On optimal harmonic synthesis from inaccurate spectral data

The problem of optimal recovery of derivatives of functions on the real line from inaccurate Fourier transforms of these functions on a finite interval is studied. Optimal recovery methods different in data handling procedures are constructed.     

Computing lattice sums for calculating the elastic moduli of bcc metals via cluster decomposition

The complete potential energy of a crystal $E\left( {\vec r_{ik} } \right)$ is presented in the form of an expansion in irreducible interactions in clusters containing pairs, triplets, and quadruplets of atoms, situated on A2 lattice sites. The full set of invariants $\left\{ {I_j \left( {\vec r_{ik} } \right)} \right\}$ , on which $\left\{ {I_j \left( {\vec r_{ik} } \right)} \right\}$ can depend is found. Vectors $\vec r_{ik}$ are presented in the form of an expansion of the base of a Brave lattice. This allows us to present $I_j \left( {\vec r_{ik} } \right)$ in the form of integers (lattice sums) multiplied by τ ^m , where τ is half of an elementary cell rib, and m = const is determined by the model. The sum of the Lenard-Jones potential and the potentials of tri- and tetra-atomic interactions was chosen as the model potential. Within this model, elastic moduli of the second and third order were calculated for crystals with A2-type structure.     

An invariant form of the potential energy function used to simulate properties of condensed matter

A relation for semiempirical and symmetrically conditioned relations between the potential energy of interaction for atomic triplets and radius vectors that connect atomic equilibrium positions in a crystal is revealed.     

NQR data on the activation energy of orientational defects in crystal lattice

The nuclear quadrupole spin-lattice relaxation related to the formation of orientational defects in crystals has been analyzed. The defects arise because of thermally activated reorientational motion of molecules and their fragments between the nonequivalent potential wells. These molecular reorientations are considered for double-and triple-well potentials, both periodic and bounded by external side walls. It was shown that, for such potentials, the temperature dependence of the relaxation time provides the data on the activation energy for transitions of molecules in the crystal lattice from the equilibrium ground-state positions to those corresponding to metastable states. We systematized the known NQR data on the activation energies for orientational defects arising in the intracrystal rotations of molecules and atomic groups possessing the imperfect two-, three-, and sixfold axial symmetries.     

Modeling of coating separation under thermomechanical loading in the beam approximation

The beam approximation is developed to solve some problems of fracture mechanics concerning the formation of separation of thin elastic coatings with allowance for the constraints acting on the connection boundaries and the influence of unsteady temperature actions.The separation end region is modeled by an elastic beam loaded by an external bending moment and by force factors from the connection with the base. This region is subjected to thermoelastic stresses caused by a sudden variation in the temperature of the surface or the adhesive layer. We estimate how the effective fracture strength of the adhesive joint varies for various modes of application of affecting factors, including variations in material properties with temperature and across the coating thickness; we also study buckling phenomena and the kinetics of local fracture processes in the end region. The results can be used when choosing the parameters of an adhesive joint so as to ensure a given effective adhesion fracture strength of the joint.     

Acoustic Wave Propagation Along Piezoelectric Plate Coated with Piezoelectric Films

Acoustical Physics - A novel solid state structure consisting of piezoelectric plate sandwiched between two piezoelectric films is suggested as propagation medium for acoustic waves. Considering,...     

A loss minimization problem

The optimal stopping problem is considered in the presence of random losses with decision making concerning non-recurrent involvement of an external financial-protection mechanism. The presence of an utility function determining the attitude of the decision-making person to a risk is taken into account. It is shown that, using the Bellman equation, optimal threshold functions can be constructed numerically and, for certain types of the utility function, such functions can even be constructed in an analytical form.     

Optimal recovery of functionals based on inaccurate data

Translated from Matematicheskie Zametki, Vol. 50, No. 6, pp. 85–93, December, 1991.