Influence of the fixation region of a press-fit hip endoprosthesis on the stress-strain state of the "bone-implant" system.

Although significant progress has been made in the development of total hip replacement, behaviour of the femoral component of an endoprosthesis in relation to the type of its fixation in the bone is still not fully understood. In this paper, behaviour of the femoral bone and the stem prosthesis is studied taking into account different types of prosthesis fixation in the medullary canal of the femur under the action of functional loads. For an analysis, a three-dimensional model of a femur has been developed based on the results of a computed tomography. The stress-strain state governing behaviour of the femoral bone and the stem prosthesis has been estimated with the use of the finite element method (FEM). The FEM analysis has shown that for the diaphyseal fixation, the area of contact between the surface of the endoprosthesis and the bone is insufficient and leads to large stresses in the implant accompanied by stress concentration in the distal femur. An increase in the area of contact between the implant and the bone raises the stiffness of the "bone-implant" system, which, in turn, reduces stresses in the implant. The applied metaphyseal-type fixation yielded an improvement of results regarding behaviour of the femoral bone and the stem prosthesis. Namely, the study yielded the distribution of stress in the bone similar to the physiological stress state.

The role of dissipation in time-dependent non-integrable focusing billiards.

In this study, we compare the dynamical properties of chaotic and nearly integrable time-dependent focusing billiards with elastic and dissipative boundaries. We show that in the system without dissipation the average velocity of particles scales with the number of collisions as ̅V∝n(α). In the fully chaotic case, this scaling corresponds to a diffusion process with α≈1/2, whereas in the nearly integrable case, this dependence has a crossover; slow particles accelerate in a slow subdiffusive manner with α<1/2, while acceleration of fast particles is much stronger and their average velocity grows super-diffusively, i.e., α>1/2. Assuming ̅V∝n(α) for a non-dissipative system, we obtain that in its dissipative counterpart the average velocity approaches to ̅V(fin)∝1/δ(α), where δ is the damping coefficient. So that ̅V(fin)∝√1/δ in the fully chaotic billiards, and the characteristics exponents α changes with δ from α(1)>1/2 to α(2)<1/2 in the nearly integrable systems. We conjecture that in the limit of moderate dissipation the chaotic time-depended billiards can accelerate the particles more efficiently. By contrast, in the limit of small dissipations, the nearly integrable billiards can become the most efficient accelerator. Furthermore, due to the presence of attractors in this system, the particles trajectories will be focused in narrow beams with a discrete velocity spectrum.

Fermi acceleration and scaling properties of a time dependent oval billiard.

We consider the phenomenon of Fermi acceleration for a classical particle inside an area with a closed boundary of oval shape. The boundary is considered to be periodically time varying and collisions of the particle with the boundary are assumed to be elastic. It is shown that the breathing geometry causes the particle to experience Fermi acceleration with a growing exponent rather smaller as compared to the no breathing case. Some dynamical properties of the particle's velocity are discussed in the framework of scaling analysis.

Hidden chromosome symmetry: in silico transformation reveals symmetry in 2D DNA walk trajectories of 671 chromosomes.

Maps of 2D DNA walk of 671 examined chromosomes show composition complexity change from symmetrical half-turn in bacteria to pseudo-random trajectories in archaea, fungi and humans. In silico transformation of gene order and strand position returns most of the analyzed chromosomes to a symmetrical bacterial-like state with one transition point. The transformed chromosomal sequences also reveal remarkable segmental compositional symmetry between regions from different strands located equidistantly from the transition point. Despite extensive chromosome rearrangement the relation of gene numbers on opposite strands for chromosomes of different taxa varies in narrow limits around unity with Pearson coefficient r = 0.98. Similar relation is observed for total genes' length (r = 0.86) and cumulative GC (r = 0.95) and AT (r = 0.97) skews. This is also true for human coding sequences (CDS), which comprise only several percent of the entire chromosome length. We found that frequency distributions of the length of gene clusters, continuously located on the same strand, have close values for both strands. Eukaryotic gene distribution is believed to be non-random. Contribution of different subsystems to the noted symmetries and distributions, and evolutionary aspects of symmetry are discussed.

Chromosome evolution with naked eye: palindromic context of the life origin.

Based on the representation of the DNA sequence as a two-dimensional (2D) plane walk, we consider the problem of identification and comparison of functional and structural organizations of chromosomes of different organisms. According to the characteristic design of 2D walks we identify telomere sites, palindromes of various sizes and complexity, areas of ribosomal RNA, transposons, as well as diverse satellite sequences. As an interesting result of the application of the 2D walk method, a new duplicated gigantic palindrome in the X human chromosome is detected. A schematic mechanism leading to the formation of such a duplicated palindrome is proposed. Analysis of a large number of the different genomes shows that some chromosomes (or their fragments) of various species appear as imperfect gigantic palindromes, which are disintegrated by many inversions and the mutation drift on different scales. A spread occurrence of these types of sequences in the numerous chromosomes allows us to develop a new insight of some accepted points of the genome evolution in the prebiotic phase.

May chaos always be suppressed by parametric perturbations?

The problem of chaos suppression by parametric perturbations is considered. Despite the widespread opinion that chaotic behavior may be stabilized by perturbations of any system parameter, we construct a counterexample showing that this is not necessarily the case. In general, chaos suppression means that parametric perturbations should be applied within a set of parameters at which the system has a positive maximal Lyapunov exponent. Analyzing the known Duffing-Holmes model by a Melnikov method, we showed that chaotic dynamics cannot be suppressed by harmonic perturbations of a certain parameter, independently from the other parameter values. Thus, to stabilize the behavior of chaotic systems, the perturbation and parameters should be carefully chosen.

Control of dynamical systems behavior by parametric perturbations: An analytic approach.

The problem of parametric suppression of deterministic chaos is considered. It is proved that certain parametric perturbations of a one-dimensional map with chaotic dynamics can lead to a transition of that map into a regime of regular behavior.