Generation Efficiencies for Propagating Modes in a Supersolid

Using Andreev and Lifshitz's supersolid hydrodynamics, we obtain the propagating longitudinal modes at non-zero applied pressure $P_{a}$ (necessary for solid 4He), and their generation efficiencies by heaters and transducers. For small $P_{a}$, a solid develops an internal pressure $P \sim P_{a}^2$. This theory has stress contributions both from the lattice and an internal pressure $P$. Because both types of stress are included, the normal mode analysis differs from previous works. Not surprisingly, transducers are significantly more efficient at producing elastic waves and heaters are significantly more efficient at producing fourth sound waves. We take the system to be isotropic, which should apply to systems that are glassy or consist of many crystallites; the results should also apply, at least qualitatively, to single-crystal hcp 4He.Comment: 10 pages. Accepted by Physical Review

Thermal Equilibration and Thermally-Induced Spin Currents in a Thin-Film Ferromagnet on a Substrate

Recent spin-Seebeck experiments on thin ferromagnetic films apply a temperature difference $\Delta T_{x}$ along the length $x$ and measure a (transverse) voltage difference $\Delta V_{y}$ along the width $y$. The connection between these effects is complex, involving: (1) thermal equilibration between sample and substrate; (2) spin currents along the height (or thickness) $z$; and (3) the measured voltage difference. The present work studies in detail the first of these steps, and outlines the other two steps. Thermal equilibration processes between the magnons and phonons in the sample, as well as between the sample and the substrate leads to two surface modes, with surface lengths $\lambda$, to provide for thermal equilibration. Increasing the coupling between the two modes increases the longer mode length and decreases the shorter mode length. The applied thermal gradient along $x$ leads to a thermal gradient along $z$ that varies as $\sinh{(x/\lambda)}$, which can in turn produce fluxes of the carriers of up- and down- spins along $z$, and gradients of their associated \textit{magnetoelectrochemical potentials} $\bar{\mu}_{\uparrow,\downarrow}$, which vary as $\sinh{(x/\lambda)}$. By the inverse spin Hall effect, this spin current along $z$ can produce a transverse (along $y$) voltage difference $\Delta V_y$, which also varies as $\sinh{(x/\lambda)}$.Comment: 14 pages, 7 figures, 1 tabl

Andreev-Lifshitz Hydrodynamics Applied to an Ordinary Solid under Pressure

We have applied the Andreev-Lifshitz hydrodynamic theory of supersolids to an ordinary solid. This theory includes an internal pressure $P$, distinct from the applied pressure $P_a$ and the stress tensor $\lambda_{ik}$. Under uniform static $P_{a}$, we have $\lambda_{ik} = (P-P_{a})\delta_{ik}$. For $P_{a} \ne 0$, Maxwell relations imply that $P \sim P_{a}^{2}$. The theory also permits vacancy diffusion but treats vacancies as conserved. It gives three sets of propagating elastic modes; it also gives two diffusive modes, one largely of entropy density and one largely of vacancy density (or, more generally, defect density). For the vacancy diffusion mode (or, equivalently, the lattice diffusion mode) the vacancies behave like a fluid within the solid, with the deviations of internal pressure associated with density changes nearly canceling the deviations of stress associated with strain. We briefly consider pressurization experiments in solid $^4$He at low temperatures in light of this lattice diffusion mode, which for small $P_{a}$ has diffusion constant $D_{L} \sim P_{a}^{2}$. The general principles of the theory -- that both volume and strain should be included as thermodynamic variables, with the result that both $P$ and $\lambda_{ik}$ appear -- should apply to all solids under pressure, especially near the solid-liquid transition. The lattice diffusion mode provides an additional degree of freedom that may permit surfaces with different surface treatments to generate different responses in the bulk.Comment: 10 pages. Accepted by Physical Review

Andreev-Lifshitz Supersolid Hydrodynamics Including the Diffusive Mode

We have re-examined the Andreev-Lifshitz theory of supersolids. This theory implicitly neglects uniform bulk processes that change the vacancy number, and assumes an internal pressure $P$ in addition to lattice stress $\lambda_{ik}$. Each of $P$ and $\lambda_{ik}$ takes up a part of an external, or applied, pressure $P_a$ (necessary for solid 4He). The theory gives four pairs of propagating elastic modes, of which one pair corresponds to a fourth-sound mode, and a single diffusive mode, which has not been analyzed previously. The diffusive mode has three distinct velocities, with the superfluid velocity much larger than the normal fluid velocity, which in turn is much larger than the lattice velocity. The mode structure depends on the relative values of certain kinetic coefficients and thermodynamic derivatives. We consider pressurization experiments in solid 4He at low temperatures in light of this diffusion mode and a previous analysis of modes in a normal solid with no superfluid component.Comment: 8 pages. Accepted by Physical Review

General approach and scope

This paper describes a joint activity involving NASA and Army researchers at the NASA Langley Research Center to develop optimization procedures aimed at improving the rotor blade design process by integrating appropriate disciplines and accounting for all of the important interactions among the disciplines. 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 will be closely coupled, while acoustics and airframe dynamics will be decoupled and be accounted for as effective constraints on the design for the first three disciplines. In phase 2, acoustics is to be integrated with the first three disciplines. Finally, in phase 3, airframe dynamics will be fully integrated with the other four disciplines. This paper deals with details of the phase 1 approach and includes details of the optimization formulation, design variables, constraints, and objective function, as well as details of discipline interactions, analysis methods, and methods for validating the procedure

An initiative in multidisciplinary optimization of rotorcraft

Described is a joint NASA/Army initiative at the Langley Research Center to develop optimization procedures aimed at improving the rotor blade design process by integrating appropriate disciplines and accounting for important interactions among the disciplines. The activity is being guided by a Steering Committee made up of key NASA and Army researchers and managers. The committee, which has been named IRASC (Integrated Rotorcraft Analysis Steering Committee), has defined two principal foci for the activity: a white paper which sets forth the goals and plans of the effort; and a rotor design project which will validate the basic constituents, as well as the overall design methodology for multidisciplinary optimization. The optimization formulation is described in terms of the objective function, design variables, and constraints. Additionally, some of the analysis aspects are discussed and an initial attempt at defining the interdisciplinary couplings is summarized. At this writing, some significant progress has been made, principally in the areas of single discipline optimization. Results are given which represent accomplishments in rotor aerodynamic performance optimization for minimum hover horsepower, rotor dynamic optimization for vibration reduction, and rotor structural optimization for minimum weight

Integrated multidisciplinary design optimization of rotorcraft

The NASA/Army research plan for developing the logic elements for helicopter rotor design optimization by integrating appropriate disciplines and accounting for important interactions among the disciplines is discussed. The optimization formulation is described in terms of the objective function, design variables, and constraints. The analysis aspects are discussed, and an initial effort at defining the interdisciplinary coupling is summarized. Results are presented on the achievements made in the rotor dynamic optimization for vibration reduction, rotor structural optimization for minimum weight, and integrated aerodynamic load/dynamics optimization for minimum vibration and weight

Integrated multidisciplinary optimization of rotorcraft: A plan for development

This paper describes a joint NASA/Army initiative at the Langley Research Center to develop optimization procedures aimed at improving the rotor blade design process by integrating appropriate disciplines and accounting for important interactions among the disciplines. The paper describes the optimization formulation in terms of the objective function, design variables, and constraints. Additionally, some of the analysis aspects are discussed, validation strategies are described, and an initial attempt at defining the interdisciplinary couplings is summarized. At this writing, significant progress has been made, principally in the areas of single discipline optimization. Accomplishments are described in areas of rotor aerodynamic performance optimization for minimum hover horsepower, rotor dynamic optimization for vibration reduction, and rotor structural optimization for minimum weight

An initiative in multidisciplinary optimization of rotorcraft

Described is a joint NASA/Army initiative at the Langley Research Center to develop optimization procedures aimed at improving the rotor blade design process by integrating appropriate disciplines and accounting for important interactions among the disciplines. The activity is being guided by a Steering Committee made up of key NASA and Army researchers and managers. The committee, which has been named IRASC (Integrated Rotorcraft Analysis Steering Committee), has defined two principal foci for the activity: a white paper which sets forth the goals and plans of the effort; and a rotor design project which will validate the basic constituents, as well as the overall design methodology for multidisciplinary optimization. The paper describes the optimization formulation in terms of the objective function, design variables, and constraints. Additionally, some of the analysis aspects are discussed and an initial attempt at defining the interdisciplinary couplings is summarized. At this writing, some significant progress has been made, principally in the areas of single discipline optimization. Results are given which represent accomplishments in rotor aerodynamic performance optimization for minimum hover horsepower, rotor dynamic optimization for vibration reduction, and rotor structural optimization for minimum weight