Mean square stabilisation of complex oscillatory regimes in nonlinear stochastic systems

A problem of stabilisation of the randomly forced periodic and quasiperiodic modes for nonlinear dynamic systems is considered. For this problem solution, we propose a new theoretical approach to consider these modes as invariant manifolds of the stochastic differential equations with control. The aim of the control is to provide the exponential mean square (EMS) stability for these manifolds. A general method of the stabilisation based on the algebraic criterion of the EMS-stability is elaborated. A constructive technique for the design of the feedback regulators stabilising various types of oscillatory regimes is proposed. A detailed parametric analysis of the problem of the stabilisation for stochastically forced periodic and quasiperiodic modes is given. An illustrative example of stochastic Hopf system is included to demonstrate the effectiveness of the proposed technique.     

On the Road to Personalized Medicine: Multiscale Computational Modeling of Bone Tissue

Personalized medicine is an emerging field, considered by many in the biomedical community to be among the upcoming approaches to medical treatment. To embrace this new challenge, physicians need a better understanding of the biological processes in the human body, as well as precise diagnostic tools and patient-specific treatments. In response, the last three decades have witnessed a major shift in tissue engineering development, from treating bone tissue at the macro-scale level only to treating it at complex multiscale levels. Researchers have begun striving for a better understanding of bone structure and mechanics, and then applying this knowledge in designing new medical treatments and procedures. Today computational methods, including finite element analyses, are the tool of choice for biomechanical research of bone tissues. Moreover, bone multiscale modeling can become a vital part of a comprehensive computerized diagnostic system for patient-specific treatment of metabolic bone diseases, fractures and bone cancer. This review paper describes the state of the art in multiscale computational methods used in analyzing bone tissue. The discussed methods and techniques can serve as a base for the creation of such an envisioned diagnostic system.     

Catalytic Oxidation of Thiol Compounds by Novel Fuel Cell-inspired Co-Porphyrin and Co-Imidazole Catalysts

The catalytic performance of pyrolyzed carbon-supported cobalt-nitrogen donor (CoN₄) catalysts for the oxidation of thiol compounds by dioxygen in aqueous solution was studied. This paper continues our previous line of research, which was inspired by the electrocatalytic reduction of oxygen on pyrolyzed carbon-supported cobalt-porphyrins and related tetra-coordinated nitrogen donor-transition metal complexes (MeN₄, where Me stands for a transition metal atom). Both pyrolyzed carbon-supported Co-imidazole and Co-porphyrin exhibited fast catalytic oxidation of the different thiols. The rate of oxidation of different thiols on the pyrolyzed CoN₄ catalysts was compared to the homogeneous rate of oxidation using 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin Co(II) tetrasodium salt as catalyst. Based on the cobalt content, the heterogeneous catalysts always outperformed the homogeneous one, and at times even exhibited 4,100-fold better catalysis. The dependence of the catalytic rate of oxidation on the preparation temperature was investigated, showing an optimal catalysis at ˜650 °C for the cobalt-imidazole catalyst. The decrease in catalytic performance after heat treatment at elevated temperature was attributed to the formation of cobalt metal acting as a generator of carbon nanotubes.     

Surface tension of helium at the superfluid critical end-point

The singularity in the vapor-liquid interfacial tension, (T), of helium at the transition to superfluidity is analyzed theoretically. The universal amplitude ratio R ⁺ =K₊( ₀ ⁺ )^d–1/k _B T , where K₊ and K_– are the amplitudes of the |T–T|^µ singularity in , with =1.34 ₃ , is known from recent work to first order in =4–d for the general n-vector model in d dimensions. Extrapolation to d=3 for n=2 indicates R ⁺ =0.05–0.08, which is shown to be consistent with the experimental data. Further analysis of the experiments establishes that the universal ratio Q=K₊/K _– exceeds 0.35, and is consistent with the recent prediction Q0.9; this demonstrates the inadequacies of earlier theoretical treatments. The existence in the observed surface tension of an anomalous, negative contribution of unknown origin at a few millikelvin beneath T is stressed.     

Improvement of Magnetic and Structural Properties of Some Ferric Compounds with Boron Addition

In the present study, we investigate the influence of boron oxide addition on magnetic and structural properties of some ferric compounds (BaFe₁₂O₁₉ and BiFeO₃). Our studies have shown that small amounts of B₂O₃ addition improve the crystalline structure, and thus improve the magnetic properties effectively. For instance, remanence and saturation magnetization of hard magnetic BaFe₁₂O₁₉ increases by half. Similar behavior was also observed in the BiFeO₃ system. There are two possible explanations for these improvements: (1) Boron atoms reside between the grains and improve the links between grains or (2) Boron substitutes for iron atoms and changes magnetic anisotropy and thus magnetic parameters.     

Local versus Global in Quasi-Conformal Mapping for Medical Imaging

A method and algorithm of flattening folded surfaces, for two-dimensional representation and analysis of medical images, are presented. The method is based on an application to triangular meshes of classical results of Gehring and Väisälä regarding the existence of quasi-conformal and quasi-isometric mappings.The proposed algorithm is basically local and, therefore, suitable for extensively folded surfaces encountered in medical imaging. The theory and algorithm guarantee minimal distance, angle and area distortion. Yet, the algorithm is relatively simple, robust and computationally efficient, since it does not require computational derivatives. Both random-starting-point and curvature-based versions of the algorithm are presented.We demonstrate the algorithm using medical data obtained from real CT images of the colon and MRI scans of the human cortex. Further applications of the algorithm, for image processing in general are also considered. The globality of this algorithm is also studied, via extreme length methods for which we develop a technique of computing straightest geodesics on polyhedral surfaces.     

Local Polaronic Effects in Compounds with Atoms of Transition Metals

The e-ph coupling may be of the different strength for different electronic bands. If coupling is strong enough for one or more bands, polaronic effects practically decouple these bands from the rest. Single ions being dressed by strong e-ph interactions move in the local potentials having two or more minima, and hence, can be viewed as the system of the Ising spins. Intersite interactions via the RKKY-type exchange by the electron-hole pairs tend to order the latter thus providing the CDW instability mechanism with a structural vector, Q that has nothing in common with the Fermi surfaces parameters. Among the most typical manifestations of such strong e-ph coupling in the system are large characteristic energy scales significantly exceeding the temperatures for the onset of the CDW phase. The available experimental data support interpretation of properties of the transition-atoms-dichalcogenides and the compounds of the A15 group in terms of the local polaronic effects.     

Structural evolution in copper layers during sliding under different lubricant conditions

Friction and wear of copper rubbed in a wide range of loads and sliding velocities were studied. The results of friction and wear experiments in PAO-4 lubricant are presented as the Stribeck curve where the boundary, mixed and elasto-hydrodynamic lubrication regimes are considered. The structural state of surface layers in different lubricant regimes is studied by optical and scanning electron microscopy and X-ray photoelectron spectroscopy analyses. The dominant friction and wear mechanisms in different lubrication regimes are discussed. Severe plastic deformation of subsurface layers under friction is correlated with the nanocrystalline structure obtained by different methods of grain refinement.     

Instantaneous measurements of nonlocal variables

Abstract

Relativistic causality imposes rigid restrictions on nondemolition (repeatable) measurements of nonlocal variables. We show that there are no causal restrictions on demolition (nonrepeatable) measurements: all Hermitian operators of multipartite quantum system can be measured instantaneously, provided unlimited supply of entanglement resources.     

Method for the determination of inorganic polysulfide distribution in aquatic systems

Inorganic polysulfides have significant technological importance, and their environmental role is gradually being unraveled. But despite their importance, there is still no method for quantification of the individual members of the polysulfide family in nonsynthetic samples. The method is based on fast, single-phase derivatization with methyl trifluoromethanesulfonate followed by one of three modes of sample treatment depending on polysulfide concentration. Under the most aggressive preconcentration treatment involving liquid-liquid extraction, solvent evaporation to dryness, dissolution in n-dodecane, and finally HPLC-UV analysis of the dimethylpolysulfane distribution, the minimum detection limits of the individual polysulfides are in the range 15-70 nM. The method was demonstrated for the analysis of synthetic solutions, natural groundwater, polysulfide fortified seawater, and surface water and for time tracing of the distribution of the individual polysulfides during the oxidation of hydrogen sulfide by hydrogen peroxide. The observed speciation was evaluated by comparison with the theoretical distribution of polysulfides at equilibrium with sulfur precipitate showing that the dominant polysulfides' (i.e., tetra- to hexasulfide) concentrations agree well with the predicted distribution (90% of the results fall within less than 30% deviation from the predicted values), whereas up to 3-fold deviation was observed for the less abundant trisulfide and octasulfide species.