Devising a method for the formation of sustainable chains of supply of raw materials from mercantile exchange to a timber processing enterprise considering uncertainties and risks

The relevant problem of guaranteed supply of high-quality raw materials to a timber processing enterprise that does not have its own sources of raw materials is considered. A method for the formation of sustainable chains of supplying raw materials to a timber processing enterprise was proposed, taking into consideration uncertainties and risks associated with the purchase of raw materials on the mercantile exchange and the implementation of the circuit of delivery to a warehouse. A dynamic model, which is a problem of stochastic nonlinear programming, the objective function of which is the cost of purchasing raw materials, was developed. The model makes it possible to form a plan for purchasing raw materials on the timber section of the mercantile exchange on a given planning horizon, taking into consideration uncertainties when it comes to the number of daily offers, their volumes, and prices. The risk of cancellation of the concluded contract due to the loss of the quality of raw materials during delivery and non-fulfillment of delivery terms was also taken into consideration. To find a solution to the model, a two-stage circuit, in which the first stage involves a procurement plan that is close to optimal, was proposed. At the second stage, a plan that is closest to the basic one in terms of the volume of purchased raw materials and minimizing the total costs is chosen for each day of implementation of a random flow of applications. The numerical solution at the first stage is found using the heuristic algorithm that uses the branch and bound method and the genetic algorithm at certain steps. At the second stage, the multi-criteria problem of mathematical programming is solved numerically. An example of the formation by a timber processing enterprise in the Far East of a suboptimal procurement plan that ensures an increase in the efficiency and sustainability of economic activity in the long term is considered

Scale-invariant spins and tumbles in turbulence

A Lagrangian perspective has yielded many new insights in our quest to reveal the intricacies of turbulent flows. Much of this progress has been possible by following the trajectories of idealised, inertialess objects (tracers) traversing through the flow. Their spins and tumbles provide a glimpse into the underlying local velocity gradients of the turbulent field. While it is known that the spinning and tumbling rates of anisotropic particles are modified in turbulence – compared with those in a random flow field – a quantitative explanation for this has remained elusive. Now, Pujara et al. (J. Fluid Mech., vol. 922, 2021, R6) have made an attempt to predict the split between spinning and tumbling rates by accessing the particle's alignment with the local vorticity. Their analysis of filtered turbulent fields reveals a Lagrangian scale invariance, whereby key quantities relating to the particle's rotational statistics are preserved from the dissipative to the integral scale.

Elastic Turbulence: An Experimental View on Inertialess Random Flow

A viscous solvent laminar flow may be strongly modified by the addition of a tiny amount of long polymer molecules, resulting in a chaotic flow called elastic turbulence (ET). ET is attributed to polymer stretching, which generates elastic stress and its back reaction on the flow. Its properties are analogous to those observed in hydrodynamic turbulence, although the formal similarity does not imply a similarity in physical mechanisms underlining these two types of random motion. Here we review the statistical and spectral properties and the spatial structure of the velocity field, the statistical and spectral properties of pressure fluctuations, and scaling of the friction factor of ET in wall-bounded and unbounded flow geometries, as observed in experiments and numerical simulations and described by theory for a wide range of control parameters and polymer concentrations.

FORMULATION OF THE PROBLEM OF PLANNING AIRCRAFT ROUTES WHEN SERVICING A RANDOM FLOW OF APPLICATIONS ARRIVING IN FLIGHT

The work is about process of ground facilities servicing by aircrafts group when receiving requests during the flight. In case of manned aircraft, servicing of one request refers to the flight from the point to another one. As for unmanned aircrafts, it is necessary to observe reached destination point at the specified speed and flight altitude. It is assumed that the distance between the points and the moments of requests appearing ranked by the Poisson law. Necessary condition of successful task solving is that the average service speed of the requests flow exceeds the average speed of their receipt. It was found that taking into account the randomness of requests, three flight situations are possible – the “idle” mode in service when the requests number is less than the number of unoccupied aircraft, the regular mode when the balance of supply and demand and the “peak” mode when the requests number is increased and there is a queue in service.