Critical Phenomena in Cracking of the Interface Between Two Prestressed Materials. 2. Exact Solution. The Case of Unequal Roots

Study is made of critical phenomena accompanying the cracking of the interface between two different materials with initial stresses. The basic relations and complex potentials for a plane problem of the three-dimensional linearized dynamic theory of elasticity are used. The exact solution is obtained for the case of unequal roots (complex parameters). The basic mechanical effects are analyzed.     

Pure operations and the covering law

The paper is devoted to the study of properties of pure operations. The main results are: Axiomatic characterization of pure operations consisting in a precise formulation of their basic properties and the representation theorem, which shows that pure operations possessing these (axiomatically defined) properties and satisfying the so-called Compatibility Postulate are in fact the usual ones, of special kind, defined by the well-known formula. The other main result of the paper is the justification of the covering law in the logic of propositions, which is shown here to follow from the Compatibility Postulate, the latter being of direct physical significance.     

Diffusion of Oligonucleotides from within Iron‐Cross‐Linked,Polyelectrolyte‐Modified Alginate Beads: A Model System for Drug Release

An analytical model to describe diffusion of oligonucleotides from stable hydrogel beads is developed and experimentally verified. The synthesized alginate beads are Fe³⁺‐cross‐linked and polyelectrolyte‐doped for uniformity and stability at physiological pH. Data on diffusion of oligonucleotides from inside the beads provide physical insights into the volume nature of the immobilization of a fraction of oligonucleotides due to polyelectrolyte cross‐linking, that is, the absence of a surface‐layer barrier in this case. Furthermore, the results suggest a new simple approach to measuring the diffusion coefficient of mobile oligonucleotide molecules inside hydrogels. The considered alginate beads provide a model for a well‐defined component in drug‐release systems and for the oligonucleotide‐release transduction steps in drug‐delivering and biocomputing applications. This is illustrated by destabilizing the beads with citrate, which induces full oligonucleotide release with nondiffusional kinetics.     

Establishing foundations of the mechanics of nanocomposites (Review)

A general idea of the mechanics of nanocomposites that allows formulating a system of approaches and methods of analysis in this area is given. The place of mechanics in materials research and the structural levels that divide mechanics into macromechanics, mesomechanics, micromechanics, and nanomechanics are discussed. A brief historical sketch of the nanomaterial technology is presented. Examples of different nanotechnologies and nanomaterials are given. Typical nanomaterials and their properties are described. Matrices and reinforcements of nanocomposite materials as well as their properties are considered separately. A classification of nanocomposites is proposed. Special attention is given to modeling in the structural mechanics of nanocomposites, the principles of continualization and homogenization, edge and near-surface effects, validity limits of the continuum approach, and two-sided estimates. A discussion is given of two basic models within the framework of the basic approach as a set of concepts, models, and problem statements and of the development of methods adequately describing mechanical phenomena in nanocomposites. The presented material is mainly taken from the book A. N. Guz, J. J. Rushchitsky, and I. A. Guz, Introduction to the Mechanics of Nanocomposites [in Russian], S. P. Timoshenko Inst. Mech., Kyiv (2010)     

Brownian motion in a solitary potential well in a bounded solid structure

The motion of a heavy Brownian particle in a low-dimensional bounded solid structure under the effect of a phonon’s excitation fluctuations is considered. Because of the finiteness of the system, the fluctuation spectrum has zero spectral density at zero frequency. The effect of this kind of noise, which is conditionally called “green” noise, is studied both analytically by using the averaging method and numerically on the basis of predictor-corrector algorithms. The effective potential is introduced, and its form is shown to govern the particle dynamics. Considering a Gaussian potential well (a trap) as an example, it is demonstrated that green noise leads to abrupt phase transitions in the system as a result of very small parameter variations (a catastrophe-type effect). The results are compared with the case of white noise in an unbounded structure. From numerical calculations, it follows that the boundedness of the structure, which changes the noise spectrum, favors a considerable increase in the lifetime of the particle in the trap.     

Dynamics of a rigid cylinder near a plane boundary in the radiation field of an acoustic wave

An approach is described for investigation of the interaction between a rigid body and a viscous fluid boundary under acoustic wave propagation. The influence of the liquid on the rigid body is determined as a mean force, which is a constant in the time component of the hydrodynamic force. This enables the use of a previously developed technique for calculation of pressure in a compressible viscous liquid. The technique takes into account the second-order terms with respect to the wave field parameters and is based on investigation of a system of initially nonlinear hydromechanics equations that can be simplified with respect to the wave motion parameters of the liquid. It has proven possible to retain the second-order terms for determination of stresses in the liquid without having to solve the system of nonlinear equations. The stresses can be expressed in terms of parameters found in the solution of the linearized equations of the compressible viscous liquid. In this way, the solution of linearized equations is expressed in terms of a scalar and vector potentials. The problem statement is derived for a rigid cylinder located near a rigid flat wall under the effects of a wave propagating perpendicular to the wall. The solution for this particular example is obtained.