SKU: 88766807665

Complexity & Criticality (V1)

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Complexity & Criticality (V1)This book provides a challenging and stimulating introduction to the contemporary topics of complexity and criticality, and explores their common basis of scale invariance, a central unifying theme of the book. Criticality refers to the behaviour of extended systems at a phase transition where scale invariance prevails. The many constituent microscopic parts bring about macroscopic phenomena that cannot be understood by considering a single part

This book provides a challenging and stimulating introduction to the contemporary topics of complexity and criticality, and explores their common basis of scale invariance, a central unifying theme of the book.Criticality refers to the behaviour of extended systems at a phase transition where scale invariance prevails. The many constituent microscopic parts bring about macroscopic phenomena that cannot be understood by considering a single part alone. The phenomenology of phase transitions is introduced by considering percolation, a simple model with a purely geometrical phase transition, thus enabling the reader to become intuitively familiar with concepts such as scale invariance and renormalisation. The Ising model is then introduced, which captures a thermodynamic phase transition from a disordered to an ordered system as the temperature is lowered in zero external field. By emphasising analogies between percolation and the Ising model, the reader's intuition of phase transitions is developed so that the underlying theoretical formalism may be appreciated fully. These equilibrium systems undergo a phase transition only if an external agent finely tunes certain external parameters to particular values.Besides fractals and phase transitions, there are many examples in Nature of the emergence of such complex behaviour in slowly driven non-equilibrium systems: earthquakes in seismic systems, avalanches in granular media and rainfall in the atmosphere. A class of non-equilibrium systems, not constrained by having to tune external parameters to obtain critical behaviour, is addressed in the framework of simple models, revealing that the repeated application of simple rules may spontaneously give rise to emergent complex behaviour not encoded in the rules themselves. The common basis of complexity and criticality is identified and applied to a range of non-equilibrium systems. Finally, the reader is invited to speculate whether self-organisation in non-equilibrium systems might be a unifying concept for disparate fields such as statistical mechanics, geophysics and atmospheric physics.Visit for animations for the models in the book (available for Windows and Linux), solutions to exercises, as well as a list with corrections.
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SKU: 88766807665

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4.1 ★★★★★
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E. Cooper
Chelsea, US
★★★★★ 4
Evisceration was nearly instantaneous but he’s hanging on!
Color: Blue
Despite my Sunshine eviscerating this prehistoric fellow and extracting the squeaker from his innards within minutes (followed by about an hour of her laying about, lazily squeaking, it has otherwise held up fairly well! Plastic squeaker aside, it doesn’t have any other plastic parts in it and the stitching has held up (my Sunshine went for the squeaker as if it were an alien about to burst forth from the dino’s belly and acted accordingly so the fabric didn’t quite hold up as well). It’s a decent size and only had a bit of fluff in its belly for me to clean up afterward. My Sunshine is an energetic chewer so I consider it a win that this thing is still even dino-shaped and only bereft of its squeaker. My Sunshine is quite happy with this little fellow and if she’s happy, I’m happy!
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Reviewed in the United States on August 20, 2025
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Rob Colvil
Belleville, US
★★★★★ 5
Became my dog's new favorite
Color: Blue
This instantly became my dog's go-to toy, and thankfully it's lasted longer than I anticipated. He was excited to play with it immediately, of course, but he also continued to go to it over all the other toys he has. He loves to rip and tear, so I didn't think this would last more than a day, but incredibly it's been going for weeks. Granted, he's torn out the squeaker and some of the crinkly plastic, as well as most of the stuffing, but there's still a recognizable dinosaur-shaped toy hanging around that he still likes to play with. The squeaker is also different than most dog toys, it's larger and lower-pitched, so that variation is fun. There's lots of crinkly plastic in the tail and feet, so even after my dog ripped open the tail and gotten that plastic out, there's still more noise-making stuff left in there. The size and amount of stuffing is also great, as it's given him many days of things to tear apart.
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Reviewed in the United States on August 21, 2025
S
Susan Bewley
Cuba, US
★★★★★ 5
My Dogs Love It!
Color: Blue, Color: Blue
Do your dogs love a specific type of toy? Since my girls were puppies, they have preferred a specific material for toys. It is a soft, bubbly texture, usually in bright colors. It is soft for them and durable enough to survive even the toughest of playmates. All the toys made from this material also have a certain crinkle paper that drives both of my girls wild, and sometimes even include a squeaker. When I saw that this adorable dinosaur fit their favorite toy's qualities, I knew I had to get it for them! First, I want to talk about the quality. This dinosaur is adorable and designed for some tough play sessions. It is more reinforced than the name-brand toys I buy, which impressed me. While my girls rarely destroy toys, I find comfort in knowing that they will likely get bored with a toy before destroying it. What shocked me more was the squeaker. This company didn't go cheap; they went for a higher quality, large squeaker that is very loud and durable. My dogs have been playing with this for nearly two hours straight, and the squeaker has been going strong. If you don't like loud squeakers, though, be warned, it is very loud and isn't stop working anytime soon! Overall, this toy has been a big hit and way cheaper than what I can buy at local pet stores. With the quality and how much my girls love it, it has been a bargain and well worth it! This is a toy that we will be purchasing more of soon.
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Reviewed in the United States on August 9, 2025
S
StacyP
Lowell, US
★★★★★ 5
Rawr!
Color: Blue, Color: Blue
My dogs love this toy; they have been playing with it for a few days, and surprisingly, it has been durable enough to withstand most of the torture. it has a fun squeaker and thankfully not too much filler, which I am thankful to have to follow behind to pick up. This is a good value toy. My dogs can usually tear a toy up in seconds but for some reason, they have chosen to keep this dinosaur alive!
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Reviewed in the United States on August 18, 2025
S
snowyh
West Palm Beach, US
★★★★★ 4
Not for Aggressive Chewers
Color: Blue, Color: Blue
Cute stuffed dino with one large squeaker in the body and crinkle paper in the feet and tail. The right size for medium to large dogs. Riley was eager to play tug-of-war with this toy when I first gave it to her. Five minutes later the novelty had worn off and she went to her toy basket to bring out her usual favorites. Being plush, this is not really a toy for aggressive chewers--after only 5 minutes she had torn open a seam and ripped off part of the tag. I'll continue to let her play with it until stuffing starts coming out (which shouldn't be long).
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Reviewed in the United States on August 13, 2025

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