In the theory of elasticity, the constraint of compatibility conditions on displacement field is not equivalent to the property of displacement field. The difference may broaden the possibility of solutions to elasticity problems, which means that the solution methods involved in solving the compatibility equations like stress-based solution method and stress function method may be invalid. The study argues the validity of the solution methods involved in solving the compatibility equations. It is concluded that the absence of constraints on local rigid body rotation causes the non-uniqueness of displacement fields for a rectangular beam purely bent and a cantilever loaded at the end.
Can a filament transmit the curvatures across the constituting modules and control them at one of its end? Inspired by the observation of protofilament - constituent biopolymer of microtubule - this question is addressed by a constructive approach. In our model a simple allosteric element in each module couples with the neighboring modules at its interfaces, which gives rise to a single degree of freedom to control the global shape of the filament. The model can be analyzed in analogy with discrete-time dynamical systems having a bifurcation of trans-critical type.
The biochemical, biophysical, and physiological properties of the PsbS protein were studied in relation to mutations of two symmetry-related, lumen-exposed glutamate residues, Glu-122 and Glu-226. These two glutamates are targets for protonation during lumen acidification in excess light. Mutation of PsbS did not affect xanthophyll cycle pigment conversion or pool size. Plants containing PsbS mutations of both glutamates did not have any rapidly inducible nonphotochemical quenching (qE) and had similar chlorophyll fluorescence lifetime components as npq4-1, a psbS deletion mutant. The double mutant also lacked a characteristic leaf absorbance change at 535 nm (ΔA535), and PsbS from these plants did not bind dicyclohexylcarbodiimide (DCCD), a known inhibitor of qE. Mutation of only one of the glutamates had intermediate effects on qE, chlorophyll fluorescence lifetime component amplitudes, DCCD binding, and ΔA535. Little if any differences were observed comparing the two single mutants, suggesting that the glutamates are chemically and functionally equivalent. Based on these results a bifacial model for the functional interaction of PsbS with photosystem II is proposed. Furthermore, based on the extent of qE inhibition in the mutants, photochemical and nonphotochemical quenching processes of photosystem II were associated with distinct chlorophyll fluorescence life-time distribution components.
The Ingenuity helicopter test flights on Mars in April 2021 marked the first time a powered aircraft has flown on another world. Students who have access to model helicopters and drones may wonder, how well could those hover on the Red Planet? The answer can be found in this journal [The Physics Teacher], using appropriate scaling of the surface gravity and atmospheric density to Martian values.
We first demonstrate how our general intuition of pseudoforces has to navigate around several pitfalls in rotating frames. And then, we proceed to develop an intuitive understanding of the different components of the pseudoforces in most general accelerating (rotating and translating) frames: we show that it is not just a sum of the contributions coming from translation and rotation separately, but there is yet another component that is a more complicated combination of the two. Finally, we demonstrate using a simple example, how these dynamical equations can be used in such frames.
Helicity plays a unique role as an integral invariant of a dynamical system. In this paper, the concept of helicity in the general setting of Hamiltonian dynamics is discussed. It is shown, through examples, how the conservation of overall helicity can imply a bound on other quantities of the motion in a nontrivial way.