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Martingale solutions for stochastic Navier–Stokes equations driven by Lévy noise
(2012-12) Sakthivel, Kumarasamy; Sritharan, Sivaguru S.; Center for Decision, Risk, Controls and SIGINT (DRCSI)
In this paper, we establish the solvability of martingale solutions for the stochastic Navier-Stokes equations with Itˆo-L ́evy noise in bounded and unbounded domains in Rd,d = 2,3. The tightness criteria for the laws of a sequence of semimartingales is obtained from a theorem of Rebolledo as for- mulated by Metivier for the Lusin space valued processes. The existence of martingale solutions (in the sense of Stroock and Varadhan) relies on a gen- eralization of Minty-Browder technique to stochastic case obtained from the local monotonicity of the drift term.
Strategic Systems of the Future (SSF)
(2012) Sritharan, S.S.; Center for Decision, Risk, Controls and SIGINT (DRCSI)
Method for Optimally Controlling Unsteady Shock Strength in One Dimension
(AIAA, 2013) Moshman, Nathan D.; Hobson,Garth V.; Sritharan, Sivaguru S.; Center for Decision, Risk, Controls and SIGINT (DRCSI)
This paper presents a new formulation and computational solution of an optimal control problem concerning unsteady shock wave attenuation. The adjoint system of equations for the unsteady Euler system in one dimension is derived and used in an adjoint-based solution procedure for the optimal control. A novel algorithm is used to satisfy all necessary first-order optimality conditions while locally minimizing an appropriate cost functional. Distributed control solutions with certain physical constraints are calculated for attenuating blast waves similar to those generated by ignition overpressure from the shuttle’s solid rocket booster during launch. Results are presented for attenuating shocks traveling at Mach 1.5 and 3.5 down to 85%, 80%, and 75% of the uncontrolled wave’s driving pressure. The control solutions give insight into the magnitude and location of energy dissipation necessary to decrease a given blast wave’s overpressure to a set target level over a given spatial domain while using only as much control as needed. The solution procedure is sufficiently flexible such that it can be used to solve other optimal control problems constrained by partial differential equations that admit discontinuities and have fixed initial data and free final data at a free final time.
Computation of Steady Incompressible Flows in Unbounded Domains
(2015-01) Gustafsson, Jonathan; Protas, Bartosz; Center for Decision, Risk, Controls and SIGINT (DRCSI)
In this study we revisit the problem of computing steady Navier- Stokes flows in two-dimensional unbounded domains. Precise quanti- tative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical fluid dynamics. Following a review of key mathematical properties of such solutions related to the slow decay of the velocity field at large distances from the obstacle, we develop and carefully validate a spectrally-accurate computational approach which ensures the correct behavior of the solution at infin- ity. In the proposed method the numerical solution is defined on the entire unbounded domain without the need to truncate this domain to a finite box with some artificial boundary conditions prescribed at its boundaries. Since our approach relies on the streamfunction- vorticity formulation, the main complication is the presence of a dis- continuity in the streamfunction field at infinity which is related to the slow decay of this field. We demonstrate how this difficulty can be overcome by reformulating the problem using a suitable background ”skeleton” field expressed in terms of the corresponding Oseen flow combined with spectral filtering. The method is thoroughly validated for Reynolds numbers spanning two orders of magnitude with the re- sults comparing favourably against known theoretical predictions and the data available in the literature.
Decision, Risk, Controls and SIGINT (DRCSI) Publication (archived)
(Monterey, California: Naval Postgraduate School., 2015-02-06) Naval Postgraduate School; Naval Postgraduate School (U.S.); Center for Decision, Risk, Controls and SIGINT (DRCSI)
DRCSI Homepage
DRCSI News: Director to Brief in U.S.-India Workshop, Center for Decision, Risk, Controls and Signals Intelligence
(Monterey, California: Naval Postgraduate School., 2015-02-06) Naval Postgraduate School (U.S.); Center for Decision, Risk, Controls and SIGINT (DRCSI)
High level defense scientists and experts from the U.S. Department of Defense will be joining the experts from India's Defense Research Development Organization (DRDO) in New Delhi in September to hold a joint scientific workshop in Directed Energy Weapon Systems, Unmanned Systems and Autonomy, and Cognitive Sciences. The U.S. team includes scientists from Army Research Laboratories (ARL), Office of Naval Research (ONR), Naval Warfare Systems Centers, Air Force Research Laboratories (AFRL), Joint Technology Office (JTO) for High Energy Lasers and DRCSI Director (S. S. Sritharan) from NPS. The meeting, organized by the Office of the Secretary of Defense (OSD), will be expected to stimulate partnerships and collaborations between United States and India in these high priority defense science disciplines.
Special Lecture Series, DRCSI poster
(Monterey, California: Naval Postgraduate School., 2014) Naval Postgraduate School (U.S.); Center for Decision, Risk, Controls and SIGINT (DRCSI)
Quasi-linear Partial Differential Equations of Fluid Dynamics and Physics Rigorous Solvability, Stochastic Analysis & Control, Special Lecture Series poster.
Past Seminars
(2013-11-21) Center for Decision, Risk, Controls and SIGINT (DRCSI)
Research
(2014-05-16) Center for Decision, Risk, Controls and SIGINT (DRCSI)
Research Directed Energy Weapons
(2014-05-16) Center for Decision, Risk, Controls and SIGINT (DRCSI)