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Large scientific parallel applications demand large amounts of memory space. Current parallel computing platforms schedule jobs without fully knowing their memory requirements. This leads to uneven memory allocation in which some nodes are overloaded. This, in turn, leads to disk paging, which is extremely expensive in the context of scientific parallel computing. To solve this problem, we propose a new peer-to-peer solution called parallel network RAM. This approach avoids the use of disk, better utilizes available RAM resources, and will allow larger problems to be solved while reducing the computational, communication, and synchronization overhead typically involved in parallel applications. We proposed several different parallel network RAM designs and evaluated the performance of each under different conditions. We discovered that different designs are appropriate in different situations.