New design parameters for biparabolic beach profiles (SW Cadiz, Spain)

165 profiles of seventy-one beaches along the Gulf of Cadiz (SW, Spain) were studied to improve the formulation of the beach profile in tidal seas. Maritime climate, degree of energy exposure and size of the sand grains were taken into account to study the two sections of the biparabolic profile. The objective of the study was the determination of more accurate formulations of the design parameters for the equilibrium profile that involves tidal seas. These formulations were modelled and validated based on existing profiles to quantify the error existing between the real profile and the modelling. This comparative analysis was extended by considering the formulations proposed by other authors. The best results were obtained with the proposal presented herein

Meander Graphs and Frobenius Seaweed Lie Algebras II

We provide a recursive classification of meander graphs, showing that each meander is identified by a unique sequence of fundamental graph theoretic moves. This sequence is called the meander’s signature and can be used to construct arbitrarily large sets of meanders, Frobenius or otherwise, of any size and configuration. In certain special cases, the signature is used to produce an explicit formula for the index of seaweed Lie subalgebra of sl(n) in terms of elementary functions

Well-posed results for nonlocal biparabolic equation with linear and nonlinear source terms

In this paper, we consider the biparabolic problem under nonlocal conditions with both linear and nonlinear source terms. We derive the regularity property of the mild solution for the linear source term while we apply the Banach fixed-point theorem to study the existence and uniqueness of the mild solution for the nonlinear source term. In both cases, we show that the mild solution of our problem converges to the solution of an initial value problem as the parameter epsilon tends to zero. The novelty in our study can be considered as one of the first results on biparabolic equations with nonlocal conditions.This research was funded by the National Research Foundation of Korea under grant number NRF-2020K1A3A1A05101625 and the support from Institute of Construction and Environmental Engineering at Seoul National University

Mechanism of Breathing Transitions in Metal–Organic Frameworks

International audienceWe present a multiscale physical mechanism and a stochastic model of breathing transitions, which represent adsorption-induced structural transformations between large-pore and narrow-pore conformations in bistable metal–organic frameworks, such as MIL-53. We show that due to interplay between host framework elasticity and guest molecule adsorption, these transformations on the level of the crystal occur via layer-by-layer shear. We construct a simple Hamiltonian that describes the physics of host–host and host–guest interactions and show that a respective Monte Carlo simulation model qualitatively reproduces the experimentally observed features of breathing transitions

Analytical investigations in aircraft and spacecraft trajectory optimization and optimal guidance

A collection of analytical studies is presented related to unconstrained and constrained aircraft (a/c) energy-state modeling and to spacecraft (s/c) motion under continuous thrust. With regard to a/c unconstrained energy-state modeling, the physical origin of the singular perturbation parameter that accounts for the observed 2-time-scale behavior of a/c during energy climbs is identified and explained. With regard to the constrained energy-state modeling, optimal control problems are studied involving active state-variable inequality constraints. Departing from the practical deficiencies of the control programs for such problems that result from the traditional formulations, a complete reformulation is proposed for these problems which, in contrast to the old formulation, will presumably lead to practically useful controllers that can track an inequality constraint boundary asymptotically, and even in the presence of 2-sided perturbations about it. Finally, with regard to s/c motion under continuous thrust, a thrust program is proposed for which the equations of 2-dimensional motion of a space vehicle in orbit, viewed as a point mass, afford an exact analytic solution. The thrust program arises under the assumption of tangential thrust from the costate system corresponding to minimum-fuel, power-limited, coplanar transfers between two arbitrary conics. The thrust program can be used not only with power-limited propulsion systems, but also with any propulsion system capable of generating continuous thrust of controllable magnitude, and, for propulsion types and classes of transfers for which it is sufficiently optimal the results of this report suggest a method of maneuvering during planetocentric or heliocentric orbital operations, requiring a minimum amount of computation; thus uniquely suitable for real-time feedback guidance implementations