Comment on the calculation of forces for multibody interatomic potentials

The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for the force acting between a pair of particles are compared. The forces coincide only if the particles interact via pair or embedded-atom potentials. However in literature both definitions are used in order to determine Cauchy stress tensor. A simplest example of the linear pure shear of perfect square lattice is analyzed. It is shown that, Hardy's definition for the stress tensor gives different results depending on the radius of localization function. The differences strongly depend on the way of the force definition.Comment: 9 pages, 2 figure

Discrete breathers assist energy transfer to ac driven nonlinear chains

One-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in six-order polynomial on-site potentials is considered. Power of the energy source in the form of single ac driven particles is calculated numerically for different amplitudes $A$ and frequencies $\omega$ within the linear phonon band. The results for the on-site potentials with hard and soft nonlinearity types are compared. For the hard-type nonlinearity, it is shown that when the driving frequency is close to (far from) the {\em upper} edge of the phonon band, the power of the energy source normalized to $A^2$ increases (decreases) with increasing $A$. In contrast, for the soft-type nonlinearity, the normalized power of the energy source increases (decreases) with increasing $A$ when the driving frequency is close to (far from) the {\em lower} edge of the phonon band. Our further demonstrations indicate that, in the case of hard (soft) anharmonicity, the chain can support movable discrete breathers (DBs) with frequencies above (below) the phonon band. It is the energy source quasi-periodically emitting moving DBs in the regime with driving frequency close to the DBs frequency, that induces the increase of the power. Therefore, our results here support the mechanism that the moving DBs can assist energy transfer from the ac driven particle to the chain.Comment: 11 pages, 13 figure

MODEL OF PROVIDING WITH DEVELOPMENT STRATEGY FOR INFORMATION TECHNOLOGIES IN AN ORGANIZATION

Subject of research. The paper presents research and instructional tools for assessment of providing with the development strategy for information technologies in an organization. Method. The corresponding assessment model is developed which takes into consideration IT-processes equilibrium according to selected efficiency factors of information technologies application. Basic results. The model peculiarity resides in applying neuro-fuzzy approximators where the conclusion is drawn upon fuzzy logic, and membership functions are adjusted through the use of neural networks. For the adequacy testing of the suggested model, due diligence result analysis has been carried out for the IT-strategy executed in the “Navigator” group of companies at the stage of implementation and support of new technologies and production methods. Data visualization with a circle diagram is applied for the comparative evaluation of the analysis results. The chosen model adequacy is proved by the agreement between predictive assessments for IT-strategy performance targets derived by means of the fuzzy cognitive model over 12 months planning horizon and the real values of these targets upon the expiry of the given planning term. Practical significance. The developed model application gives the possibility to solve the problem of sustainability assessment for the process of providing the required IT-strategy realization level based upon the fuzzy cognitive map analysis and to reveal IT-objectives changing tendencies for an organization over the stated planning interval

Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chain

The effect of discrete breathers (DBs) on macroscopic properties of the Fermi-Pasta-Ulam chain with symmetric and asymmetric potentials is investigated. The total to kinetic energy ratio (related to specific heat), stress (related to thermal expansion), and Young's modulus are monitored during the development of modulational instability of the zone boundary mode. The instability results in the formation of chaotic DBs followed by the transition to thermal equilibrium when DBs disappear due to energy radiation in the form of small-amplitude phonons. It is found that DBs reduce the specific heat for all the considered chain parameters. They increase the thermal expansion when the potential is asymmetric and, as expected, thermal expansion is not observed in the case of symmetric potential. The Young's modulus in the presence of DBs is smaller than in thermal equilibrium for the symmetric potential and for the potential with a small asymmetry, but it is larger than in thermal equilibrium for the potential with greater asymmetry. Our results can be useful for setting experiments on the identification of DBs in crystals by measuring their macroscopic properties.Comment: 9 pages, 10 figures; v3: some changes in the text, references added; matches the published versio

Position-Sensitive Measurements of a Single-Mode Laser Beam Spot Using the Dividing Plate Method

New position-sensitive experimental results have been obtained using the Dividing Plates method to detect the displacement of a single-mode laser beam spot of various diameters. Measurements show that with this method it is possible to attain sensitivities down to 0.18 µm$^{–1}$ for a laser beam spot diameter of 8.8 µm displaced over 2.4 µm diameter zone, defined as the area where measurements non-linearities are within 1%. The achievable measurement accuracy is limited by ADC noise and corresponds to ±0.030 nm. Application of the Dividing Plates method for position-sensitive measurements allows to build a compact version of the Precision Laser Inclinometer, the Compact PLI, with reduced overall dimensions of 20 × 20 × 20 cm$^{3}$ and weight of approximatively 10 kg

Mathematical Modeling of the “Bone-Fixator” System during the Treatment of Intertrochanteric Fractures

Relevance — the need for an objective justification in choosing the type of fixation in the treatment patients with pertrochanteric hip fractures.Objective — to study the changes in the properties of a consolidating trochanteric fracture fixed by a dynamic cephalomedullary nail when subjected to cyclic dynamic loads.Materials and methods. A mathematical model was developed for trochanteric fracture of the femur (A1 according to AO classification) when fixed with a dynamic cephalomedullary nail. Then, the properties of the system were studied (pressure between fragments, mechanical stress in the bone and fixation device, displacement amplitude, neck-diaphysis angle) under a virtual load of a 80 kg body at various amount of insertion of the dynamic screw (from 10 mm to 0 mm).Results. In the process of shortening the femoral neck axis by 1 cm, the stability of the ‘bone-metal fixation device’ system increases, as indicated by a decrease in the maximum amplitude of displacements in the system under load by 16.8%, a decrease in the maximum stress in the fixation elements by 20.2%, a decrease in pressure at the site of contact of fragments by 19.8%. In addition, there was a decrease in the neck-diaphysis angle by 2.8%.Conclusion. The mathematical modeling of the ‘bone-metal fixation device’ system simulating conditions of dynamic osteosynthesis showed that there is a potential increase in the stability of the cephalomedullary system and that favorable conditions are created for the consolidation of the fracture when subjected to cyclic load of body mass