Supercritical percolation on graphs of polynomial growth

We consider Bernoulli percolation on transitive graphs of polynomial growth. In the subcritical regime ($p<p_c$), it is well known that the connection probabilities decay exponentially fast. In the present paper, we study the supercritical phase ($p>p_c$) and prove the exponential decay of the truncated connection probabilities (probabilities that two points are connected by an open path, but not to infinity). This sharpness result was established by [CCN87] on $\mathbb Z^d$ and uses the difficult slab result of Grimmett and Marstrand. However, the techniques used there are very specific to the hypercubic lattices and do not extend to more general geometries. In this paper, we develop new robust techniques based on the recent progress in the theory of sharp thresholds and the sprinkling method of Benjamini and Tassion. On $\mathbb Z^d$, these methods lead to a completely new proof of the slab result of Grimmett and Marstrand.Comment: 52 pages, 8 figures, corrected typo

Mechanical strength and thermophysical properties of PM212: A high temperature self-lubricating powder metallurgy composite

A powder metallurgy composite, PM212, composed of metal bonded chromium carbide and solid lubricants is shown to be self-lubricating to a maximum application temperature of 900 C. The high temperature compressive strength, tensile strength, thermal expansion and thermal conductivity data needed to design PM212 sliding contact bearings and seals are reported for sintered and isostatically pressed (HIPed) versions of PM212. Other properties presented are room temperature density, hardness, and elastic modulus. In general, both versions appear to have adequate strength to be considered as sliding contact bearing materials, but the HIPed version, which is fully dense, is much stronger than the sintered version which contains about 20 percent pore volume. The sintered material is less costly to make, but the HIPed version is better where high compressive strength is important

Approximation on slabs and uniqueness for Bernoulli percolation with a sublattice of defects

Let Ld = (Zd;Ed) be the d-dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on Ld in which every edge inside the s-dimensional sublattice (Formula Presented) is open with probability q and every other edge is open with probability p.</p

Approximation on slabs and uniqueness for Bernoulli percolation with a sublattice of defects

Let Ld = (Zd;Ed) be the d-dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on Ld in which every edge inside the s-dimensional sublattice (Formula Presented) is open with probability q and every other edge is open with probability p.</p

Approximation on slabs and uniqueness for Bernoulli percolation with a sublattice of defects

Let Ld = (Zd;Ed) be the d-dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on Ld in which every edge inside the s-dimensional sublattice (Formula Presented) is open with probability q and every other edge is open with probability p.</p

Approximation on slabs and uniqueness for Bernoulli percolation with a sublattice of defects

Let Ld = (Zd;Ed) be the d-dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on Ld in which every edge inside the s-dimensional sublattice (Formula Presented) is open with probability q and every other edge is open with probability p.</p

The Canadian Cooperative Wildlife Health Centre and Surveillance of Wild Animal Diseases in Canada, Volume 38, May 1997

The Canadian Cooperative Wildlife Health Centre (CCWHC) was established in 1992 as an organization among Canada\u27s 4 veterinary colleges, with a mandate to apply veterinary medicine to wildlife management and conservation in Canada. A major function of the CCWHC is nation-wide surveillance of wild animal diseases. Disease surveillance is conceived as consisting of 4 different activities: detection, diagnosis, information management, and use of information. In the CCWHC surveillance program, detection of disease is carried out by a wide range of professional and avocational field personnel, and much effort is expended to stimulate and support this activity. Diagnosis is done by personnel of provincial and federal veterinary laboratories and the CCWHC. Information management is achieved through a national database of wildlife disease incidents developed and maintained by the CCWHC. Use of information is enabled through established channels for distribution of information derived from the surveillance program to persons responsible for wildlife programs and policies, and to the public. There has been a high demand for the services of the CCWHC since its establishment. The CCWHC responds to approximately 2000 requests for information annually, distributes its newsletter to over 1700 recipients, examines approximately 1200 wild animal submissions each year, and has accumulated records of over 5000 disease incidents in its database. Technical information from the CCWHC has benefited federal, provincial/territorial, and non-government wildlife agencies; endangered species recovery programs; federal and provincial veterinary services; and federal and provincial public health programs