Visualizing {110} Surface Structure of Equilibrium-form ZIF-8 Crystals by Low-dose Cs-corrected TEM

The properties of Zeolitic imidazolate frameworks (ZIFs) crystals highly depend on the structures of the low-energy surfaces, such as {110} of ZIF-8. However, the atomic/molecular configurations of the ZIF-8 {110}...

Again About the "Magmatic" Nature of Topaz Crystals From Chamber Pegmatites of Volyn (Ukrainian Shield)

Various aspects of the genesis of primary fluid inclusions (0.01-1.0 sometimes up to 2 mm) with a large number of mineral inclusions in topaz crystals from chamber pegmatites of Volyn were analyzed. The data could be interpreted in two fundamentally different ways. The first argues for crystals grown in a magmatic melt; the second for an aqueous solution, with a density close to critical. The essence of the discrepancy is the reliability of the identification of the nature of mineral phases in the primary inclusions, if they are crystals captured during growth (xenogenic) or daughter crystals from the fluid. The xenogenic origin of the phases is indicated by the following observations: 1) The location of the mineral inclusions on the growing faces of the topaz crystals depends on the orientation of the crystal’s axis [001] relative to the horizontal plane. It determines the faces on which small mineral phases could be deposited from an aqueous suspension during the growth of topaz crystals. The studied crystals are dominated by individuals in which the mineral inclusions are located on the growing faces {011}, {021}, (001) (and others) of the crystal head. During growth, they were approximately in an upright position. 2) The filling of primary fluid inclusions is not constant. The volume of mineral phases in the inclusions varies from 40 to 95%, often 70-75%, the rest of the volume is gas and aqueous solution. Liquid-gas (liquids ˂ 40%) inclusions without or with < 5% solid phases are very rare. In addition, the ratio between the volumes of different mineral phases in the inclusions is not constant. 3) Light rims (Becke lines) around the inclusions record a change in the refractive indices (caused by a different chemical composition) of topaz when inclusions are acquiring the equilibrium form of the negative crystal. 4) The xenogenic nature of the mineral phases of the primary fluid inclusions in topaz is indirectly confirmed by the value of the fluid pressure (260-300 MPa)of the magmatic melt (determined by the method of homogenization of these inclusions), as it denies the possibility of chamber pegmatite formation at depths of 9-11 km. Thus, the peculiar mineral inclusions were deposited on the face of growing topaz crystals of small mineral phases from a turbid aqueous suspension, which boiled violently. We conclude that topaz crystals in chamber pegmatites of Volyn grew in aqueous solution at a temperature of 380-415ºС and a pressure of 30-40 MPa.

COMPRESSED ELEMENTS WITH A VARIABLE IN LENGTH STIFFNESS EQUILIBRIUM FORM STABILITY DETERMINATION

One of the most powerful modern methods of calculating complex building structures is the finite element method in theform of a displacement method for discrete systems, which involves the creation of a finite element model, that is, splittingthe structure into separate elements within each of which the functions of displacements and stresses are known. On the basisof the displacement method and the methods of iterations and half-division, an algorithm for stability calculation of the firstkind equilibrium form of compressed reinforced concrete columns with hinged fixing at the ends, considering the stiffnesschanging has been developed. The use of the above methods enables to determine the minimum critical load or stress at thefirst bifurcation and their stability loss corresponding form. The use of matrix forms contributes to simplification of high order stability loss equation. This approach enables to obtain the form of stability loss that corresponds to the critical load.

Rapid response of New England (USA) rivers to shifting boundary conditions: Processes, time frames, and pathways to post-flood channel equilibrium

The time scale of channel recovery from disturbances indicates fluvial resiliency. Quantitative predictions of channel recovery are hampered by multiple possible recovery pathways and stable states and limited long-term observations that provide benchmarks for testing proposed metrics. We take advantage of annual channel-change measurements following Tropical Storm Irene’s 2011 landfall in New England (eastern USA) to document geomorphic recovery processes and pathways toward equilibrium. A covariate metric demonstrates that channels can adjust rapidly to ongoing boundary condition shifts, but that they adjust along a continuum of possible stable states. Moreover, the covariate equilibrium metric indicates sensitivity to warm-season high discharges that, in this region, are increasing in frequency. These data also show that the channels are resilient in that they are able to recover an equilibrium form within 1–2 yr of disturbances.

Duplex selections, equilibrium points, and viability tubes

Existence of viable trajectories to nonautonomous differential inclusions are proven for time-dependent viability tubes. In the convex case we prove a double-selection theorem and a new Scorza-Dragoni type lemma. Our result also provides a new and palpable proof for the equilibrium form of Kakutani’s fixed point theorem.

Calculation of The Stability of the Form of Equilibrium of Discrete Systems

The paper presents an algorithm for calculating the stability of the equilibrium form of the first kind of compressed discrete systems by the displacements method in combination with the methods of iterations and bisection. The use of the methods makes it possible to effectively determine the minimum critical stress or strain at the first bifurcation and their corresponding form of stability loss, both for statically determined and statically undetermined systems. This approach, using matrix forms, makes it possible to significantly simplify the calculations of the analytical condition for the stability loss of compressed discrete systems (the stability loss equation), which has high orders, as well as to construct the form of stability loss corresponding to a critical load, that is, to solve the problem of loss of equilibrium stability. The calculation actually leads to solving a nonlinear transcendental equation, which is the equation of stability loss. The difficulty lies in the absence of an analytical solution of such an equation due to the presence of complex of Zhukovsky functions, which have transcendental functions in their structure. Such solution can be performed only with the use of numerical methods. This algorithm for calculating the loss of equilibrium of the first kind of compressed discrete systems by displacement in combination with the methods of iteration and bisection is implemented in the software complex "Persist" for PC in Windows OS. The program was approbated and implemented in the educational process at the Department of Structural and Theoretical Mechanics of Poltava National Technical Yuri Kondratyuk University during the training of specialists in engineering specialties.

Anisotropic compact stars in non-conservative theory of gravity

We develop anisotropic compact stars in the scenario of non-conservative theory such as Rastall theory. We consider the Krori and Barua static spherically symmetric metrics and find their unknown constants by using the masses and radii of well-known compact stars. We investigate the anisotropic compact star through various physical quantities such as anisotropic behavior, regularity conditions, stability and surface redshift. It is found that the present compact stars are stable and are in the stellar equilibrium form.

Form-finding of free-form tensegrity structures by genetic algorithm–based total potential energy minimization

Free-form tensegrities are composed of randomly connected cable and strut elements. The complexity of these structures causes determination of their self-equilibrium form to be a formidable task. There can be an infinite number of solutions with different forms, but it is difficult to identify the best form in terms of stability. Based on the fact that stability of structures is inversely proportional to potential energy, a genetic algorithm minimization process is developed to determine the self-equilibrium form of free-form regular tensegrity structures. The capability of the form-finding process on determination of the most stable form with minimum potential energy is investigated using two main parameters of free-form regular tensegrities which are cable–strut length ratio at rest and number of strut elements. The computational performance of the proposed method is also tested using free-form tensegrities with different number of structural elements.