Eigenvalues of a statistical mechanics matrix

We consider the problem of finding the spectrum of an n × n matrix which arises in the study of a certain model of long-range interactions in a one-dimensional statistical mechanics system. Our analysis exhibits a curious resemblance of the suitably normalized distribution of eigenvalues to the Marčenko–Pastur law in the limit n → ∞.     

Strongly orthogonal geminals: size-extensive and variational reference states

Properties and some applications of strongly orthogonal geminals (APSG) are reviewed emphasizing the motivations for their use and their shortcomings. An overview presents some techniques capable of improving the APSG function.     

Solubility of methane in octane + ethanol at temperatures from 303.15 K to 333.15 K and pressures up to 12.01 MPa

Solubility of methane in octane + ethanol was measured at temperatures ranging from 303.15 K to 333.15 K and pressures ranging from 2.60 MPa to 12.01 MPa. Experimental data were analyzed using the Soave-Redlich-Kwong equation of state with three types of mixing rules, and the estimated average deviation from the experimental solubility data was less than 3.5 %.     

Design of polyglycidol-containing microspheres for biomedical applications

The paper presents a short review on the synthesis, characterisation and selected medical applications of poly(styrene/α-tert-butoxy-ω-vinylbenzyl-polyglycidol) (P(S/PGL)) microspheres. The soap-free emulsion-polymerisation of styrene and α-tert-butoxy-ω-vinylbenzyl-polyglycidol macromonomer (PGL) in water yielded core-shell microspheres with a low particle-diameter dispersity (ratio of the weight average particle diameter and the number average particle diameter). The interfacial fraction of PGL units, estimated by XPS, was in the range of 0–42 mole % depending on the concentration of the macromonomer in the polymerisation feed. The studies of adsorption of model proteins showed that the surface fraction of adsorbed protein was significantly reduced when the PGL interfacial fraction was higher than 40 mole %. The P(S/PGL) particles with covalently immobilised proteins were used for the preparation of photonic crystal assemblies suitable for applications in optical biosensors and the medical diagnostic test for the detection of Helicobacter pylori antibodies in the blood serum.     

Synthesis and properties of new biotin compounds containing hexyltriethylene glycol chain

The synthesis of a new halogenide containing hexyltriethylene glycol chain functionalized with biotin is reported. The general possibility of this linker to use as the building block for biotinylated compounds syntheses is demonstrated. Two biotinylated esters with different properties for useful surface modification and as fluorescence probes for proteins marking were synthesized. The properties of mentioned compounds were investigated by using surface plazmon resonance ellypsometry and fluorescence spectroscopy.     

Nanoscale Broadband Viscoelastic Spectroscopy of Soft Materials Using Iterative Control

A novel approach to nanoscale broadband viscoelastic spectroscopy is presented. The proposed approach utilizes the recently developed modeling-free inversion-based iterative control (MIIC) technique to achieve accurate measurement of the material response to the applied excitation force over a broad frequency band. Scanning probe microscope (SPM) and nanoindenter have become enabling tools to quantitatively measure the mechanical properties of a wide variety of materials at nanoscale. Current nanomechanical measurement, however, is limited by the slow measurement speed: the nanomechanical measurement is slow and narrow-banded and thus not capable of measuring rate-dependent phenomena of materials. As a result, large measurement (temporal) errors are generated when material is undergoing dynamic evolution during the measurement. The low-speed operation of SPM is due to the inability of current approaches to (1) rapidly excite the broadband nanomechanical behavior of materials, and (2) compensate for the convolution of the hardware adverse effects with the material response during high-speed measurements. These adverse effects include the hysteresis of the piezo actuator (used to position the probe relative to the sample); the vibrational dynamics of the piezo actuator and the cantilever along with the related mechanical mounting; and the dynamics uncertainties caused by the probe variation and the operation condition. In the proposed approach, an input force signal with frequency characteristics of band-limited white-noise is utilized to rapidly excite the nanomechanical response of materials over a broad frequency range. The MIIC technique is used to compensate for the hardware adverse effects, thereby allowing the precise application of such an excitation force and measurement of the material response (to the applied force). The proposed approach is illustrated by implementing it to measure the frequency-dependent plane-strain modulus of poly(dimethylsiloxane) (PDMS) over a broad frequency range extending over 3 orders of magnitude (~1 Hz to 4.5 kHz).     

Soret and Dufour Effects on Double-Diffusive Free Convection Over a Vertical Truncated Cone in Porous Media with Variable Wall Heat and Mass Fluxes

This work studies the Soret and Dufour effects on the double-diffusive free convection over a downward-pointing vertical truncated cone with variable wall heat and mass fluxes in fluid-saturated porous media. A coordinate transformation is used to derive the nondimensional boundary-layer governing equations, and the obtained nonsimilar equations are then solved by the cubic spline collocation method. Results for local surface temperature and the local surface concentration are presented as functions of Soret parameters, Dufour parameters, power-law exponents, buoyancy ratios, and Lewis numbers. Results show that increasing the Dufour parameter tends to increase the local surface temperature, while it tends to decrease the local surface concentration. An increase in the Soret number leads to a decrease in the local surface temperature for buoyancy assisting flows, while it leads to an increase in the local surface temperature for buoyancy opposing flows. Increasing the Soret number tends to increase the local surface concentration. Moreover, the local surface temperature and the local surface concentration of the truncated cones with higher power-law exponents are lower than those with lower exponents.     

Study of Heat Transport in Bénard-Darcy Convection with g-Jitter and Thermo-Mechanical Anisotropy in Variable Viscosity Liquids

The effects of temperature-dependent viscosity, gravity modulation and thermo-mechanical anisotropies on heat transport in a low-porosity medium are studied using the Ginzburg–Landau model. The effect of gravity modulation is to decrease the Nusselt number, Nu and variable viscosity leads to increase in Nu. The thermo-mechanical anisotropies have opposite effect on Nu with thermal anisotropy decreasing the heat transport.     

A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.