Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory

The theoretical formulation for bending analysis of functionally graded (FG) rotating disks based on first order shear deformation theory (FSDT) is presented. The material properties of the disk are assumed to be graded in the radial direction by a power law distribution of volume fractions of the constituents. New set of equilibrium equations with small deflections are developed. A semi-analytical solution for displacement field is given under three types of boundary conditions applied for solid and annular disks. Results are verified with known results reported in the literature. Also, mechanical responses are compared between homogeneous and FG disks. It is found that the stress couple resultants in a FG solid disk are less than the stress resultants in full-ceramic and full-metal disk. It is observed that the vertical displacements for FG mounted disk with free condition at the outer surface do not occur between the vertical displacements of the full-metal and full-ceramic disk. More specifically, the vertical displacement in a FG mounted disk with free condition at the outer surface can even be greater than vertical displacement in a full-metal disk. It can be concluded from this work that the gradation of the constitutive components is a significant parameter that can influence the mechanical responses of FG disks.     

Integration of microcolumns and microfluidic fractionators on multitasking centrifugal microfluidic platforms for the analysis of biomolecules

This work demonstrates the development of microfluidic compact discs (CDs) for protein purification and fractionation integrating a series of microfluidic features, such as microreservoirs, microchannels, and microfluidic fractionators. The CDs were fabricated with polydimethylsiloxane (PDMS), and each device contained multiple identical microfluidic patterns. Each pattern employed a microfluidic fractionation feature with operation that was based on the redirection of fluid into an isolation chamber as a result of an overflow. This feature offers the advantage of automated operation without the need for any external manipulation, which is independent of the size and the charge of the fractionated molecules. The performance of the microfluidic fractionator was evaluated by its integration into a protein purification microfluidic architecture. The microfluidic architecture employed a microchamber that accommodated a monolithic microcolumn, the fractionator, and an isolation chamber, which was also utilized for the optical detection of the purified protein. The monolithic microcolumn was polymerized “in situ” on the CD from a monolith precursor solution by microwave-initiated polymerization. This technique enabled the fast, efficient, and simultaneous polymerization of monoliths on disposable CD microfluidic platforms. The design of the CD employed allows the integration of various processes on a single microfluidic device, including protein purification, fractionation, isolation, and detection.      

Dilating covariant representations of the non-commutative disc algebras

Let φ be an isometric automorphism of the non-commutative disc algebra An for n?2. We show that every contractive covariant representation of (An,φ) dilates to a unitary covariant representation of (On,φ). Hence the C^∗-envelope of the semicrossed product Anφ_×Z⁺ is Onφ_×Z.     

A note on a quadratic rational map with two Siegel disks

Suppose f（z） is a quadratic rational map with two Siegel disks. If the rotation numbers of the Siegel disks are both of bounded type, the Hausdorff dimension of the Julia set satisfies Dim （J（f））〈2.     

含钒多金属氧酸盐的抑菌活性

按文献方法合成了α-Na₁₀[PW₉V₃(H₂O)₃O₃₇]·16H₂O、α-Na10[PW11V(H₂O)O₃₇]·16H₂O和[H₃O]₃[NH₄]₁₈[Mo₅₇V₆O₁₈₃(NO)₆(H₂O)₄₈]·56H₂O（分别简称α-PW₉V₃、α-PW₁₁V和Mo₅₇V₆）含V多金属氧酸盐。 采用纸片法分别测试了它们对大肠杆菌、枯草芽孢杆菌、酵母菌和黑曲霉菌的抑菌活性。 3种化合物均有不同程度的抑菌作用, 其中α-PW₁₁V的抑菌效果最好。     

Some general univalence criteria for a family of integral operators

The main object of the present paper is to discuss some extensions of univalence conditions for a family of integral operators. Several other closely-related results are also considered. Many known univalence conditions are shown to follow upon specializing the parameters involved in our main results.     

Separation impact of a circular disk floating on the surface of an ideal incompressible fluid of infinite depth

The three-dimensional mixed problem of the separation impact of a circular disk floating on the surface of an ideal incompressible unlimited fluid is considered. The position and shape of the contact area between the body and the fluid (and the separation zone) are not known and depend on the relation between the translational and angular velocities acquired by the disk upon impact. Because of this, the problem in question is nonlinear and belongs to the class of free-boundary problems. The problem is solved using the method of Hammerstein-type nonlinear boundary integral equations. This approach allows the fluid flow after impact and the unknown zone of separation of fluid particles to be determined simultaneously. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 76–86, July–August, 2009.     

On Local and Global Measurements of the Speed of Light on Rotating Platforms

The paper shows that, conceptually and operationally, the speed of light measured locally in the inertial comoving frame of a point on the rim of a rotating disk is different from the one measured globally for a round trip along the rim, obtained dividing the length of the rim (as measured in the relative space of the disk) by the time of flight of the light beam (as measured by a clock at rest on the disk). As a consequence, contrary to some recent claims, the anisotropy found in the global value, obtained by the above procedure, in no way conflicts with the local isotropy, and the internal consistency of the special relativity theory remains unchallenged.     

New Perspectives on the Relativistically Rotating Disk and Non-Time-Orthogonal Reference Frames

The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light, are not applicable to rotating frames. Different postulates based on the Sagnac experiment are proposed, and from these postulates a new relativistic theory of rotating frames is developed following steps similar to those initially followed by Einstein for rectilinear motion. The resulting theory agrees with all experiments, resolves problems with the traditional approach to the rotating disk, and exhibits both traditionally relativistic and non-relativistic characteristics. Of particular note, no Lorentz contraction exists on the rotating disk circumference, and the disk surface, contrary to the assertions of Einstein and others, is found to be Riemann flat. The variable speed of light found in the Sagnac experiment is then shown to be characteristic of non-time-orthogonal reference frames, of which the rotating frame is one. In addition, the widely accepted postulate for the equivalence of inertial and non-inertial standard rods with zero relative velocity, used liberally in prior rotating disk analyses, is shown to be invalid for such frames. Further, the new theory stands alone in correctly predicting what was heretofore considered a spurious non-null effect on the order of 10^–13 found by Brillet and Hall in the most accurate Michelson-Morley type test to date. The presentation is simple and pedagogic in order to make it accessible to the non-specialist.     

A Simulation of an Anion‐Induced Adsorption of Metal Ions in Pseudopolarography Using a Thin Mercury Film Covered Rotating Disk Electrode

A theory of the influence of anion‐induced adsorption of metal ions in pseudopolarography using the thin mercury film covered rotating disk electrode is developed. The model is developed assuming that the metal ion is forming several labile complexes with the ligand which is present in a great excess, and that only one complex species is adsorbed following a linear isotherm. The results obtained assuming steady‐state conditions are compared with the simulation of transient processes using Galerkin and finite difference methods. It is shown that the adsorption of metal complexes on the disk electrode surface does not prevent the determination of the stability constants.