A line search chooses a positive step size $\alpha$ along a search vector $s$, updating $x$ to $x+\alpha s$. For a differentiable function $f$, a descent direction makes sufficiently short steps decrease the objective function; an Armijo condition quantifies the decrease, while the Wolfe conditions also prevent accepting an unnecessarily short step.

A provisioned dung mass surrounding the developmental site of an individual dung-beetle offspring. Its food quantity and maternal contributions can be manipulated separately.

Heinrich Kirchauer authored a dissertation treatment of photolithography that explains photoresist contrast through the exposure-response curve. The account relates photoresist thickness after development to exposure dose, separating the onset of clearing from complete removal. This makes contrast a measurable process characteristic rather than simply visual darkness.^[ref]

Margaret J. Sobkowicz is the first-listed author of Controlled dispersion of carbon nanospheres through surface functionalization by Margaret J. Sobkowicz and others. The study changes the surface chemistry of carbon nanospheres to control their dispersion. It gives a concrete example of how the interface between a particle and its surroundings can determine material processing behaviour.^[ref]

Hans J. Queisser coauthored Detailed Balance Limit of Efficiency of p-n Junction Solar Cells by William Shockley and Hans J. Queisser. The analysis balances photon absorption and radiative emission to constrain the efficiency of an idealized single-junction solar cell. The result is an upper limit under stated optical and recombination assumptions, so a comparison with a real solar cell must identify which assumptions apply.^[ref]

Bed Poudel is the first-listed author of High-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys by Bed Poudel and others. The work connects nanostructure and phonon scattering at grain boundaries and defects to reduced thermal conductivity. This provides an experimental example of improving performance measured by the thermoelectric figure of merit by changing the microstructure of a bulk material.^[ref]

Yanzhong Pei is the first-listed author of Convergence of electronic bands for high performance bulk thermoelectrics by Yanzhong Pei and others. The study uses convergence of electronic bands in lead telluride-based alloys to improve performance measured by the thermoelectric figure of merit. It illustrates how electronic structure can be engineered alongside heat transport when optimizing the thermoelectric figure of merit.^[ref]

Frederick Charles Frank helped develop the theory of dislocations and crystal growth. A dislocation can influence how new atomic layers form at a crystal surface, linking a defect inside a solid to its growth behaviour. The University of Bristol's history identifies these fields, together with surface physics, as major parts of his work.^[ref]

Frank Nabarro developed the theory of dislocations and their role in plastic deformation. His work connected microscopic defects to macroscopic resistance to deformation, and his monograph Theory of Crystal Dislocations helped organize the subject. A scientific obituary by a colleague describes both the theoretical contributions and his long influence on materials science.^[ref]

Erich Schmid studied the plastic deformation of single crystals, connecting applied loading to the resolved shear stress acting on a slip system. Schmid's law expresses the geometric projection that underlies this connection. The University of Vienna's account of his scientific work describes his research on crystal deformation and his jointly authored treatment of crystal plasticity.^[ref]

Michael Ashby develops methods for material selection in engineering design. Materials selection charts compare properties across families of materials, while material performance index values express what a particular design objective rewards. This connects a choice of material to a component's function and constraints, such as low mass with adequate stiffness. His institutional profile identifies materials and design as central themes of his work.^[ref]

Egon Orowan developed the dislocation account of plastic deformation in crystals. Motion of a dislocation permits successive local rearrangements instead of simultaneous sliding of an entire atomic plane, helping explain why measured strengths can be much lower than ideal-crystal estimates. The National Academy memoir traces his 1934 contribution and later work on deformation and failure.^[ref]

The course examples connect material performance index values to materials selection charts; the shaft and flywheel examples identify carbon-fibre-reinforced polymers among candidates with high specific strength. Their numerical properties concern specified examples and should not be treated as universal beam compression allowables.

Nature 216, 575–576. The opening description identifies Dounreay-irradiated type316 specimens and thin-foil electron microscopy.

Atomistic construction and relaxation of several loop types in zirconium, examining orientation, energy and shape.

Journal of Nuclear Materials 47, 187–197. The abstract describes autoradiographs of RAPSODIE-irradiated pins and effects of thermal diffusion, evaporation–condensation and oxygen chemistry.

NRC discussion of high-burnup fuel damage and the established peak-cladding-temperature and oxidation criteria.

Program announcement describing development of doped oxide, silicide and alternative cladding concepts with work planned through 2021.

Nature 211, pp.291–292. The accessible abstract discusses reduced high-temperature ductility, thin-foil observations of bubbles and a helium embrittlement mechanism involving grain boundaries. The abstract was inspected; the subscription-only full article was not required for the stated claim.

An official technical note explaining Charpy impact test transition curves. Section2 describes absorbed energy, lateral expansion and fracture-appearance measures of the ductile-to-brittle transition.