New approach in classification of integrable hydrodynamic chains is established. This is the method of the Hamiltonian hydrodynamic reductions. Simultaneously, this approach yields explicit Hamiltonian hydrodynamic reductions of the Hamiltonian hydrodynamic chains. The concept of reducible Poisson brackets is established. Also this approach is useful for non-Hamiltonian hydrodynamic chains. The...

We consider a model of diffusion in random media with a two-way coupling (i.e., a model in which the randomness of the medium influences the diffusing particles and where the diffusing particles change the medium). In this particular model, particles are injected at the origin with a timedependent rate and diffuse among random traps. Each trap has a finite (random) depth, so that when it has ab...

Massively-parallel, distributed-memory algorithms for the Lagrangian particle hydrodynamic method (Samulyak et al., 2018) have been developed, verified, and implemented. The key component of parallel is a management module that includes construction octree databases, dynamic adaptation refinement octrees, migration between subdomains. based on p4est (parallel forest k-trees) library. massively-...

In the procedure of designing an underwater vehicle or robot, its maneuverability and controllability must be simulated and tested, before the product is finalized for manufacturing. Since the hydrodynamic forces and moments highly affect the dynamic and maneuverability of the system, they must be estimated with a reasonable accuracy. In this study, hydrodynamic coefficients of an autonomous un...

Polluted aquifers can be decontaminated using either ZVI (zero valent iron) permeable reactive barriers (PRB) or injected ZVI. The placement of within the aquifer may take several decades to remediate contaminant plume. Remediation is further complicated by acting as an adsorbent remove some pollutants, while for other it acts a remediation catalyst. This study investigates alternative decontam...