8,107 research outputs found
Energy efficient engine: Turbine transition duct model technology report
The Low-Pressure Turbine Transition Duct Model Technology Program was directed toward substantiating the aerodynamic definition of a turbine transition duct for the Energy Efficient Engine. This effort was successful in demonstrating an aerodynamically viable compact duct geometry and the performance benefits associated with a low camber low-pressure turbine inlet guide vane. The transition duct design for the flight propulsion system was tested and the pressure loss goal of 0.7 percent was verified. Also, strut fairing pressure distributions, as well as wall pressure coefficients, were in close agreement with analytical predictions. Duct modifications for the integrated core/low spool were also evaluated. The total pressure loss was 1.59 percent. Although the increase in exit area in this design produced higher wall loadings, reflecting a more aggressive aerodynamic design, pressure profiles showed no evidence of flow separation. Overall, the results acquired have provided pertinent design and diagnostic information for the design of a turbine transition duct for both the flight propulsion system and the integrated core/low spool
Symmetrized importance samplers for stochastic differential equations
We study a class of importance sampling methods for stochastic differential
equations (SDEs). A small-noise analysis is performed, and the results suggest
that a simple symmetrization procedure can significantly improve the
performance of our importance sampling schemes when the noise is not too large.
We demonstrate that this is indeed the case for a number of linear and
nonlinear examples. Potential applications, e.g., data assimilation, are
discussed.Comment: Added brief discussion of Hamilton-Jacobi equation. Also made various
minor corrections. To appear in Communciations in Applied Mathematics and
Computational Scienc
Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility
We perform a classification of the Lie point symmetries for the
Black--Scholes--Merton Model for European options with stochastic volatility,
, in which the last is defined by a stochastic differential equation
with an Orstein--Uhlenbeck term. In this model, the value of the option is
given by a linear (1 + 2) evolution partial differential equation in which the
price of the option depends upon two independent variables, the value of the
underlying asset, , and a new variable, . We find that for arbitrary
functional form of the volatility, , the (1 + 2) evolution equation
always admits two Lie point symmetries in addition to the automatic linear
symmetry and the infinite number of solution symmetries. However, when
and as the price of the option depends upon the second
Brownian motion in which the volatility is defined, the (1 + 2) evolution is
not reduced to the Black--Scholes--Merton Equation, the model admits five Lie
point symmetries in addition to the linear symmetry and the infinite number of
solution symmetries. We apply the zeroth-order invariants of the Lie symmetries
and we reduce the (1 + 2) evolution equation to a linear second-order ordinary
differential equation. Finally, we study two models of special interest, the
Heston model and the Stein--Stein model.Comment: Published version, 14pages, 4 figure
Cheng Equation: A Revisit Through Symmetry Analysis
The symmetry analysis of the Cheng Equation is performed. The Cheng Equation
is reduced to a first-order equation of either Abel's Equations, the analytic
solution of which is given in terms of special functions. Moreover, for a
particular symmetry the system is reduced to the Riccati Equation or to the
linear nonhomogeneous equation of Euler type. Henceforth, the general solution
of the Cheng Equation with the use of the Lie theory is discussed, as also the
application of Lie symmetries in a generalized Cheng equation.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae
journa
Dear Wife : the Civil War letters of Chester K. Leach
Occasional paper (University of Vermont. Center for Research on Vermont) ; no. 20
Self-assembly of a columnar polymeric calcium phosphinate derived from camphene
(2,2-Dimethylbicyclo[2.2.1] hept-3-ylmethyl)phosphinic acid (RPO₂H₂), readily prepared from camphene and hypophosphorous acid, formed a polymeric calcium salt [{Ca(RPO₂H) ₂ (RPO₂H₂)(H₂O)}n], with both terminal and triply bridging phosphinate groups, and an overall columnar structure with an inorganic core and a pseudo-close-packed sheath of terpene moieties
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