during its course
of expansion the fireball temperature can  approach values close to $T_c$.
Recent lattice QCD results show that the quark-gluon matter do not satisfy ideal EoS near $T_c$
and the ratio $\zeta/s$ show a strong peak around $T_c$ \cite{Bazavov:2009,Meyer:2008}.
The bulk viscosity contribution in this regime can be much larger than that of the the shear viscosity.
Recently the role of bulk viscosity in heating and expansion of the fireball was analyzed
using one dimensional hydrodynamics\cite{fms08}.
Another complication that bulk viscosity brings in hydrodynamics of
heavy-ion collisions is phenomenon of cavitation\cite{kr:2010cv}. Cavitation arises
when the fluid pressure becomes smaller than the vapour pressure. Since the
bulk viscosity (and also shear viscosity) contributes to the pressure gradient
with a negative contribution, it may be possible for the effective fluid pressure
to become zero. Once the cavitation sets in, the hydrodynamical description
breaks down. It was shown in Ref.\cite{kr:2010cv} that cavitation may happen in
RHIC experiments when the effect of bulk viscosity is included in manner consistent
with the lattice results. It was shown that the cavitation may significantly
reduce the time of hydrodynamical evolution.

Keeping the above discussion in mind, we aim to study the effect of bulk viscosity and
cavitation on the thermal photon production in heavy ion collisions.
As far as we know no such study exists in the literature. Furthermore, the calculations for the photon
production rates in the absence of viscous effects, are done using thermal distribution function of the particle species
(e.g., quark, anti-quark etc.)\cite{Peitz-Thoma:02R}. However, it is well known that viscous effects can lead to the modification of
the thermal distribution functions\cite{deGroot}. This may have observational effect on the photon spectra\cite{dusling09}.
In this work we incorporate the viscous modification in the distribution function arising due to bulk and shear viscosities.
Finite $\zeta$ effect can either
significantly reduce the time for the hydrodynamical evolution (by onset of cavitation)
or  it can increase the time by which the system reaches $T_c$. Moreover the \textit{non-ideal}
gas EoS can also significantly influence the hydrodynamics.
In what follows, we use equations of relativistic second order hydrodynamics to
incorporate the effects of finite viscosity. We take the value of $\zeta/s$ same
as that in Ref.\cite{kr:2010cv} and keep $\eta/s=1/4\pi$. Further we use one dimensional
boost invariant hydrodynamics in the same spirit as in Refs.\cite{fms08,kr:2010cv}.
One of the limitations of this approach is that the effects of transverse flow cannot
be incorporated. As the boost-invariant hydrodynamics is known to lead to under-estimation
of the effects of bulk viscosity\cite{fms08}, we believe that our study of the photon
spectra will provide a conservative estimate of the effect. However it should also be noted that the effect of
transverse flow could remain small as cavitation can restrict the time for hydrodynamical evolution.

\section{FORMALISM}
\subsection{Viscous Hydrodynamics}
We represent the energy momentum tensor of the dissipative QGP formed in high energy nuclear collisions as
\begin{equation}
T^{\mu\nu}=\varepsilon \, u^\mu\,u^\nu\, - P\, \Delta^{\mu\nu} + \Pi^{\mu\nu}
\label{Tmunu}
\end{equation}
where $\varepsilon$, $P$ and $u^\mu$ are the energy density, pressure and four velocity of the fluid element respectively.
The operator $\Delta^{\mu\nu}~=~g^{\mu\nu} - u^\mu\,u^\nu$ acts as a projection perpendicular to four velocity.
The viscous contributions to $T^{\mu\nu}$ are represented by
\begin{equation}
 \Pi^{\mu\nu} = \pi^{\mu\nu}-\,\Delta^{\mu\nu}\, \Pi
\end{equation}
where $\pi^{\mu\nu}$, the traceless part of $\Pi^{\mu\nu}$; gives the contribution of shear viscosity and $\Pi$ gives the
bulk viscosity contribution. The corresponding hydrodynamics equations are given by,
\begin{eqnarray}
D \varepsilon + (\varepsilon+P)\, \Theta-\Pi^{\mu\nu}\nabla_{(\mu}\,u_{\nu)}=0\label{edot}\\
(\varepsilon+P)\,Du^{\alpha}-\nabla^{\alpha}P\,+\,\Delta_{\alpha\nu}\,\partial_\mu \Pi^{\mu\nu}=0
\end{eqnarray}
where $D\equiv u^\mu\partial_\mu$, $\Theta\equiv\partial_{\mu}\,u^\mu$, $\nabla_{\alpha}=\Delta_{\mu\alpha}\partial^{\mu}$
and $A_{(\mu}\,B_{\nu)}=\frac{1}{2}
[A_\mu\,B_\nu+A_\nu\,B_\mu]$ gives the symmetrization. \\

We employ Bjorken's prescription\cite{bjor} to describe the one dimensional boost invariant expanding flow,
were we use the convenient parametrization of the coordinates using the proper time $\tau = \sqrt{t^2-z^2}$ and space-time
rapidity $y=\frac{1}{2}\,ln[\frac{t+z}{t-z}]$; $t=\tau$ cosh$\,y$ and $z=\tau$ sinh$\,y$. Then the four velocity is given by,
\begin{equation}
u^\mu=(\rm{cosh}\,y,0,0,\rm{sinh}\,y).
\end{equation}
We note that with this transformation of the coordinates, $D=\frac{\partial\,}{\partial\tau}$ and $\Theta=1/\tau$.

Form of the energy momentum tensor in the local rest frame
of the fireball is then given by\cite{Teaney03,SHC06,AM07,AM-prl02}:
\begin{equation}
T^{\mu\nu} = \left(
\begin{array}{cccc}
\varepsilon & 0 & 0 & 0 \\
0 & P_{\perp} & 0 & 0 \\
0 & 0 & P_{\perp} & 0 \\
0 & 0 & 0 & P_{z}
\end{array} \right)
\label{Tmunu}
\end{equation}
where the effective pressure of the expanding fluid
in the transverse and longitudinal directions are respectively given by
\begin{eqnarray}
P_{\perp} &=& P + \Pi + \frac{1}{2}  \Phi
\nonumber \\
P_{z} &=& P + \Pi - \Phi
\label{pressures}
\end{eqnarray}
Here $\Phi$ and $\Pi$ are the non-equilibrium contributions to the  equilibrium pressure $P$
coming from shear and bulk viscosities respectively. Respecting the symmetries in the
transverse directions the traceless
shear tensor has the form $\pi^{ij} = \mathrm{diag}(\Phi/2, \Phi/2,-\Phi)$.

In the first order Navier-Stokes dissipative hydrodynamics
\begin{equation}
  \label{NS}
  \Pi = -\zeta \partial_\mu u^\mu \quad \rm{and} \quad \pi^{\mu\nu} = \eta
   \nabla^{\langle\mu} u^{\nu\rangle} \, ,
\end{equation}
with $\zeta,\eta>0$ and $\nabla_{\langle\mu} u_{\nu\rangle}=2\nabla_{(\mu}\,u_{\nu)}
-\frac{2}{3}\,\Delta_{\mu\nu}\nabla_\alpha u^\alpha$. So for first order theories with Bjorken flow we have
\begin{equation}
 \Pi=-\frac{\zeta}{\tau}\quad \rm{and} \quad\Phi=\frac{4\eta}{3\tau}.
\end{equation}
The Navier-Stokes hydrodynamics is known to have
 instabilities and acausal behaviours\cite{lindblom,BRW-06}-- second order theories removes such
unphysical artifacts.

We use causal dissipative second order hydrodynamics of Isreal-Strewart\cite{Israel:1979wp} to study the
expanding plasma in the fireball. In this theory we have evolution equations for $\Pi$ and $\Phi$ governed by
their relaxation times $\tau_{\Pi}$ and $\tau_{\pi}$.
We refer \cite{AM-DR:04,ROM:09R} for more details on the recent developments
in the theory and its application to relativistic heavy ion collisions.

Under these assumptions, the set of equations (i.e., equation of motion (\ref{edot}) and relaxation equations
for viscous terms) dictating the longitudinal expansion of the medium are given by\cite{AM07,BRW-06,Heinz05}
\begin{eqnarray}
   \frac{\partial\varepsilon}{\partial\tau} &=& - \frac{1}{\tau}(\varepsilon
  + P +\Pi - \Phi) \, ,
  \label{evo1} \\
  \frac{\partial\Phi}{\partial\tau} &=& - \frac{\Phi}{\tau_{\pi}}+\frac{2}{3}\frac{1}{\beta_2\tau}
  -\left[ \frac{4\tau_{\pi}}{3\tau}\Phi +\frac{\lambda_1}{2\eta^2}\Phi^2\right]
  \, ,
  \label{evo2} \\
   \frac{\partial\Pi}{\partial\tau} &=& - \frac{\Pi}{\tau_{\Pi}} - \frac{1}{\beta_0\tau} .
\label{evo3}
\end{eqnarray}
where $\Phi=\pi^{00}-\pi^{zz}$.
The terms in the square bracket in Equation(\ref{evo2})
are needed for the conformality of the
theory\cite{Baier:2008:JHEP}. The coefficients $\beta_0$ and $\beta_2$ are related with the relaxation time by
\begin{equation}
 \tau_\Pi=\zeta\,\beta_0\,,\tau_\pi=2\eta\,\beta_2.
\end{equation}
We use the $\mathcal N\,=\,4$ supersymmetric Yang-Mills theory expressions for $\tau_\pi$ and $\lambda_1$
\cite{Baier:2008:JHEP,Okamura:N=4,shiraz:N=4}:
\begin{equation}\label{tau_pi}
  \tau_{\pi} = \frac{2-\ln 2}{2\pi T}
\end{equation}
and
\begin{equation}
 \lambda_1 = \frac{\eta}{2\pi T} \, .\label{lambda}
\end{equation}
We set $\tau_\pi(T)=\tau_\Pi(T)$ as we don't have any reliable prediction for $\tau_\Pi$\cite{fms08}.

In order to close the hydrodynamical evolution equations (\ref{evo1} - \ref{evo3}) we need to supply the EoS.

\subsection{Equation of state, $\zeta/s$ and $\eta/s$}

We are interested in the effect of bulk viscosity on the hydrodynamical evolution of the plasma
and recent studies show that near the critical temperature $T_c$ effect of bulk viscosity becomes
important\cite{karsch07,Kharzeev:2007wb,GDMoore08,ROM-SON09,caron09}.
We use the recent lattice QCD result of A. Bazavov $\it{et ~al.}$\cite{Bazavov:2009} for equilibrium equation of state
(EoS) (\textit{non-ideal}: $\varepsilon-3P\neq 0$).
Parametrised form of their result for trace anomaly is given by
\begin{equation}
\frac{\varepsilon-3P}{T^4} = \left(1-\frac{1}{\left[1+\exp\left(\frac{T-c_1}{c_2}\right)\right]^2}\right)
\left(\frac{d_2}{T^2}+\frac{d_4}{T^4}\right)\ ,
\label{e3pt4}
\end{equation}
where values of the coefficients are $d_2= 0.24$~GeV$^2$, $d_4=0.0054$~GeV$^4$, $c_1=0.2073$~GeV,
and $c_2=0.0172$~GeV\cite{kr:2010cv}. Their calculations predict a crossover from QGP to hadron gas around 0.2-0.18 GeV.
We take critical temperature $T_c$ as 0.19 GeV throughout the analysis.
The functional form of the pressure is given by \cite{Bazavov:2009}
\begin{equation}
\frac{P(T)}{T^4} - \frac{P(T_0)}{T_0^4} = \int_{T_0}^T dT' \,\frac{\varepsilon-3P}{T'^5}\ ,
\label{pt4}
\end{equation}
with $T_0~$= 50 MeV and $P(T_0)$ = 0 \cite{kr:2010cv}.

From Equations (\ref{e3pt4}) and (\ref{pt4}) we get $\varepsilon$ and $P$ in terms of $T$.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{zeta-s.pdf}
\caption{$(\varepsilon-3P)/T^4\, ,\zeta/s$ (and $\eta/s=1/4\pi$) as functions of temperature T.
One can see around critical temperature ($T_c=.190$ GeV)  $\zeta\gg\eta$ and departure of equation of state
from ideal case is large.}
\label{fig1}
\end{figure}

We rely upon the lattice QCD calculation results for determining $\zeta/s$. We use the result of
Meyer\cite{Meyer:2008}, which indicate the existence a peak of $\zeta/s$ near $T_c$, however the height
and width of this curve are not well understood.
We follow parametrization of Meyer's
result from Ref.\cite{kr:2010cv}, given by
\begin{equation}
\frac{\zeta}{s} = a \exp\left( \frac{T_c - T}{\Delta T} \right) + b \left(\frac{T_c}{T}\right)^2\quad{\rm for}\ T>T_c,
\label{zetabys}
\end{equation}
where $b$ = 0.061. The parameter $a$ controls the height and $\Delta T$ controls the width of the $\zeta/s$ curve
and are given by
\begin{equation}
a=0.901,\, \Delta T=\frac{T_c}{14.5} .\label{zetacurve}
\end{equation}
We will change these values to explore the various cases of $\zeta/s$ to account for the uncertainty of the height
and width of the curve.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{zeta-delt-a.pdf}
\caption{Various bulk viscosity scenarios by changing the width of the curve through the parameter $\Delta T$.}
\label{fig1a}
\end{figure}

We use the lower bound of the shear viscosity to entropy density ratio known as KSS bound\cite{kss05}
\begin{equation}
\eta/s=1/4\pi \label{KSS}
\end{equation}
in our calculations. We note that the entropy density is obtained from the relation
\begin{equation}
 s=\frac{\varepsilon+P}{T}\label{s}.
\end{equation}

In Fig.[\ref{fig1}] we plot the trace anomaly $(\varepsilon-3P)/T^4$ and $\zeta/s$ for desired temperature range.
We also plot the constant value of $\eta/s=1/4\pi$ for a comparison. It is clear that the \textit{non-ideal}
EoS deviates from the \textit{ideal} case ($\varepsilon=3P$) significantly around the critical temperature.
Around same temperature $\zeta/s$ starts to dominate over $\eta/s$ significantly. We would like to note that these
results are qualitatively in agreement with Ref.\cite{fms08}.

In Fig.[\ref{fig1a}] we show the change in bulk viscosity profile by varying the width of the
$\zeta/s$ curve by keeping the height intact.

\subsection{Thermal photons}
\label{photons}

During QGP phase thermal photons are
originated from various sources, like \textit{Compton scattering} $q(\bar q)g\rightarrow q(\bar q)\gamma$ and annihilation
processes $q\bar q\rightarrow g\gamma$.
Recently Aurenche \textit{et al.} showed that two
loop level \textit{bremsstrahlung} process contribution to photon production is as important as \textit{Compton} or
\textit{annihilation} contributions evaluated up to one loop level\cite{aurenche:98}. They also discussed a new mechanism for hard
photon production through the annihilation of an off-mass shell quark and an antiquark,
with the off-mass shell quark coming from scattering
with another quark or gluon.
These processes in the context of hydrodynamics of heavy ion collisions were studied in
Refs.\cite{dk99:EPJC,thoma07}. Until recently only the processes of
\textit{Compton scattering} and \textit{$q\bar q$-annihilation} were considered in studying the photon production
rates.

The production rate for hard ($E > T$) thermal photons from
equilibrated QGP evaluated to the one loop order using perturbartive thermal QCD based on hard thermal loop (HTL)
resummation to account medium effects. The \textit{Compton scattering} and \textit{$q\bar q$-annihilation}
contribution to the photon production rate is\cite{kapu91,baier92,traxler95}

\begin{equation}
 E\frac{dN}{d^4xd^3p}~=~\frac{1}{2\pi^2}\alpha\alpha_s \left(\sum_f e_f^2\right)~T^2~e^{-E/T}~\rm{ln}
\left(\frac{cE}{\alpha_s T}\right),\label{Compt+Ann}
\end{equation}
where the constant $c\approx$ 0.23 and $\alpha$ and $\alpha_s$ are the  electromagnetic and strong
coupling constants respectively. In the summation $f$ is over the flavours of the quarks and $e_f$ is the electric charge of the
quark in units of the charge of the electron.

The rate of photon production due to \textit{Bremsstrahlung} processes is given by\cite{aurenche:98}
\begin{equation}\label{Brems}
 E\frac{dN}{d^4xd^3p}~=~\frac{8}{\pi^5}\alpha\alpha_s \left(\sum_f e_f^2\right)~\frac{T^4}{E^2}~e^{-E/T}~(J_T-J_L)~I(E,T),
\end{equation}
where $J_T\approx1.11$ and $J_L\approx−1.06$ for two flavours and three colors of quarks\cite{thoma07}.
The expression for $I(E,T)$ is given by
\begin{widetext}
\begin{equation}
 I(E,T)=\left[ 3\zeta(3) +\frac{\pi^2}{6}\frac{E}{T}+\left(\frac{E}{T}\right)^2 \rm{ln}(2)
        + 4~\rm{Li}_3\left(-e^{-|E|/T}\right) + 2\left(\frac{E}{T}\right)\rm{Li}_2\left(-e^{-|E|/T}\right)
        - \left(\frac{E}{T}\right)^2~\rm{ln}\left(1+e^{-|E|/T}\right)\right],
\end{equation}
\end{widetext}

where $\rm{Li}$ are the polylogarithmic functions given by
\begin{equation*}
\rm{Li_a}(z)=\sum_{n=1}^{+\infty}\frac{z^n}{n^a}.
\end{equation*}
Next the rate due to $q\bar q$\textit{-annihilation with an additional scattering in the medium} is given by,
\begin{equation}\label{A+S}
 E\frac{dN}{d^4xd^3p}~=~\frac{8}{3\pi^5}\alpha\alpha_s \left(\sum_f e_f^2\right)~E~T~e^{-E/T}~(J_T-J_L).
\end{equation}

We use the parametrization of $\alpha_s(T)$ by Karsch\cite{karsch88}:
\begin{equation}
 \alpha_s(T)=\frac{6\pi}{(33-2N_f)~\rm{ln(8T/T_c)}}
\end{equation}
for our rate calculations. Here $N_f$ is the number of quark flavors in consideration.\\

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{photonE-T.pdf}
\caption{Hard thermal photon rates in QGP as a function of energy for a fixed temperature T=250 MeV. Photon rates are
plotted for different relevant processes.}
\label{fig2}
\end{figure}
In Fig.[\ref{fig2}], we plot the different photon rates for a fixed temperature $T=250~MeV$. It shows the contributions from
\textit{Bremsstrahlung} (Brems), \textit{annihilation with scattering} (A+S) and \textit{Compton scattering} together with
\textit{$q\bar q$-annihilation} (C+A). \textit{Bremsstrahlung} contributes to the photon production rate
upto $E\sim 1~GeV$ only, afterwards A+S and C+A processes become dominant. We might mention here that this observation is
in agreement with Ref.\cite{thoma07}.\\

The total photon rate is obtained by adding different temperature depended photon rate expressions.
Once the evolution of temperature is known from the hydrodynamical model, the \textit{total photon spectrum}
is obtained by integrating the total rate over the space time history of the collision\cite{thoma},
\begin{eqnarray}\label{tot-yield}
\left(\frac{dN}{d^2p_T dy}\right)_{y,p_T}&=&\int d^4x\left(E\frac{dN}{d^3pd^4x}\right)\\
&=&Q\int_{\tau_0}^{\tau_1}
d\tau ~\tau \int_{-y_{nuc}}^{y_{nuc}}dy^{'}
\left(E\frac{dN}{d^3pd^4x}\right)\nonumber
\end{eqnarray}
where $\tau_0$ and $\tau_1$ are the initial and final values of time we are interested.
$y_{nuc}$ is the rapidity of the nuclei whereas $Q$ is its transverse cross-section.
For a $Au$ nucleus $Q \sim 180 fm^2$. $p_T$ is the photon momentum
in direction perpendicular to the collision axis.
The quantity $\left(E\frac{dN}{d^3pd^4x}\right)$ is  Lorentz invariant
and it is evaluated in the local rest frame in equation (\ref{tot-yield}).
Now the photon energy in this frame, i.e., in the frame comoving with
the plasma, is given as $p_T cosh(y-y^\prime)$. So once the rapidity and $p_T$ are given we get the
total photon spectrum.

\subsection{Viscous corrections to the distribution functions}

Viscous effects contribute in two ways in kinetic theory: Firstly, it can change the width (temperature) of the distribution
function. Secondly, it can modify the momentum dependence of the distribution function. The first effect is incorporated when we
calculate the temperature as a function of time using dissipative hydrodynamics. To include the second effect one needs to
compute the change in the distribution function as a function of momentum using the techniques of kinetic theory\cite{deGroot}.
In the following we give some details of such a calculation.

In section \ref{photons}, while writing the photon rates, we have used Boltzmann distribution function of type
$f=f_0=e^{-pu/T}$. In order to incorporate the modification due to viscous effects we write the distribution function as
$f=f_0+\delta f$, with $\delta f=\delta f_\eta + \delta f_\zeta$, where $\delta f_\eta$ and $\delta f_\zeta$ represent change
in the distribution function due to shear and bulk viscosity respectively. We calculate $\delta f$ using 14-moment Grad's
method. It ought to be mentioned that recent results show that calculation of $\delta f$ using this method fails near freezeout
region by making $\delta f$ even larger than $f_0$ and $f<0$ \cite{sasaki09,koide09,piotr10}. It is therfore important to here
that we are applying these corrections to calculate the photon production rate of hard thermal photons in the regime $T>T_c$.
We have found that for $p_T$ below 3 GeV, this approximation is reasonable but beyond it, this approximation
breaks down as the contribution arising from the viscous correction $\delta f$ to the distribution function becomes larger
than $f_0$\cite{Monnai-Hirano09}. With this caveat we proceed to calculate
$\delta f$ applying the techniques used in Refs.\cite{Teaney03,DT08}.

We write the viscous correction to the (Boltzmann) distribution function as
\begin{eqnarray}
f(p) &=& f_0+\delta f = f_0+\delta f_\eta+\delta f_\zeta \\ \nonumber
&=& f_0\bigg(1 + \frac{C}{2 T^3} p^{\alpha}p^{\beta}
    \nabla_{\langle\alpha} u_{\beta\rangle}
+ \frac{A}{2 T^3} p^{\alpha}p^{\beta}\Delta_{\alpha\beta}\Theta\bigg)
\end{eqnarray}
where we restrict the corrections to $f$ upto quadratic order in momentum.
In order to find the coefficients $A$ and $C$ we first express
the energy momentum tensor using $f$,
\begin{eqnarray}
 T^{\mu\nu} &=&  \int \frac{d^3p}{(2 \pi)^3 E} p^{\mu}p^{\nu} f \\ \nonumber
&=&  T^{\mu\nu}_{o} + \eta \nabla^{\langle\mu}u^{\nu\rangle}   + \zeta \Delta^{\mu\nu} \;\Theta,
\end{eqnarray}
so that we have
\begin{eqnarray}
\eta \nabla^{\langle\mu}u^{\nu\rangle} &=& \frac{C}{2 T^3}\left[ \int \frac{d^3p}{(2 \pi)^3 E} p^{\mu}p^{\nu} p^{\alpha} p^{\beta}
       f_{o}\right] \nabla_{\langle\alpha}u_{\beta\rangle},\label{eta-f-c}\\
\zeta \Delta^{\mu\nu} \;\Theta &=& \frac{A}{2 T^3}\left[ \int \frac{d^3p}{(2 \pi)^3 E} p^{\mu}p^{\nu} p^{\alpha} p^{\beta}
       f_{o}\right] \Delta_{\alpha\beta} \Theta.\label{zeta-f-c}
\end{eqnarray}
Now from Eq.[\ref{eta-f-c}] we get the correction $\delta f_\eta$ due to the shear viscosity as given in Ref.\cite{Teaney03}
by finding out $C$ and we will not repeat that calculation here. Next we will find out the coefficient $A$  by constructing
a fourth rank symmetric tensor out of $\Delta^{\mu\nu}$ and $u^\mu$ representing the term in square brackets in Eq.[\ref{zeta-f-c}],
\begin{eqnarray}\label{tnsr}
 \frac{A}{2 T^3}\left[ \int \frac{d^3p}{(2 \pi)^3 E} p^{\mu}p^{\nu} p^{\alpha} p^{\beta}
       f_{o}\right]= a_{o}  \left(u^{\mu} u^{\nu} u^{\alpha} u^{\beta}\right) \\ \nonumber
 + a_{1}\left( \Delta^{\mu\nu} u^{\alpha} u^{\beta} + \mbox{permutations} \right) ~~~~~~~~~\\ \nonumber
+ a_{2} \left( \Delta^{\mu\nu} \Delta^{\alpha \beta} +
\Delta^{\mu\alpha}\Delta^{\nu\beta} + \Delta^{\mu\beta}\Delta^{\nu\alpha} \right) \;.
\end{eqnarray}
Now substituting this expression in Eq. [\ref{zeta-f-c}] and by noting $\Delta_{\mu\nu}\;u^\nu=0\;,~ \Delta_{\mu\nu}\Delta^{\mu\nu}=3$
and $\Delta^{\mu\nu}\Delta_{\mu\alpha}=\Delta^\nu_\alpha$ we get $\zeta=5 a_2$. Now by contracting both sides of
Eq. [\ref{tnsr}] with $\frac{1}{45} \left( \Delta_{\mu\nu} \Delta_{\alpha\beta} +
\Delta_{\mu\alpha}\Delta_{\nu\beta} + \Delta_{\mu\beta}\Delta_{\nu\alpha} \right)$ we get,
\begin{equation}
 \frac{A}{2 T^3}\int \frac{d^3p}{(2 \pi)^3 E} f_{o} \frac{3}{45}\left[p^2-(u.p)^2\right]^2= a_{2} = \zeta/5.
\end{equation}
Evaluating this expression in the local rest frame of the fluid $u^{\mu}=(1,\vec 0 )$ we get
\begin{equation}
   \zeta = \frac{1}{3} \frac{A}{2T^3} \int \frac{d^3p}{(2\pi)^3 E}
         f_{o} \, {|{\bf p}|}^{4} \;.
\end{equation}
Now for a Boltzmann gas with $f_0=e^{-pu/T}$ we can calculate the integral and comparing the result with that of the entropy density
$s$ of an ideal boson gas\cite{Teaney03} we find, $A=\frac{2}{5}\;\zeta/s$. So the viscous correction to the
distribution function due to both shear \cite{Teaney03} and bulk viscosities are given as
\begin{equation}
 f = f_0\bigg(1 + \frac{\eta/s}{2 T^3} p^{\alpha}p^{\beta}
    \nabla_{\langle\alpha} u_{\beta\rangle}
+ \frac{2}{5}\frac{\zeta/s}{2 T^3} p^{\alpha}p^{\beta}\Delta_{\alpha\beta}\Theta\bigg).\label{delF}
\end{equation}

Using the Bjorken's flow one can calculate $\nabla_{\langle\alpha} u_{\beta\rangle}$ and $\Delta_{\alpha\beta}\Theta$ for the
present problem. Four velocity can be written as $u^\alpha=(cosh~y',0,0,sinh~y')$, where $y'$ is the rapidity.
Let the four momentum of a particle be parametrised
as $p^{\alpha}$ = $(m_T coshy,p_T cos\phi_p,p_T sin\phi_p,m_Tcoshy)$, where $m_T^2$ = $p_T^2+m^2$\cite{Teaney03}.

Finally we write the distribution function including viscous correction as
\begin{eqnarray}
f = f_0\bigg(1 &+& \frac{\eta/s}{2 T^3} \left[\frac{2}{3\tau}p_T^2-\frac{4}{3\tau}m_T^2sinh^2(y-y') \right] \\ \nonumber
&-& \frac{2}{5}\frac{\zeta/s}{2 T^3} \left[\frac{p_T^2}{\tau}+\frac{m_T^2}{\tau}sinh^2(y-y') \right]\bigg).\label{delFb}
\end{eqnarray}

This expression for distribution function will be used in estimating the photon production rates in Eq.[\ref{tot-yield}].

\section{RESULTS AND DISCUSSION}

\begin{table}
\caption{Initial conditions for RHIC}
\vskip 0.1 in
\begin{center}
\begin{tabular}{ccc}
\hline

\multicolumn{1}{c}{$y_{nuc}$}&
\multicolumn{1}{c}{$\tau_0$} &
\multicolumn{1}{c}{$\rm{T_0}$} \\
\hline
\hline
$~$   &$(fm/c)$ &$(GeV)$\\
\hline
5.3   &0.5  &.310 \\
\hline
\end{tabular}
\end{center}
\end{table}

In order to understand the temporal evolution of temperature $T(\tau)$, pressure $P(\tau)$ and viscous stresses
- $\Phi(\tau)~\rm{and}~\Pi(\tau)$, we numerically solve the hydrodynamical equations describing the longitudinal expansion
of the plasma: Eqs.[\ref{evo1}-\ref{evo3}]. We use the \textit{non-ideal} EoS obtained from Eq.[\ref{e3pt4}] and Eq.[\ref{pt4}].
Information about viscosity coefficients $\zeta$ and $\eta$ are obtained from Eqs.[\ref{zetabys}-\ref{KSS}]
using Eq.[\ref{s}]. We need to specify the initial conditions to solve the hydrodynamical equations,
namely the initial time $\tau_0$ and $T_0$.
We use the initial values relevant for RHIC experiment given in Table I, taken from Ref.\cite{dk99:EPJC}.
We will take initial values of viscous contributions as $\Phi(\tau_0)=0$ and $\Pi(\tau_0)=0$.
We would like to note that our hydrodynamical results are in agreement with that of Ref.\cite{kr:2010cv}.

Once we get the temperature profile we calculate the photon production rates.
Total photon spectrum $E\frac{dN}{d^3pd^4x}$ (as a function of rapidity, $y$ and transverse momentum
of photon, $p_T$) is obtained by adding different photon rates using
Eqs. [\ref{Compt+Ann},\ref{Brems},\ref{A+S}] and convoluting with the space time evolution of
the heavy-ion collision with Eq.[\ref{tot-yield}]. The final value of time $\tau_1$ is the time at which temperature
evolves to critical value $\tau_f$, i.e.; $T(\tau_1)=T_c$. In all calculations we will consider the photon
production in mid-rapidity region ($y=0$) only.

We will be exploring various values of viscosity and its effect on the system.
Since there is an ambiguity regarding the height and width of $\zeta/s$ curve, we will vary the parameters
$a~\rm{and}~\Delta T$ from its base value given in Eq.[\ref{zetacurve}]. By this we will able to study the effect of
variation of $\zeta$ on the system. The varied values of the parameters are represented by  $a'~\rm{and}~\Delta T'$.
We note that unless specified we will be using the base values of bulk viscosity parameters (from Eq.[\ref{zetacurve}]) in our
calculations.
Throughout the analysis we will keep the shear viscosity $\eta$ to its base value given by Eq.[\ref{KSS}].

In order to understand the effect of \textit{non-ideal} EoS in hydrodynamical evolution and subsequent photon spectra we
compare these results with that of an \textit{ideal} EoS ($\varepsilon=3P$).
We consider the EoS of a relativistic gas of massless quarks and gluons. The pressure of such a system is given by
\begin{equation}
P=a~T^4\,;\,a=\left(16+\frac{21}{2}N_f\right)~\frac{\,\pi^2}{90}\label{idealP}
\end{equation}
where $N_f=2$ in our calculations. Hydrodynamical evolution equations of
such an EoS within ideal (without viscous effects) Bjorken flow can be solved analytically and the
temperature dependence is given by\cite{bjor}
\begin{equation}
T = T_0~\left(\frac{\tau_0}{\tau}\right)^{1/3} \label{idealT},
\end{equation}
where $\tau_0~\rm{and}~T_0$ are the initial time and temperature.
While considering the viscous effect of this \textit{ideal} EoS, we will solve the set of hydrodynamical equations
(\ref{evo1} - \ref{evo2}), since effect of bulk viscosity can be neglected in the relativistic limit
when the equation of state $P=\varepsilon/3$ is obeyed \cite{wein}.

\subsection*{Hydrodynamics with \textit{non-ideal} and \textit{ideal} EoS }
\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{T-prof-ideal-vs-e3pt4.pdf}
\caption{Temperature profile using massless (\textit{ideal}) and \textit{non-ideal} EoS in RHIC scenario.
Viscous effects are neglected in both cases. System evolving with \textit{non-ideal} EoS takes a significantly larger
time to reach $T_c$ as compared to $ideal$ EoS scenario.}
\label{fig3}
\end{figure}
Fig.[\ref{fig3}] shows plots of temperature versus time for
the \textit{ideal} and \textit{non-ideal} equation of states. The temperature profiles are obtained
from the hydrodynamics without incorporating the effect of viscosity. The figure
shows system with \textit{non-ideal} EoS takes almost the double time than the system with
\textit{ideal} massless EoS to reach $T_c$. So even when the effect of viscosity is not considered, inclusion of
the \textit{non-ideal} EoS makes significant change in temperature profile of the system. This can affect the corresponding
photon production rates.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{T-var-cases.pdf}
\caption{Figure shows time evolution of temperature with \textit{non-ideal} EoS for different combinations of bulk
($\Pi$) and shear ($\Phi$) viscosities. Non zero value of bulk viscosity refers to Eqs.[\ref{zetabys}-\ref{zetacurve}]
and non zero shear viscosity is calculated from Eq.[\ref{KSS}].}
\label{fig4}
\end{figure}
Next we analyse the viscous effects on the temperature profile. The role of shear viscosity in the boost invariant hydrodynamics
of heavy ion collisions, for a chemically nonequilibrated system, was already considered in Ref.\cite{skv-photon}.
We consider possible
combinations of $\Phi$ and $\Pi$ in \textit{non-ideal} EoS case and study the corresponding temperature
profiles as shown in Fig.[\ref{fig4}]. As expected viscous effects is slowing down temperature evolution.
For the case of non zero bulk and shear viscosities ($\Pi\neq 0;~\Phi\neq 0$), temperature takes the longest
time to reach $T_c$ as indicated by the top most curve. This is about 35$\%$ larger than the case without viscosity (the
lowest curve). The remaining two curves show that the bulk viscosity dominates over the shear
viscosity when the value of $T$  approaches $T_c$ and this makes the system to spend more time around $T_c$.
However the intersection point of the two curves may vary
with values of $a$ and $\Delta T$ as highlighted by Fig.[\ref{fig1a}].

\subsection*{\textit{Non-ideal} EoS and Cavitation}

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{pz-delT-blue.pdf}
\caption{Longitudinal pressure $P_z$ for various viscosity cases shown in Fig.[\ref{fig1a}].}
\label{fig5}
\end{figure}

Let us note here the fact that, the bulk viscosity contribution $\Pi$ is negative\cite{kr:2010cv}.
From the definition of longitudinal pressure $P_{z} = P + \Pi - \Phi$
it is clear that if either $\Pi$ or $\Phi$ is large enough it can drive $P_z$ to negative values.
$Pz=0$ defines the condition for the onset of \textit{cavitation}. During the course of expansion
when $P_z$ vanishes, the fluid will break apart into fragments and the hydrodynamic treatment will
become invalid (see for e.g., Ref.\cite{kr:2010cv}).
Recent experiments at RHIC suggest $\eta/s$ to its smallest value $\sim 1/4\pi$.
Such a small value of $\eta/s$ alone is inadequate to induce cavitation. Therefore we vary the bulk viscosity values
by changing $a~\rm{and}~\Delta T$ to study the effect cavitation. In the discussion that follows we will use $\tau_c$ to denote
the time when cavitation occurs.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{cavitations.pdf}
\caption{Temperature is plotted as a function of time. With peak value ($a$) of $\zeta/s$ remains same while width
($\Delta T$) varies. In all the three curves, solid lines end at cavitation time $\tau_c$ denoted by a dark circle.
The dashed lines in each curves show how the system would evolve till $T_c$ if cavitation is ignored. Figure shows
that larger the width parameter shorter the cavitation time.}
\label{fig7}
\end{figure}

In Figs.[\ref{fig5}-\ref{fig7}] we plot $P_z$ and $T$ as functions of the proper time for different values of $\Delta T$ while
keeping $a$ (=0.901) fixed. As may be inferred from Fig.[\ref{fig5}], higher value of $\Delta T$ leads to a shorter cavitation time.
For the values of $a~\rm{and}~\Delta T$ given by Eq.[\ref{zetacurve}]
we find that around $\tau_c=2.5~fm/c$, $P_z$ becomes zero as shown by the lowest curve in Fig.[\ref{fig5}].
In this case, the cavitation occurs when the temperature reaches the value about 210 MeV, as may be seen in Fig.[\ref{fig7}].
Had we ignored the cavitation, the system would have taken a time $\tau_f=5.5~fm/c$ to reach $T_c$, which is significantly
larger than $\tau_c$. This shows that cavitation occurs rather abruptly without giving any sign
in the temperature profile of the system. The hydrodynamic evolution without implementing the cavitation constraint
can lead to over-estimation of the evolution time and the photon production.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{a-delT-tc.pdf}
\caption{Cavitation time $\tau_c$ as a function of different values of
height ($a'$) and width ($\Delta T'$) of $\zeta/s$ curve.}
\label{fig8}
\end{figure}

We have carried out a similar analysis shown in Figs.[\ref{fig5}-\ref{fig7}] by keeping $\Delta T$ fixed ($=T_c/14.5$)
and varying parameter $a$. In Fig.[\ref{fig8}] we show the cavitation times corresponding to changes in $a$ and $\Delta T$
(denoted by $a'$ and $\Delta T'$). The dashed curve in Fig.[\ref{fig8}] shows $\tau_c$ as a function of $a$,
while keeping $\Delta T$ fixed. The curve shows that $\tau_c$ decreases with with increasing $a$.
Solid line shows how $\tau_c$ varies while keeping $a$ fixed and changing $\Delta T$.

\subsection*{Thermal Photon Production}

We have already seen that the calculation of photon production rates require the initial time $\tau_0$,
final time $\tau_1$ and $T(\tau)$. $\tau_1$ and $T(\tau)$ are determined from the hydrodynamics. Generally $\tau_1$
is taken as the time taken by the system to reach $T_c$, i.e.; $\tau_f$. Since hydrodynamics ceases to be valid beyond the
cavitation time, we must set $\tau_1=\tau_c$. Thus photon production from QGP will be influenced by cavitation,
temperature profile and \textit{non-ideal} EoS near $T_c$.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{phrate-ideal-vs-e3pt4.pdf}
\caption{Photon flux as function of transverse momentum for different equation of states.
No effect of viscosity included in the hydrodynamical equations and in the distribution functions.}
\label{fig9}
\end{figure}
Fig.[\ref{fig9}] shows the photon production rate calculated using \textit{ideal} (massless) and \textit{non-ideal} EoS.
The figure shows that \textit{non-ideal} EoS case can yield significantly larger photon flux
as compared to the \textit{ideal} EoS. At $p_T=1$ GeV, photon flux for the \textit{non-ideal} EoS is about 60$\%$ larger
than that of \textit{ideal} EoS case. This is because the calculation of the
photon flux is done by performing time integral over the interval between the initial time $\tau_0$ and
the final time $\tau_1$. $\tau_0$ is same for both the system while the
$\tau_1$ for the case with \textit{non-ideal} EoS is two times larger than the \textit{ideal} EoS, as may be seen in Fig.[\ref{fig3}].
Further, since the \textit{non-ideal} EoS allows the system to have consistently higher
temperature over a longer period as compared to the massless \textit{ideal-gas} EoS, more photons
are produced.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{rate-over-estimation.pdf}
\caption{Photon spectrum obtained by considering the effect of cavitation (dashed line). For a comparison we plot the
spectrum without incorporating the effect of cavitation (solid line). Viscous correction to the distribution function
is not considered.}
\label{fig10a}
\end{figure}

Next, we consider the question that how the cavitation can affect the photon production rate.
We emphasize that the rates should only be integrated up to the cavitation time $\tau_c$.
Fig.[\ref{fig10a}] shows the case when there is no viscous correction to the distribution function. In the dashed curve the effect of
cavitation is taken into account and $\tau_1=\tau_c=2.5~fm/c$. The solid line represents the same case but without the effect
of the cavitation and $\tau_1=\tau_f=5.5~fm/c$. It can be seen from the curve that ignoring cavitation leads to an over-estimation
of the rate by about 200$\%$ at $p_T=0.5$ GeV and about 50$\%$ at $p_T=2$ GeV.
It is thus clear that the information about the cavitation time is crucial for correctly estimating thermal photon production rate.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{rate-over-estimation-deltaF.pdf}
\caption{Same as in Fig.[\ref{fig10a}] but with incorporating viscous correction to the distribution function.}
\label{fig10b}
\end{figure}

Fig.[\ref{fig10b}] shows the similar comparison between cavitation and no-cavitation cases as in Fig.[\ref{fig10a}],
but with the inclusion of viscous correction to the distribution function. The solid curve shows the case when cavitation is ignored.
The dashed curve shows the effect of cavitation. First we note that as can be seen from Fig.[\ref{fig1}], $\zeta/s\gg\eta/s$
near $T_c$, while $\eta/s$ dominates over $\zeta/s$ when $T\gg T_c$. If one ignores the cavitation effect, then the
hydrodynamical code can allow for temperature to evolve upto $T_c$. Moreover, we have also observed that $\delta f_\zeta$
contribution dominates over $\delta f_\eta$ contribution for $p_T<$1.5 GeV (A similar behaviour is reported in
the Ref.\cite{Monnai-Hirano09}). Let us first note that for $\delta f=0$, the photon flux without cavitation is higher as compared
the same with cavitation at the starting $p_T$ ($\sim 0.5$ GeV). This feature also continues when $\delta f\neq 0$ as can be
seen in Fig.[\ref{fig10b}]. The negative contribution of $\delta f_\zeta$ on the curve without cavitation (solid curve) makes it
plummate faster than the curve with cavitation with increasing $p_T$ (dashed curve) and both the curves intersect at $p_T \sim$1.1
GeV. Beyond this, the shear viscosity starts becoming more effective and prevents this faster plummation of the solid curve.
Moreover, $\delta f_\zeta$ contribution dominates at $p_T~<1.5$ GeV  Thus in the regime $p_T~<1.5$, ignoring the cavitation effect
can lead to over-estimation of the photon flux; e.g., at $p_T$ = 0.5 GeV over-estimation is 150$\%$. Whereas there is an
under-estimation of the photon flux when the effect of cavitation is not included in the high $p_T$ regime.
E.g., for the following $p_T$ values 1.5, 2.0 and 3.0 (in GeV) under-estimations are around 50$\%$, 65$\%$ and 30$\%$ respectively.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{cav-ph-rates-deltaF-Grad.pdf}
\caption{Photon production rates showing the effect of different cavitation time. Viscous corrections
to the distribution functions has been included.}
\label{fig11}
\end{figure}

In Fig.[\ref{fig11}] we plot photon production rates for various cavitation times obtained by varying $\Delta T$
(with $a=0.901$ is fixed). Here the enhancement in the photon production when $\Delta T$ is reduced to half of its base
value is about 75$\%$ at $p_T=0.5$ GeV and about 55$\%$ at $p_T=1$ GeV. A further reduction of the parameter value
to $\Delta T/4$ is enhancing the photon production by about 120$\%$ at $p_T=0.5$ GeV and about 85$\%$ at $p_T=1$ GeV.
The reason is a reduction in $\Delta T$ amounts to increase in the cavitation time (see e.g., Fig.[\ref{fig5}]),
which in turn increases the time interval over which photon production is calculated.
Therefore this increases the photon flux.

\begin{figure}
\includegraphics[width=8.5cm,height=6cm]{ph-rates-deltaF-Grad.pdf}
\caption{Viscous corrections to the distribution function and photon production rate. The solid line shows the
photon production rate without the viscous corrections to the distribution function and the other lines shows the cases with
addition of viscous corrections due to shear and bulk viscosities.}
\label{fig12}
\end{figure}

In Fig.[\ref{fig12}] we show the effect of viscous corrections to the distribution function on
photon production. Here we consider the cavitation scenario with $\Delta T$ ($=T_c/14.5$) and $a$ (=0.901).
The solid curve shows the case $\delta f=0$. We can see from the figure that when we include only the shear
viscosity correction ($\delta f=\delta f_\eta$), it enhances the photon production particularly in high $p_T$
regime\cite{dusling09}. Next we consider the corrections arising due to bulk viscosity $\delta f=\delta f_\zeta$ only.
The effective pressure due to $\Pi$ is negative and we have seen that it is crucial for the cavitation to occur
(See Eq.[\ref{pressures}]). As a result number of particle
with higher momenta are decreasing and therfore there is a reduction in photon rate as compared to the case without
the viscous correction\cite{Monnai-Hirano09}. As it is clear from the figure, the effect of bulk viscosity is to oppose
the contribution from the shear viscosity. The combined effect of both shear and bulk viscosity corrections
($\delta f=\delta f_\eta+\delta f_\zeta$) can be seen in the graph just below the top-most curve. It is clear from
the graph that effect of viscous corrections to the distribution functions increases in the high $p_T$ regime.

\section{SUMMARY AND CONCLUSIONS}

Using the second order relativistic hydrodynamics we have analyzed
the role of non-ideal effects near $T_c$ arising due to the equation of
state, bulk-viscosity and cavitation on the thermal photon production from QGP.
Since the experiments at RHIC imply extremely small values for $\eta/s$,
we take the value $1/4\pi$ for shear viscosity.
We have shown using non-ideal EoS from the recent lattice results that
the hydrodynamical expansion gets significantly slow down as compared
to the case with the massless EoS. This, in turn, enhances the flux of hard
thermal photons.

Bulk viscosity plays a dual role in heavy-ion collisions: On one hand it enhances
the time by which the system attains the critical temperature, while on the
other hand it can make the hydrodynamical treatment invalid much before
it reaches $T_c$. Another result we would
like to emphasize is that if the viscous correction $\delta f$ to the distribution function is not included,
then ignoring cavitation can lead to a significant over-estimation of the photon production rate. But when
the viscous corrections are included the situation can become more complex. In the low $p_T$ regime ($<$1.1 GeV)
there is a significant over-estimation in the photon flux if cavitation is ignored.
On the other hand, in the high $p_T$ regime ($>$1.1 GeV) the photon flux is under-estimated
when the cavitation is ignored!

redpajama_set_name: RedPajamaArXiv


text:
namespace Apache.Ignite.Core.Tests
{
    using System;
    using System.Threading;
    using Apache.Ignite.Core.Cache;
    using Apache.Ignite.Core.Cache.Configuration;
    using Apache.Ignite.Core.Common;
    using Apache.Ignite.Core.Lifecycle;
    using Apache.Ignite.Core.Tests.Process;
    using NUnit.Framework;

    /// <summary>
    /// Client reconnect tests.
    /// </summary>
    [Category(TestUtils.CategoryIntensive)]
    public class ReconnectTest
    {
        /** */
        private const string CacheName = "cache";

        /// <summary>
        /// Tests the cluster restart scenario, where client is alive, but all servers restart.
        /// </summary>
        [Test]
        public void TestClusterRestart()
        {
            var serverCfg = new IgniteConfiguration(TestUtils.GetTestConfiguration())
            {
                CacheConfiguration = new[] {new CacheConfiguration(CacheName)}
            };

            var clientCfg = new IgniteConfiguration(TestUtils.GetTestConfiguration())
            {
                IgniteInstanceName = "client",
                ClientMode = true
            };

            var server = Ignition.Start(serverCfg);

            Assert.AreEqual(1, server.GetCluster().GetNodes().Count);

            var client = Ignition.Start(clientCfg);

            Assert.AreEqual(2, client.GetCluster().GetNodes().Count);

            ClientReconnectEventArgs eventArgs = null;

            client.ClientReconnected += (sender, args) => { eventArgs = args; };

            var cache = client.GetCache<int, int>(CacheName);

            cache[1] = 1;

            Ignition.Stop(server.Name, true);

            var cacheEx = Assert.Throws<CacheException>(() => cache.Get(1));
            var ex = cacheEx.InnerException as ClientDisconnectedException;

            Assert.IsNotNull(ex);

            // Wait a bit for cluster restart detection.
            Thread.Sleep(1000);

            // Start the server and wait for reconnect.
            Ignition.Start(serverCfg);

            // Check reconnect task.
            Assert.IsTrue(ex.ClientReconnectTask.Result);

            // Wait a bit for notifications.
            Thread.Sleep(100);

            // Check the event args.
            Assert.IsNotNull(eventArgs);
            Assert.IsTrue(eventArgs.HasClusterRestarted);

            // Refresh the cache instance and check that it works.
            var cache1 = client.GetCache<int, int>(CacheName);
            Assert.AreEqual(0, cache1.GetSize());

            cache1[1] = 2;
            Assert.AreEqual(2, cache1[1]);

            // Check that old cache instance still works.
            Assert.AreEqual(2, cache.Get(1));
        }

        /// <summary>
        /// Tests the failed connection scenario, where servers are alive, but can't be contacted.
        /// </summary>
        [Test]
        public void TestFailedConnection()
        {
            var cfg = new IgniteConfiguration
            {
                SpringConfigUrl = "config\\reconnect-test.xml",
                JvmClasspath = TestUtils.CreateTestClasspath(),
                JvmOptions = TestUtils.TestJavaOptions()
            };

            var proc = StartServerProcess(cfg);

            Ignition.ClientMode = true;

            using (var ignite = Ignition.Start(cfg))
            {
                var reconnected = 0;
                var disconnected = 0;
                ignite.ClientDisconnected += (sender, args) => { disconnected++; };
                ignite.ClientReconnected += (sender, args) => { reconnected += args.HasClusterRestarted ? 10 : 1; };

                Assert.IsTrue(ignite.GetCluster().ClientReconnectTask.IsCompleted);

                var cache = ignite.CreateCache<int, int>(CacheName);

                cache[1] = 1;

                // Suspend external process to cause disconnect
                proc.Suspend();

                var ex = Assert.Throws<CacheException>(() => cache.Get(1));

                Assert.IsTrue(ex.ToString().Contains(
                    "javax.cache.CacheException: class org.apache.ignite.IgniteClientDisconnectedException: " +
                    "Operation has been cancelled (client node disconnected)"));

                var inner = (ClientDisconnectedException) ex.InnerException;

                Assert.IsNotNull(inner);

                var clientReconnectTask = inner.ClientReconnectTask;

                Assert.AreEqual(ignite.GetCluster().ClientReconnectTask, clientReconnectTask);
                Assert.AreEqual(1, disconnected);
                Assert.AreEqual(0, reconnected);

                // Resume process to reconnect
                proc.Resume();

                Assert.IsFalse(clientReconnectTask.Result);

                Assert.AreEqual(1, cache[1]);
                Assert.AreEqual(1, disconnected);

                Thread.Sleep(100);  // Wait for event handler
                Assert.AreEqual(1, reconnected);
            }
        }

        /// <summary>
        /// Starts the server process.
        /// </summary>
        private static IgniteProcess StartServerProcess(IgniteConfiguration cfg)
        {
            return new IgniteProcess(
                "-springConfigUrl=" + cfg.SpringConfigUrl, "-J-ea", "-J-Xcheck:jni", "-J-Xms512m", "-J-Xmx512m",
                "-J-DIGNITE_QUIET=false");
        }

        /// <summary>
        /// Test set up.
        /// </summary>
        [SetUp]
        public void SetUp()
        {
            Ignition.StopAll(true);
            IgniteProcess.KillAll();
        }

        /// <summary>
        /// Test tear down.
        /// </summary>
        [TearDown]
        public void TearDown()
        {
            Ignition.StopAll(true);
            IgniteProcess.KillAll();
            Ignition.ClientMode = false;
        }
    }
}

redpajama_set_name: RedPajamaGithub


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The preferred airport for Valenza Hotel & Cafe is Kuala Lumpur (KUL-Kuala Lumpur Intl.).