A methodology for the formulation of water retention models in deformable soils

This paper presents a novel approach to soil–water retention modelling that is based on the analysis of the material pore network. The approach postulates the existence of a differential coupling function, which relates the variation of water ratio to the variation of void ratio at constant suction. Distinct differential coupling functions have been considered, and the most general option has been integrated in a closed-form relationship between water ratio and void ratio with a suction-dependent integration constant, whose expression describes the isochoric retention behaviour. Four alternative expressions of the suction-dependent integration constant have been proposed resulting in four different, but equivalent, models linking degree of saturation, void ratio and suction. Each model predicts the variation of degree of saturation by means of four parameters, namely two parameters accounting for the effect of void ratio and two parameters accounting for the effect of suction. The models have been calibrated against laboratory data from soils with distinct particle size distributions and have shown accurate predictions of degree of saturation at different levels of suction and void ratio. Validation against additional data has also indicated that the models can extrapolate the soil behaviour to stress paths and suction levels beyond those considered during calibration.

DESIGN OF A CONTROLLER FOR IDEAL POSITIONING SERVOSYSTEM

Urgency of the research. In advanced mechatronics, motion systems are the key technology, since mechanical systems such as Microelectronics manufacturing equipments are often required for high speed and accuracy. As a result, the increasing influence of the dynamics of the mechanical system on the quality of the position servosystem is noticeable. One of the important dynamic effects is the dynamics of the mechatronic system's vibroisolation, which arises as a result of the reaction force generated by the action variable. Target setting. The aim of the paper was to design a PID controller for an ideal positioning servosystem. Ideal positioning servosystem consists of a one mass which is actuated by the Fservo force. Actual scientific researches and issues analysis. In modern controllers, in the correction error value, classic feedback combines with forwarding feedback. The forward control is based on the fact that if the model of the mechanical actuator is known and all the initial conditions are zero, the desired position can be reached without the use of feedback. Uninvestigated parts of general matters defining. From a theoretical point of view, it has been devoted to ideal positioning servosystem for quite a long time, but the results achieved are rarely used in practice. One of the reasons is their theoretical focus, using complex mathematics, and as a result there is a great gap between theory and engineering practice. The research objective. Design of PID controller is based on equation for crossover frequencies, which allows to determine the derivative and integration constant of a PID controller for a given bandwidth. The statement of basic materials. The most important dynamic effects that impact the properties of actuators are actuator flexibility, flexibility of system limited mass and rigidity of the stationary part of the system. From the equation for the eigenfrequency ωDP of the low-pass second order filter is determined. Finally, the specific gain P is determined to suit the amplitude and phase margin. This completes the design of the ideal positioning servosystem. Conclusions. PID controller for an ideal positioning servosystem is design based on equation for crossover frequencies, which allows to determine the derivative and integration constant of a PID controller for a given bandwidth.

Static spherically symmetric solutions in a subclass of Horndeski theories of gravity

In this paper, we will consider a subclass of models of Horndeski theories of gravity and we will check for several Static Spherically Symmetric solutions. We will find a model which admits an exact black hole (BH) solution and we will study its thermodynamics by using the Euclidean Action. We will see that, in analogy with the case of General Relativity (GR), the integration constant of the solution can be identified with the mass of the BH itself. Other solutions will be discussed, by posing special attention on the possibility of reproducing the observed profiles of the rotation curves of galaxies. a

Riccati Parametric Deformations of the Cornu Spiral

In this article, a parametric deformation of the Cornu spiral is introduced. The parameter is an integration constant which appears in the general solution of the Riccati equation and is related to the Fresnel integrals. The Argand plots of the deformed spirals are presented and a supersymmetric (Darboux) structure of the deformation is revealed through the factorization approach.

Large Deflection of Prismatic Cantilever Beam Exposed to Combination of End Inclined Force and Tip Moment

The large deflection of a prismatic Euler-Bernoulli cantilever beam under a combination of end-concentrated coplanar inclined force and tip-concentrated moment is investigated. The angle of inclination of the applied force with respect to the horizontal axis remains unchanged during deformation. The cantilever beam is assumed to be naturally straight, slender, inextensible and elastic. The large deflection of the cantilever beam induces geometrical nonlinearity; hence, the nonlinear theory of bending and the exact expression of curvature are used. Based on an elliptic integral formulation, an accurate numerical solution is obtained in terms of an integration constant that should satisfy the boundary conditions associated with the cantilever beam. For some special cases this integration constant is exactly found, which leads to closed form solution. The numerical solution obtained is quite simple, accurate and involves less computational time compared with other techniques available in literature. The details of elastica and its corresponding orientation curves are presented and analyzed for extremely large load combinations. A comparative study with pre-obtained results has been made to verify the accuracy of the presented solution; an excellent agreement has been obtained.

The atoms of space, gravity and the cosmological constant

I describe an approach which connects classical gravity with the quantum microstructure of spacetime. The field equations arise from maximizing the density of states of matter plus geometry. The former is identified using the thermodynamics of null surfaces while the latter arises due to the existence of a zero-point length in the spacetime. The resulting field equations remain invariant when a constant is added to the matter Lagrangian, which is a symmetry of the matter sector. Therefore, the cosmological constant arises as an integration constant. A nonzero value [Formula: see text] of the cosmological constant renders the amount of cosmic information [Formula: see text] accessible to an eternal observer finite and hence is directly related to it. This relation allows us to determine the numerical value of [Formula: see text] from the quantum structure of spacetime.

Study and Application of Integrated Online Check of the Counties

In order to make the relay protection setting value online checking work more scientific and perfect, this paper studies the integration of county of relay protection setting value online verification scheme based on. Firstly, the county to achieve the integration constant value on-line check the general introduction, focuses on the display data acquisition and the checking calculation; then the county integration interface setting strategy of online check, describes the intelligent interface of intelligent don't know County, interface verification principle and interface design check the principle of selection; finally summing junction surface setting technique of on-line verification.