Undisturbed Case Research Articles

Soliton lattice in copper metaborate, CuB 2 O 4 , in the presence of an external magnetic field

The spontaneous formation of a magnetic soliton lattice in copper metaborate, CuB2O4, is also stable at a temperature of 4.2 K in the presence of an external magnetic field up to 1.3 T applied along the tetragonal [110] direction similar to the undisturbed case, where it is stable up to a temperature of 10 K. Increasing the external magnetic field induces a phase transition from the incommensurate to the commensurate structure similar to increasing the temperature at zero field as reported earlier. The formation of domain walls (solitons) can therefore be associated with combined effects of Dzyaloshinskii interaction and anisotropy. The T/H phase diagrams show a coexistence region of commensurate and incommensurate phases, in agreement with the theory of a solition lattice at fields up to 1.3 T.

An Experimental Study of the Effect of Vibrations on Supercritical Fluid Transfer Processes under Microgravity Conditions

On the basis of the data obtained in experiments onboard the Mirorbital complex (OC) in March and April 1999 with the ALICE-2 instrument, the influence of vibrations on heat propagation from a point-like source in the hexafluoride sulfur (SF6) under supercritical parameters is analyzed. The appearance of two different heat propagation regimes is found: along and across the direction of vibrations. Upon the occurrence of the second-type regime, the heating region first stretches in the direction perpendicular to the direction of vibrations and then propagates at a rate typical for the undisturbed case. The temperature relaxation process is analyzed, which takes place near the heater after its turn-off. The relaxation rate grows as the intensity of vibrations increases and the initial temperature tends to the critical one. The determining dimensionless parameters of the problem are suggested.

Freestream Disturbance Effects on an Airfoil Pitching at Constant Rate

Effects of freestream disturbances on the dynamic stall process of an NACA 0012 airfoil undergoing ramp-type pitching motion from 0-30 deg were studied using measurements of unsteady surface pressures. A thin circular cylinder was located upstream of the test airfoil and was offset vertically between -0.133 and 0.133 chord lengths with respect to the airfoil pitching axis to provide the freestream disturbances. The measurements were carried out at a constant chord Reynolds number of 8 x 10 4 for a relatively low reduced pitch-rate range k = 0.01-0.04. As compared with the undisturbed flow case, the imposed freestream disturbances were able to produce a significant increase in absolute magnitude of the peak suction pressure near the leading edge, resulting in a noticeable phase delay in stall process. The growth of the leading-edge suction peak caused by insertion of the upstream rod was found to be sensitive to its vertical offset position. Nevertheless, the pressure variation caused by the freestream disturbances was appreciable only in the forward 20% chord from the leading edge, bringing a lower effect on the airfoil lift and momentum coefficients

Effects of leading-edge roughness on fluid flow and heat transfer in the transitional boundary layer over a flat plate

Abstract An experimental study was undertaken to gain insight into the physical mechanisms that affect the laminar-turbulent transition process downstream of the leading-edge roughness condition. Sandpaper strips and small cylinders were attached to the leading edge of a heated test surface to simulate leading edge roughness typical of gas turbine blades. The roughness Reynolds numbers ranged from 2 to 2840. For free-stream velocities less than 5 m s −1 , the maximum roughness height was the primary contributor to deviations from the undisturbed case, irrespective of the roughness geometry. At higher free-stream velocities (5–7 m s −1 ), three of the rough leading-edge conditions induced a dual-slope region between the laminar and turbulent Stanton number correlations. Boundary layer measurements indicated that the first segment of the dual-slope was laminar, but the wall heat transfer significantly deviates from the laminar correlation. The second segment was transitional. The dual-slope behaviour and a waviness in the Stanton number distribution observed at higher free-stream velocities are believed to have been caused by nonlinear amplification caused by the finite disturbances at the leading edge.

An application of minimax robust optimal control theory for selective vibrational excitation in molecules

In recent investigations control theory was applied to design electromagnetic fields capable of producing vibrational excitation in molecular systems. This approach has been applied to linear or non-linear classical approximations of molecular systems or to quantal systems using distributed cost functionals. Practical computations of molecular optimal control theory for large molecules especially with anharmonic potentials become difficult due to the increased dimensionality and the mixed nature of the boundary conditions. This paper proposes to approach the control design for such systems by treating a portion of the molecule containing the target and dipole bonds in full detail while the effect of the remainder of the system is modelled as a disturbance of limited energy. The optimal fieldminimizes the cost functional which is simultaneouslymaximized with respect to the disturbance. Such assumptions give rise to a robust controller akin to theH∞ theory of robust estimation. We investigate the various field designs for truncated harmonic systems associated with different disturbance energies and demonstrate that the existence of the solution to the associated Ricatti equation ensures the existence of the equilibrium game point. In addition, in the range of physically reasonable disturbance energy the optimal field could be accurately predicted from an asymptotic expansion involving only the undisturbed reference case. As an application we show the optimal field design for a 20 atom truncated molecular chain containing both the target bond (the 5th bond) and the dipole bonds (1st and 9th) where the disturbance only affects the end bond of the system attached to the remainder of the chain. In an effort to improve on the efficiency of the bond energy deposition we investigate shortened target times and also a 40 atom truncated chain. This approach presents very conservative estimates of possible disturbances but provides insight into the sensitivity of different configurations with respect to external disturbances. The minimax approach can be generalized to non-linear molecular systems by modelling the original system as a linear system plus an energy constrained disturbance.

Robust optimal control theory for selective vibrational excitation in molecules: A worst case analysis

Recent research has demonstrated that optimal electromagnetic fields capable of producing selective vibrational excitation in molecules can be designed employing linear quadratic control methods using a cost functional that balances the energy distribution in the molecule, the fluence of the optical field, and a final cost to insure the desired excitation. Practical computations of molecular control theory for large molecules especially with anharmonic potentials become difficult to obtain due to the increased dimensionality and the accompanying uncertainty in the Hamiltonian. In this paper we reduce the complexity of the problem by treating a portion of the molecule including the target and optical dipoles in full detail, while the remainder of the molecule is modeled as an external disturbance of bounded energy. The optimal control field now minimizes the cost functional which is simultaneously maximized with respect to the energy constrained external disturbance to assure robustness. This optimal design process is commensurate with taking the most pessimistic view of the disturbance. This conservative view was born out in the numerical calculations such that practical laboratory studies should reach results much improved over the worst case design. As an illustration we investigate disturbances of varying energy content for a truncated 20 atom molecular chain where the uncontrolled remainder of the chain is the source of the system disturbance. The sensitivity of the system with respect to the disturbance was found to be strongly dependent on the distance of the disturbance to the target bond and the dipole arrangement. In addition, in the range of physically reasonable disturbance energy the optimal field could be accurately predicted from an asymptotic expansion involving only the reference undisturbed case. Although the present paper takes advantage of linear system techniques, the same robust optimal control procedure can be generalized to nonlinear systems by a variety of means.

Numerical Simulation of Tropical Cumulus Clouds and Their Interaction with the Subcloud Layer

A two-dimensional numerical model, with an emphasis on turbulent processes in the boundary layer and in clouds, was developed for simulating an ensemble of cumulus clouds. The model was used to investigate the response of tropical cumulus clouds to imposed large-scale vertical advection by performing two simulations which were identical except that one was with upward large-scale vertical velocity (the 'disturbed' case) and the other was without any advection (the 'undisturbed' case). The results showed that deep cumulus clouds formed in the disturbed case, while only shallow clouds formed in the undisturbed case. The subcloud layer (SCL) in the disturbed case was strongly affected by cumulus circulations and rain evaporation, with both cumulus updrafts and downdrafts being important contributors to the SCL sensible and latent heat fluxes. Cumulus-scale circulation in the disturbed SCL determined where new clouds formed by creating convergence zones and moisture anomalies.

Non-KAM Hamiltonians

The properties of Hamiltonians H(P1, P2, Q1, Q2) = P1G1 (Q1, Q2) + P2G2 (Q1, Q2), with arbitrary analytic G1 and G2, 2π-periodic in Q1 and Q2, are investigated analytically and numerically. Such H cannot be separated into two parts, H = H0 + H1, such that the KAM theorem would apply for |H1| ≪ |H0|.Orbits in phase space proceed on nested tori (integrable cases) or move towards infinity (integrability remains open). No chaotic regions are observed. From the theory of circle maps it follows that non-KAM Hamiltonians are integrable if a winding number w is sufficiently irrational, a condition which is analogous to that in the KAM case. In contrast to KAM, however, there is no restriction to small deviations from an undisturbed integrable case. The regions of rational vs. irrational w in parameter space are intricately interspersed.

Elliptical inhomogeneities in groundwater flow — An analytical description

In order to be able to decide whether and how heterogeneities should be taken into account for modelling a groundwater flow problem, the magnitude of those disturbances must be estimated. Therefore, in this paper we solve the problem of a uniform flow in a homogeneous medium with an elliptical shaped inhomogeneity with a different value for the permeability and positioned under an arbitrary angle with respect to the undisturbed flow. We calculate the ratio of the flow rate through this body with respect to the undisturbed case. Besides its use in solving groundwater flow problems, this formula may be helpful for problems relevant to field reconnaisance.

Über die bestimmung der optischen konstanten dünnster oberflächenschichten und das problem der schichtdicke

The Fresnel reflection coefficients of a phase boundary disturbed by values of the optical constants differing from the values in the adjacent phases (boundary phase) are derived. The derivation on the basis of Maxwells' theory uses integral boundary conditions. The deviations from the ideal reflection properties, caused by a boundary phase with uniaxial symmetry, are proportional to the difference of the dielectric constants (for the tangential component) and to the difference of the reciprocal values of the dielectric constants (for the normal component) to the value in the undisturbed case, integrated over the boundary phase. An optical thickness of the boundary phase can not be determined by means of ellipsometry or reflection spectroscopy.

On Protuberance Noise Environments

A review of three-dimensional or local protuberance environments is presented with emphasis on the role of the boundary layer. The boundary layer is observed to participate significantly in the generation or propagation of acoustic disturbances throughout the adjacent region. Deductions on boundary layer quantitative effects are made based on data presented by (1) Robertson (1969) and (2) various other investigators. These data are respectively associated with relatively high and low (or roughness) regimes of proturberance height with respect to the boundary layer thickness. Insights are also obtained from the data on two-dimensional and axisymmetric steps contributed by various researchers in the past decade. Highest fluctuating pressures, forward and aft of cylindrical protuberances, typically occur in cases where protuberance height is on the order of 1.0–2.0 boundary layer thicknesses. Cylindrical protuberance configurations, having a minimum height (h) of 0.125 boundary layer thickness (δ), caused a local increase in rms fluctuating pressures (relative to undisturbed case) of 4.0 or more in all cases tested. Comments are included on roughness (h/δ < 0.1) noise sources and amplitudes as a function of height and distribution parameters.