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Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book, first published in 2006, are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.

Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.

Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.

Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book, first published in 2006, are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.

This work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups.

This work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups.

This work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups.

This work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups.

This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.

This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.

The 18" Khiva No Perc Beaker Water Pipe by Diamond Glass is a durable and functional option for experienced smokers who prefer big, smooth hits. This pipe offers a straightforward and efficient smoking experience. It has beaker design, thick base, and 19mm female joint. The lack of percolation adds to the simplicity while still providing cool and smooth hits.  Looking to add to your collection or simply seeking a reliable and stylish smoking pipe? This water pipe is a great choice! Hurry up to order from our online headshop!

The Tsunami Stereo Showerhead Water Pipe 14" features an ice-catcher. This allows you to ultra-chill your hits through the sleek and classy design. It has a percolation mechanism that supplies through a large number of micropores. Hurry up to order from our online headshop.

Key Features: Optimal Height: Standing at 8 inches, this dab rig is designed for optimal functionality without sacrificing portability. The moderate height ensures a comfortable grip while providing ample space for effective percolation. Sphere Perc: The highlight of this rig is the Sphere Perc, a distinctive feature that sets it apart. The sphere design enhances filtration by diffusing and cooling the vapor as it passes through, delivering smooth and flavorful hits. Premium Glass Construction: Crafted from premium borosilicate glass, Diamond Glass ensures durability and heat resistance. The use of high-quality materials not only enhances the longevity of the rig but also contributes to its aesthetic appeal. 14mm Female Joint: The 14mm female joint adds versatility to the rig, allowing compatibility with various dab nails and accessories. This feature opens up possibilities for customization based on personal preferences. Stable Base: The rig is equipped with a stable base, ensuring a secure foundation during your dabbing sessions. Stability is crucial for a worry-free experience, minimizing the risk of accidental tipping. Sleek and Modern Design: Diamond Glass is known for its commitment to sleek and modern designs. The clean lines and elegant shape of the 8" Retort Sphere Perc Dab Rig reflect the brand's dedication to aesthetics without compromising on functionality. Enhance Your Dabbing Ritual: Diamond Glass continues to uphold its reputation for delivering top-quality dab rigs, and the 8" Retort Sphere Perc Dab Rig is no exception. Elevate your dabbing ritual with the perfect combination of form and function, all embodied in this striking and efficient dab rig. Order from our online headshop, Olofly! Note: Always follow safety guidelines and practice responsible consumption when using any dab rig or smoking accessory.

The 18" Khiva No Perc Beaker Water Pipe by Diamond Glass is a durable and functional option for experienced smokers who prefer big, smooth hits. This pipe offers a straightforward and efficient smoking experience. It has beaker design, thick base, and 19mm female joint. The lack of percolation adds to the simplicity while still providing cool and smooth hits.  Looking to add to your collection or simply seeking a reliable and stylish smoking pipe? This water pipe is a great choice! Hurry up to order from our online headshop!

The Tsunami Stereo Showerhead Water Pipe 14" features an ice-catcher. This allows you to ultra-chill your hits through the sleek and classy design. It has a percolation mechanism that supplies through a large number of micropores. Hurry up to order from our online headshop.

The 18" Khiva No Perc Beaker Water Pipe by Diamond Glass is a durable and functional option for experienced smokers who prefer big, smooth hits. This pipe offers a straightforward and efficient smoking experience. It has beaker design, thick base, and 19mm female joint. The lack of percolation adds to the simplicity while still providing cool and smooth hits.  Looking to add to your collection or simply seeking a reliable and stylish smoking pipe? This water pipe is a great choice! Hurry up to order from our online headshop!

The Grav Empress Water Pipe blends scientific practicality with aesthetic beauty into a single form, resulting in a stunning piece of art. The pipe provides fixed downstream leading to the installed eight-slot percolation chamber. The percolator produces gorgeous bubbles in all directions around the chamber's base. Hurry up to order from our online headshop!

Key Features: Height: With a height of 14 inches, this Tsunami water pipe offers a perfect balance between visual impact and practicality. The elevated stature allows for an immersive smoking experience. Quad Rocket Percs: Experience unparalleled percolation with the Quad Rocket Percs. These four rocket-shaped percolators are strategically placed to maximize smoke diffusion, ensuring a smooth and cooled hit with each draw. Quality Borosilicate Glass: Crafted from premium borosilicate glass, this water pipe is not only visually appealing but also durable and heat-resistant. The use of high-quality materials ensures a clean and enjoyable smoking experience. Sturdy Base: The water pipe is equipped with a sturdy base, providing stability during use and minimizing the risk of accidental tipping. The wide base enhances overall balance and safety. Straight Tube Design: The straight tube design contributes to the classic appearance of the water pipe. This design allows for a straightforward and enjoyable smoking experience. 14mm Female Joint: Featuring a 14mm female joint, the water pipe offers compatibility with various accessories and attachments, allowing users to customize their smoking setup based on personal preferences. Flared Mouthpiece: The flared mouthpiece ensures a comfortable and secure seal around the mouth, facilitating easy and effortless draws from the water pipe. Impressive Aesthetics: Beyond its functional features, the water pipe boasts an eye-catching design with Quad Rocket Percs. The attention to detail in the craftsmanship adds an artistic and captivating element to the overall aesthetics. Percolated Smoke: The Quad Rocket Percs not only enhance percolation but also create a visually stunning effect as smoke passes through the water pipe. Each hit becomes a sensory experience, combining aesthetics and functionality. Customizable Experience: The 14mm female joint allows users to explore various accessories and attachments, providing flexibility in customizing the smoking experience to individual preferences. The 14" Tsunami Rocktapus Quad Rocket Water Pipe is an excellent choice for those seeking a distinctive and high-performing water pipe. Whether you're a seasoned smoker or a collector, this water pipe offers a unique and enjoyable smoking experience with a touch of visual flair. Order from our online headshop, Olofly!

The Tsunami Nectar Collector Kit demonstrates that Tsunami Glasses has created an invention that fulfills the requirement of being economical, accessible, tiny, portable, and simple to use. The kit contains many vents to allow percolation, which filters, chills, and softens the water. Take it with you the next time you go to a group event and see how much everyone enjoys it, whether they are a novice or experienced smokers. Available on our online headshop. Tsunami Nectar Collector Kit Features and Specifications: • Borosilicate Glass • Concentrate Pipe • Highest Quality Materials • Includes Glass Dish • Includes Nectar Collector Tip

The Tsunami Nectar Collector Kit demonstrates that Tsunami Glasses has created an invention that fulfills the requirement of being economical, accessible, tiny, portable, and simple to use. The kit contains many vents to allow percolation, which filters, chills, and softens the water. Take it with you the next time you go to a group event and see how much everyone enjoys it, whether they are a novice or experienced smokers. Available on our online headshop. Tsunami Nectar Collector Kit Features and Specifications: • Borosilicate Glass • Concentrate Pipe • Highest Quality Materials • Includes Glass Dish • Includes Nectar Collector Tip