Coordinate finite-type submanifolds

A submanifold of a Euclidean space is called a coordinate finite-type submanifold if its coordinate functions are eigenfunctions of . We prove that the compact coordinate finite-type submanifolds are minimal submanifolds of quadratic hypersurfaces of Euclidean spaces. Moreover, we classify the compact coordinate finite-type submanifolds of codimension 2.     

A new methodology for the construction of numerical methods for the approximate solution of the Schr?dinger equation

In the present paper we introduce a new methodology for the development of numerical methods for the numerical solution of the one-dimensional Schr?dinger equation. The new methodology is based on the requirement of vanishing the phase-lag and its derivatives. The efficiency of the new methodology is proved via error analysis and numerical applications. T. E. Simos is Highly Cited Researcher, Active Member of the European Academy of Sciences and Arts. Corresponding Member of the European Academy of Sciences and European Academy of Arts, Sciences and Humanities.     

Conformal hypersurfaces with the same third fundamental form

We classify all hypersurfaces in a Euclidean space which allow conformal deformations, other than the ones obtained through conformal diffeomorphisms of the Euclidean space, preserving the third fundamental form.     

Time-scale for critical growth of partial and supercavitation development over impulsively translating projectiles

A physical mechanism is proposed to explain an experimentally observed critical time scale that governs the partial cavity development over blunt free flying cylindrical projectiles. The projectiles were ejected using a modified gas-gun mechanism consisting of a barrel and explosive charge. Upon ignition, high-pressure gases forced a projectile down the launch barrel and into quiescent water. Results indicate that initial small cavities created at the projectile forebody are convected downstream where they subsequently grow towards the forebody, partially enveloping the projectile in a vapor cavity. The time at which the initially stable bubbles rapidly expand signifies that the partial cavity development process has begun. When this time is quantified and is non-dimensionalized appropriately, a time-scale for the critical growth (CGTS) for the cavitation is revealed. A plausible explanation of the partial cavity development process observed in these experiments is that the process is due to the interaction between small cavitation bubbles shed from the projectile forebody and the vortex ring generated by the impulsively started projectile. This interaction mediates the destabilization and spontaneous growth of small unstable bubbles resulting in the formation of partial cavitation over the projectile. An additional supercavitation formation mechanism was observed and is attributed to the launch mechanism. This process is not due to pure hydrodynamic cavitation, but rather an effect we term “gas-leakage” whereby the driving gases contaminated the aft flow field near the projectile and thus facilitated supercavitation to occur on a reduced time scale. This mechanism is equivalent to off-body ventilated supercavitation.     

Spherical 2-type hypersurfaces

A hypersurface (not necessarily compact) of a hypersphereS ⁿ⁺¹ of a Euclidean spaceE ⁿ⁺² is of 2-type if and only if it has constant nonzero mean curvature inS ⁿ⁺¹ and constant scalar curvature, unless it is a portion of a small hypersphere inS ⁿ⁺¹. This shows that the 2-type compact hypersurfaces of a hypersphere are mass-symmetric.     

Hypersurfaces with constant scalar curvature and constant mean curvature

Non-spherical hypersurfaces inE ⁴ with non-zero constant mean curvature and constant scalar curvature are the only hypersurfaces possessing the following property: Its position vector can be written as a sum of two non-constant maps, which are eigenmaps of the Laplacian operator with corresponding eigenvalues the zero and a non-zero constant.     

Acoustic source separation for the detection of coronary artery sounds

Coronary artery disease (CAD) is the leading cause of death in the United States, being responsible for more than 20% of all deaths in the country. This is in large part due to the difficulty of diagnostic screening for CAD. Phonoangiography seeks to detect CAD via the acoustic signature associated with turbulent flow near an abnormally constricted, or stenosed, region. However, the usefulness of the technique is severely hindered by the low strength of the CAD signal compared to the background noise within the chest. In this work, acoustic finite element analysis (FEA) was performed on physiologically accurate chest geometries to demonstrate the feasibility of an original acoustic source separation methodology for isolating coronary sounds. This approach is based upon pseudoinversion of mixing matrices determined through a combination of experiment and computation. This allows calculation of the sound emitted by the coronary arteries based upon measurements of the acoustic velocity on the chest surface. This work demonstrates the feasibility of such a technique computationally and examines the vulnerability of the proposed approach to measurement errors.     

Catalytic ignition and autothermal combustion of JP-8 and its surrogates over a Pt/γ-Al2O3 catalyst

With the aim of utilizing JP-8 fuel for small scale portable power generation systems, catalytic combustion of JP-8 is studied. The surface ignition, extinction and autothermal combustion of JP-8, of a six-component surrogate fuel mixture, and the individual components of the surrogate fuel over a Pt/γ-Al₂O₃ catalyst are experimentally investigated in a packed bed flow reactor. The surrogate mixture exhibits similar ignition–extinction behavior and autothermal temperatures compared to JP-8 suggesting the possibility of using this surrogate mixture for detailed kinetics of catalytic combustion of JP-8. It is shown that JP-8 ignites at low temperatures in the presence of catalyst. Upon ignition, catalytic combustion of JP-8 and the surrogate mixture is self-sustained and robust combustion is observed under fuel lean as well as fuel rich conditions. It is shown that the ignition temperature of the hydrocarbon fuels increases with increasing equivalence ratio. Extinction is observed under fuel lean conditions, whereas sustained combustion was also observed for fuel rich conditions. The effect of dilution in the air flow on the catalytic ignition and autothermal temperatures of the fuel mixture is also investigated by adding helium to the air stream while keeping the flow rate and the equivalence ratio constant. The autothermal temperature decreases linearly as the amount of dilution in the flow is increased, whereas the ignition temperature shows no dependence on the dilution level under the range of our conditions, showing that ignition is dependent only on the type and relative concentration of the active species.     

Integral curvature and topological obstructions for submanifolds

We provide integral curvature bounds for compact Riemannian manifolds that allow isometric immersions into a Euclidean space with low codimension in terms of the Betti numbers.