Differential equation based method for accurate approximations in optimization

A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses

The Therapeutic Bond Scales: Psychometric Characteristics and Relationship to Treatment Effectiveness

The Therapeutic Bond Scales assess the quality of the therapeutic relationship from the patient\u27s perspective. The therapeutic bond is composed of 3 aspects: working alliance, empathic resonance, and mutual affirmation. Scales were developed to measure these aspects and the therapeutic bond as a whole. The correlations between these scales and 2 measures of outcome (session quality assessed by the patient and termination outcome evaluated by nonparticipant raters) were examined. All scales were significantly correlated with session quality. Therapeutic bond was significantly correlated with termination outcome in both a linear and a curvilinear fashion, suggesting that, at least in the initial phase of therapy, the therapeutic bond can be too high as well as too low

NEW CORRECTIONS OF ORDER α3(Zα)4\alpha^3(Z\alpha)^4 AND α2(Zα)6\alpha^2(Z\alpha)^6 TO THE LAMB SHIFT

Two corrections to the Lamb shift, induced by the polarization operator insertions in the external photon lines are calculated.Comment: 4 pages, revtex, no figure

Rotor blade dynamic design

The rotor dynamic design considerations are essentially limitations on the vibratory response of the blades which in turn limit the dynamic excitation of the fuselage by forces and moments transmitted to the hub. Quantities which are associated with the blade response and which are subject to design constraints are discussed. These include blade frequencies, vertical and inplane hub shear, rolling and pitching moments, and aeroelastic stability margin

Sensitivity derivatives and optimization of nodal point locations for vibration reduction

A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location; for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed

Recent advances in multidisciplinary optimization of rotorcraft

A joint activity involving NASA and Army researchers at NASA LaRC to develop optimization procedures to improve the rotor blade design process by integrating appropriate disciplines and accounting for all of the important interactions among the disciplines is described. The disciplines involved include rotor aerodynamics, rotor dynamics, rotor structures, airframe dynamics, and acoustics. The work is focused on combining these five key disciplines in an optimization procedure capable of designing a rotor system to satisfy multidisciplinary design requirements. Fundamental to the plan is a three-phased approach. In phase 1, the disciplines of blade dynamics, blade aerodynamics, and blade structure are closely coupled while acoustics and airframe dynamics are decoupled and are accounted for as effective constraints on the design for the first three disciplines. In phase 2, acoustics is integrated with the first three disciplines. Finally, in phase 3, airframe dynamics is integrated with the other four disciplines. Representative results from work performed to date are described. These include optimal placement of tuning masses for reduction of blade vibratory shear forces, integrated aerodynamic/dynamic optimization, and integrated aerodynamic/dynamic/structural optimization. Examples of validating procedures are described

Radiative-Recoil Corrections of Order α(Zα)5(m/M)m\alpha(Z\alpha)^5(m/M)m to Lamb Shift Revisited

The results and main steps of an analytic calculation of radiative-recoil corrections of order $\alpha(Z\alpha)^5(m/M)m$ to the Lamb shift in hydrogen are presented. The calculations are performed in the infrared safe Yennie gauge. The discrepancy between two previous numerical calculations of these corrections existing in the literature is resolved. Our new result eliminates the largest source of the theoretical uncertainty in the magnitude of the deuterium-hydrogen isotope shift.Comment: 14 pages, REVTE

Persistence in the Voter model: continuum reaction-diffusion approach

We investigate the persistence probability in the Voter model for dimensions d\geq 2. This is achieved by mapping the Voter model onto a continuum reaction-diffusion system. Using path integral methods, we compute the persistence probability r(q,t), where q is the number of ``opinions'' in the original Voter model. We find r(q,t)\sim exp[-f_2(q)(ln t)^2] in d=2; r(q,t)\sim exp[-f_d(q)t^{(d-2)/2}] for 2<d<4; r(q,t)\sim exp[-f_4(q)t/ln t] in d=4; and r(q,t)\sim exp[-f_d(q)t] for d>4. The results of our analysis are checked by Monte Carlo simulations.Comment: 10 pages, 3 figures, Latex, submitted to J. Phys. A (letters