Stationary viscoelastic wave fields generated by scalar wave functions

The usual Helmholtz decomposition gives a decomposition of any vector valued function into a sum of gradient of a scalar function and rotation of a vector valued function under some mild condition. In this paper we show that the vector valued function of the second term i.e. the divergence free part of this decomposition can be further decomposed into a sum of a vector valued function polarized in one component and the rotation of a vector valued function also polarized in the same component. Hence the divergence free part only depends on two scalar functions. Further we show the so called completeness of representation associated to this decomposition for the stationary wave field of a homogeneous, isotropic viscoelastic medium. That is by applying this decomposition to this wave field, we can show that each of these three scalar functions satisfies a Helmholtz equation. Our completeness of representation is useful for solving boundary value problem in a cylindrical domain for several partial differential equations of systems in mathematical physics such as stationary isotropic homogeneous elastic/viscoelastic equations of system and stationary isotropic homogeneous Maxwell equations of system. As an example, by using this completeness of representation, we give the solution formula for torsional deformation of a pendulum of cylindrical shaped homogeneous isotropic viscoelastic medium

非線形拡散方程式に対するODE型の解の漸近展開

Tohoku University赤木剛朗課

DEMB: Cache-aware scheduling for distributed query processing

Leveraging data in distributed caches for large scale query processing applications is becoming more important, given current trends toward building large scalable distributed systems by connecting multiple heterogeneous less powerful machines rather than purchasing expensive homogeneous and very powerful machines. As more servers are added to such clusters, more memory is available for caching data objects across the distributed machines. However the cached objects are dispersed and traditional query scheduling policies that take into account only load balancing do not effectively utilize the increased cache space. We propose a new multi-dimensional range query scheduling policy for distributed query processing frameworks, called DEMB, that employs a probability distribution estimation derived from recent queries. DEMB accounts for both load balancing and the availability of distributed cached objects to both improve the cache hit rate for queries and thereby decrease query turnaround time and throughput. We experimentally demonstrate that DEMB produces better query plans and lower query response times than other query scheduling policies

EM-KDE: A locality-aware job scheduling policy with distributed semantic caches

In modern query processing systems, the caching facilities are distributed and scale with the number of servers. To maximize the overall system throughput, the distributed system should balance the query loads among servers and also leverage cached results. In particular, leveraging distributed cached data is becoming more important as many systems are being built by connecting many small heterogeneous machines rather than relying on a few high-performance workstations. Although many query scheduling policies exist such as round-robin and load-monitoring, they are not sophisticated enough to both balance the load and leverage cached results. In this paper, we propose distributed query scheduling policies that take into account the dynamic contents of distributed caching infrastructure and employ statistical prediction methods into query scheduling policy. We employ the kernel density estimation derived from recent queries and the well-known exponential moving average (EMA) in order to predict the query distribution in a multi-dimensional problem space that dynamically changes. Based on the estimated query distribution, the front-end scheduler assigns incoming queries so that query workloads are balanced and cached results are reused. Our experiments show that the proposed query scheduling policy outperforms existing policies in terms of both load balancing and cache hit ratio. (C) 2015 Elsevier Inc. All rights reservedclose0